Downloads
Reference tables as spreadsheets, printable formula sheets, and calculator results export.
Everything on the site stays free to read: the guides, the worked examples, the calculators, the converters and every table on the page. The downloads below are for people who want to take the data with them: spreadsheets of the reference tables, one-page formula sheets to print, practice problem sets for the FE exam with worked answers, and the results of a calculator exported to CSV or Excel or exported from a calculator.
Members can download everything, as often as they like. A free account includes one sample download so you can see exactly what you get, and each item below shows a preview before you decide. Plans are on the account page.
Printable formula sheets
FORMULA SHEET · MEMBERS
Mechanical Formula Sheet
Stress, section properties, beams, torsion, columns, bolts, gears, springs and vibration.
33 formulas: stress, strain and safety, section properties, beams, torsion and power, columns, bolts, gears and springs, vibration.
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Electrical and Electronics Formula Sheet
Ohm’s law, networks, capacitors, filters, AC power, three-phase and wire sizing.
27 formulas: dc basics, capacitors, inductors and filters, ac and three-phase power, wire and cable.
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Fluids and Thermal Formula Sheet
Pipe flow, pumps, pneumatics, heat transfer and moist air.
22 formulas: fluid flow, pumps and actuators, heat transfer, gases and moist air.
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Machining Formula Sheet
Speeds, feeds, removal rate, power, tool life and finish for milling, drilling and turning.
13 formulas: speed and feed, removal rate, force and power, tool life, time and finish.
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Fits and Tolerances Formula Sheet
Clearance and interference, tolerance grades, stack-ups and process capability.
11 formulas: limits and fits, tolerance grades (iso 286), stack-ups, process capability.
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Controls and Automation Formula Sheet
PID, tuning rules, signal scaling, motion axes, steppers and machine safety distance.
15 formulas: pid and tuning, signals, motion, communication and safety.
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Statics and Dynamics Formula Sheet
Equilibrium, friction, centroids, kinematics, Newton’s laws, work and energy, momentum and rotation.
24 formulas: statics, kinematics (constant acceleration), kinetics.
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Thermodynamics Formula Sheet
First and second laws, ideal gas processes, cycles, efficiency and refrigeration.
19 formulas: laws and properties, ideal gas processes, cycles and efficiency.
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Hydraulics and Pneumatics Formula Sheet
Pressure, force, flow, speed, power, orifices, accumulators and air consumption.
16 formulas: hydraulic circuits, accumulators and fluids, pneumatics.
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Machine Design and Fatigue Formula Sheet
Combined stress, failure theories, fatigue, pressure vessels, bolts, bearings and keys.
20 formulas: stress, fatigue, fasteners, bearings and keys.
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Welding and Joining Formula Sheet
Weld strength, heat input, joint design, rivets and adhesives.
12 formulas: weld strength, process numbers, other joints.
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Gears, Belts and Chains Formula Sheet
Ratios, speeds, center distances, tooth forces, belts, chains and efficiency.
19 formulas: gears, belts and chains, efficiency.
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Motors and Drives Formula Sheet
AC induction, DC, stepper and servo formulas, VFD basics and sizing.
16 formulas: ac induction motors, vfds, dc, stepper and servo.
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Statistics and Engineering Math Formula Sheet
Descriptive statistics, the normal distribution, regression, calculus, trigonometry and algebra.
21 formulas: statistics, calculus, algebra and trigonometry.
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Electronic Components Formula Sheet
Diodes, transistors, op-amps, regulators and filters for everyday circuit design.
19 formulas: diodes and leds, transistors, op-amps, power and filters.
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Embedded and Digital Formula Sheet
Number systems, timers, PWM, ADC, serial buses and data rates.
18 formulas: numbers and logic, timers, pwm and adc, buses and links.
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3D Printing Formula Sheet
Flow rate, print time, material use, cost, accuracy and thermal numbers for FDM printing.
15 formulas: extrusion, time and material, accuracy and mechanics.
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PLC and Automation Quick Reference
Ladder symbols, scaling, timers and counters, network numbers and standard signal ranges.
17 formulas: ladder logic, signals and scaling, networks and safety.
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Units and Conversion Quick Reference
The conversion factors engineers use every day, with the exact definitions.
20 formulas: length, mass and force, pressure and energy, flow, speed and temperature, handy ratios.
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FORMULA SHEET · MEMBERS
CNC and G-code Quick Reference
The G and M codes you use most, with the speed and feed formulas next to them.
24 formulas: motion (g-codes), cycles and m-codes, numbers to keep nearby.
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FORMULA SHEET · MEMBERS
Bearings and Lubrication Formula Sheet
Rolling bearing life, equivalent load, reliability factors, speed limits, viscosity ratio, friction and shaft fits.
15 formulas: rating life, speed, friction, heat, lubrication.
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FORMULA SHEET · MEMBERS
Bolted Joints Formula Sheet
Proof load and preload, tightening torque, joint stiffness, external load sharing, separation, shear and thread engagement.
15 formulas: strength and preload, joint stiffness and external load, shear and engagement.
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FORMULA SHEET · MEMBERS
Piping and Pipe Flow Formula Sheet
Continuity, Reynolds number, friction factor, Darcy-Weisbach, minor losses, Hazen-Williams, pump power, NPSH, wall thickness and surge.
18 formulas: flow and friction, pumping, pipe mechanics.
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FORMULA SHEET · MEMBERS
Heat Exchangers Formula Sheet
Energy balance, LMTD and effectiveness-NTU methods, overall coefficient, fouling and typical U values.
17 formulas: energy balance and lmtd, effectiveness-ntu, overall coefficient.
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Sensors and Signals Formula Sheet
Analog scaling, RTD and thermistor temperature, strain gauges and load cells, encoders, ADC resolution, sampling and filters.
17 formulas: analog signals, temperature, force, position, speed.
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PCB Design Formula Sheet
Trace current and resistance, copper weight, controlled impedance estimates, delay, critical length, via inductance and decoupling.
17 formulas: traces and copper, transmission lines, vias, power and decoupling.
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Soldering Quick Reference Sheet
Alloy melting points, iron and reflow temperatures, joint heat, paste and stencil ratios and wire per joint.
15 formulas: alloys and temperatures, heat and flow, paste and stencil.
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GD&T Quick Reference Sheet
The geometric characteristics, material condition and bonus tolerance, virtual condition, position conversions and fastener formulas.
16 formulas: characteristics, material condition, position and fasteners.
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FORMULA SHEET · MEMBERS
Tolerance Stack-up and Process Capability Sheet
Worst-case, RSS and modified RSS stacks, Cp and Cpk, defect rates by sigma level and sample-size basics.
16 formulas: stack-up methods, capability, defect rates (centered, normal).
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Pneumatics and Compressed Air Formula Sheet
Cylinder force, air consumption, receiver sizing, compression, choked flow, valve flow coefficients and typical pressures.
15 formulas: cylinders, air supply, flow.
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FORMULA SHEET · MEMBERS
Control Tuning Formula Sheet
PID forms, Ziegler-Nichols and lambda tuning rules, second-order response relations and sampling guidance.
16 formulas: pid forms, tuning rules (first order plus dead time: gain k, time constant t, dead time l), second-order response.
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FORMULA SHEET · MEMBERS
Sheet Metal Formula Sheet
Bend allowance, setback and deduction, flat pattern length, press-brake and punching force, springback and design rules.
15 formulas: bending, forces, design rules.
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Exam prep
EXAM PREP · MEMBERS
FE practice set 1: Statics
Beam reactions, cables, friction, centroids, moments and a hinged beam: 6 problems with worked answers.
6 problems with worked answers: beam reactions, two-cable support, block on an incline, centroid of an l-section, moment of a force, hinged beam and cable.
Sample problem. A simply supported beam spans 6 m. It carries a 12 kN point load 2 m from support A and a uniform load of 3 kN/m over the whole span. Find the reaction at each support.
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EXAM PREP · MEMBERS
FE practice set 2: Dynamics
Kinematics, projectiles, energy, rotation, vibration and impact: 6 problems with worked answers.
6 problems with worked answers: constant acceleration, projectile, energy and a spring, flywheel, natural frequency, impact.
Sample problem. A car accelerates uniformly from rest to 100 km/h in 8 s. Find the acceleration and the distance covered.
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FE practice set 3: Mechanics of Materials
Axial, bending, torsion, Mohr’s circle, buckling and pressure vessels: 6 problems with worked answers.
6 problems with worked answers: axial load, bending stress, shaft torsion, mohr’s circle, euler buckling, pressure vessel.
Sample problem. A 20 mm diameter steel rod (E = 200 GPa) is 1.5 m long and carries a 60 kN axial tension. Find the stress and the elongation.
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FE practice set 4: Fluid Mechanics
Hydrostatics, Bernoulli, Reynolds number, pipe friction, pump power and buoyancy: 6 problems with worked answers.
6 problems with worked answers: hydrostatics, continuity and bernoulli, reynolds number, pipe friction loss, pump power, buoyancy.
Sample problem. A tank holds 3 m of water. Find the gauge pressure at the bottom and the force on a 1 m wide, 3 m high vertical wall.
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EXAM PREP · MEMBERS
FE practice set 5: Thermodynamics and Heat Transfer
Ideal gas, isothermal work, Carnot, refrigeration, conduction and water heating: 6 problems with worked answers.
6 problems with worked answers: ideal gas, isothermal expansion, carnot engine, refrigerator, wall conduction, water heater.
Sample problem. What volume do 2 kg of air occupy at 300 K and 100 kPa (R = 287 J/kg K)?
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EXAM PREP · MEMBERS
FE practice set 6: Machine Design
Bolts, gears, bearing life, fatigue, keys and springs: 6 problems with worked answers.
6 problems with worked answers: bolt preload, spur gear pair, bearing life, fatigue safety factor, key shear, compression spring.
Sample problem. An M10 class 8.8 bolt (tensile stress area 58 mm², proof strength 600 MPa) is preloaded to 75 percent of proof. Find the preload and the tightening torque (K = 0.2).
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EXAM PREP · MEMBERS
FE practice set 7: Economics and Statistics
Compound interest, loan payments, break-even, the normal distribution, Cpk and sample statistics: 6 problems with worked answers.
6 problems with worked answers: future value, loan payment, break-even, normal distribution, process capability, sample statistics.
Sample problem. How much is $5 000 worth after 8 years at 6 percent interest compounded annually?
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EXAM PREP · MEMBERS
FE practice set 8: Electrical and Controls
RC circuits, three-phase current, power factor, op-amps, PID tuning and 4–20 mA scaling: 6 problems with worked answers.
6 problems with worked answers: rc circuit, three-phase motor current, power factor correction, op-amp amplifier, pid tuning, 4–20 ma scaling.
Sample problem. A 10 kΩ resistor charges a 100 nF capacitor. Find the time constant, the time to reach 90 percent of the supply, and the cut-off frequency of the same RC as a low-pass filter.
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EXAM PREP · MEMBERS
FE practice set 9: Electronics
Voltage dividers, LED resistors, transistor switches, op-amps, a buck converter and a 555 timer: 6 problems with worked answers.
6 problems with worked answers: voltage divider, led resistor, transistor switch, non-inverting amplifier, buck converter, 555 astable.
Sample problem. A divider has R1 = 10 kΩ on top and R2 = 4.7 kΩ to ground, fed from 12 V. Find the output unloaded and with a 10 kΩ load on the output.
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EXAM PREP · MEMBERS
FE practice set 10: Manufacturing and Materials
Spindle speed and feed, material removal rate, bend allowance, fillet welds, thermal expansion and tool life: 6 problems with worked answers.
6 problems with worked answers: spindle speed and feed, material removal rate, bend allowance, fillet weld, thermal expansion, tool life.
Sample problem. A 12 mm three-flute end mill cuts at 120 m/min with a chip load of 0.05 mm per tooth. Find the spindle speed and the table feed rate.
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EXAM PREP · MEMBERS
FE practice set 11: Instrumentation and Measurement
4–20 mA scaling, an RTD, a strain gauge bridge, ADC resolution, aliasing and measurement uncertainty: 6 problems with worked answers.
6 problems with worked answers: level transmitter, pt100 sensor, strain gauge, adc resolution, sampling and aliasing, measurement uncertainty.
Sample problem. A 4–20 mA level transmitter spans 0 to 5 m and reads 9.6 mA. What is the level?
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EXAM PREP · MEMBERS
FE practice set 12: Pumps and Piping
Pipe friction, pump power, affinity laws, NPSH, fitting losses and water hammer: 6 problems with worked answers.
6 problems with worked answers: pipe friction, pump power, affinity laws, npsh available, fittings and valves, water hammer.
Sample problem. Water (ρ = 998 kg/m³, μ = 1.0 mPa s) flows at 10 L/s through 100 m of 77.9 mm inside-diameter steel pipe with roughness 0.045 mm. Find the velocity, the Reynolds number, the friction factor (Swamee-Jain) and the pressure drop.
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Reference tables
TABLE DOWNLOAD · MEMBERS
Material properties table
Density, stiffness, strength, expansion, conductivity and melting point of 24 metals and plastics, with specific strength and stiffness.
| Material | Group | Density (kg/m3) | Young modulus (GPa) |
|---|---|---|---|
| Mild steel A36 | Steel and iron | 7850 | 200 |
| Alloy steel 4140 (annealed) | Steel and iron | 7850 | 205 |
| Stainless steel 304 | Steel and iron | 8000 | 193 |
| Stainless steel 316 | Steel and iron | 8000 | 193 |
Preview: first 4 of 24 rows and 4 of 12 columns.
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AWG wire gauge table
Diameter, area, copper resistance and mass for AWG 0000 to 40.
| AWG | Diameter (mm) | Diameter (in) | Area (mm2) |
|---|---|---|---|
| 0000 (4/0) | 11.684 | 0.46 | 107.2193 |
| 000 (3/0) | 10.4049 | 0.40964 | 85.0288 |
| 00 (2/0) | 9.2658 | 0.3648 | 67.4309 |
| 0 (1/0) | 8.2515 | 0.32486 | 53.4751 |
Preview: first 4 of 44 rows and 4 of 7 columns.
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Metric thread table (coarse)
Pitch, tap drill, pitch and minor diameters and tensile stress area for M1 to M48.
| Thread | Major diameter (mm) | Coarse pitch (mm) | Tap drill, about 75 percent thread (mm) |
|---|---|---|---|
| M1 | 1 | 0.35 | 0.65 |
| M2 | 2 | 0.45 | 1.55 |
| M3 | 3 | 0.6 | 2.4 |
| M4 | 4 | 0.7 | 3.3 |
Preview: first 4 of 22 rows and 4 of 7 columns.
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TABLE DOWNLOAD · MEMBERS
Preferred values: E6, E12, E24 and E96
Standard resistor and capacitor values with their ideal 10^(n/N) positions.
| Series | Position in decade | Value (multiply by 1, 10, 100 ...) | Ideal 10^(n/N) |
|---|---|---|---|
| E6 | 1 | 1 | 1 |
| E6 | 2 | 1.5 | 1.4678 |
| E6 | 3 | 2.2 | 2.1544 |
| E6 | 4 | 3.3 | 3.1623 |
Preview: first 4 of 138 rows and 4 of 5 columns.
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ASCII table
All 128 characters in decimal, hex, binary and octal.
| Decimal | Hex | Binary | Octal |
|---|---|---|---|
| 0 | 00 | 00000000 | 000 |
| 1 | 01 | 00000001 | 001 |
| 2 | 02 | 00000010 | 002 |
| 3 | 03 | 00000011 | 003 |
Preview: first 4 of 128 rows and 4 of 5 columns.
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Standard atmosphere table
Temperature, pressure, density and speed of sound from sea level to 20 km, in metric and imperial altitude.
| Altitude (m) | Altitude (ft) | Temperature (C) | Pressure (kPa) |
|---|---|---|---|
| 0 | 0 | 15 | 101.325 |
| 1000 | 3281 | 8.5 | 89.875 |
| 2000 | 6562 | 2 | 79.495 |
| 3000 | 9843 | -4.5 | 70.109 |
Preview: first 4 of 21 rows and 4 of 7 columns.
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Water properties vs temperature
Density, viscosity, specific heat, conductivity and vapor pressure of water from 0 to 100 C.
| Temperature (C) | Density (kg/m3) | Dynamic viscosity (mPa s) | Kinematic viscosity (mm2/s) |
|---|---|---|---|
| 0 | 999.8 | 1.792 | 1.7924 |
| 10 | 999.7 | 1.307 | 1.3074 |
| 20 | 998.2 | 1.002 | 1.0038 |
| 30 | 995.7 | 0.797 | 0.8004 |
Preview: first 4 of 11 rows and 4 of 7 columns.
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Inch fractions to decimal and millimeters
Every 1/64 inch from 1/64 to 1 inch.
| Fraction of an inch | Decimal inch | Millimeters |
|---|---|---|
| 1/64 | 0.015625 | 0.3969 |
| 1/32 | 0.03125 | 0.7938 |
| 3/64 | 0.046875 | 1.1906 |
| 1/16 | 0.0625 | 1.5875 |
Preview: first 4 of 64 rows and 3 of 3 columns.
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Unified inch thread table (UNC and UNF)
#4 to 1 inch: pitch, pitch and minor diameters, tensile stress area and tap drill.
| Thread | Major diameter (in) | Threads per inch | Pitch (in) |
|---|---|---|---|
| #4-40 UNC | 0.112 | 40 | 0.025 |
| #4-48 UNF | 0.112 | 48 | 0.02083 |
| #6-32 UNC | 0.138 | 32 | 0.03125 |
| #6-40 UNF | 0.138 | 40 | 0.025 |
Preview: first 4 of 28 rows and 4 of 8 columns.
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Metric fine thread table
Common fine pitches from M8 to M48 with diameters and stress area.
| Thread | Major diameter (mm) | Fine pitch (mm) | Tap drill, about 75 percent thread (mm) |
|---|---|---|---|
| M8 x 1 | 8 | 1 | 7 |
| M10 x 1.25 | 10 | 1.25 | 8.75 |
| M10 x 1 | 10 | 1 | 9 |
| M12 x 1.5 | 12 | 1.5 | 10.5 |
Preview: first 4 of 16 rows and 4 of 7 columns.
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SI prefixes
Quetta to quecto with symbols and powers of ten.
| Prefix | Symbol | Scientific form | Power of ten |
|---|---|---|---|
| quetta | Q | E+30 | 30 |
| ronna | R | E+27 | 27 |
| yotta | Y | E+24 | 24 |
| zetta | Z | E+21 | 21 |
Preview: first 4 of 24 rows and 4 of 5 columns.
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Sheet steel gauge table
Gauge 3 to 30 with thickness in inches and millimeters and mass per area.
| Gauge | Thickness (in) | Thickness (mm) | Mass of steel sheet (kg/m2) |
|---|---|---|---|
| 3 | 0.2391 | 6.073 | 47.674 |
| 4 | 0.2242 | 5.695 | 44.703 |
| 5 | 0.2092 | 5.314 | 41.712 |
| 6 | 0.1943 | 4.935 | 38.741 |
Preview: first 4 of 28 rows and 4 of 5 columns.
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Steel pipe sizes (NPS and DN, Schedule 40 and 80)
Outside and inside diameter, wall, flow area and mass per meter for NPS 1/2 to 12.
| Nominal size | DN | Schedule | Outside diameter (mm) |
|---|---|---|---|
| NPS 1/2 | 15 | Sch 40 | 21.34 |
| NPS 1/2 | 15 | Sch 80 | 21.34 |
| NPS 3/4 | 20 | Sch 40 | 26.67 |
| NPS 3/4 | 20 | Sch 80 | 26.67 |
Preview: first 4 of 28 rows and 4 of 8 columns.
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Resistivity of metals and alloys
Resistivity, conductivity, temperature coefficient and percent IACS for 15 materials.
| Material | Resistivity at 20 C (ohm m) | Conductivity (MS/m) | Temperature coefficient (per K) |
|---|---|---|---|
| Silver | 1.59E-8 | 62.893 | 0.0038 |
| Copper (annealed, IACS) | 1.724E-8 | 58.005 | 0.00393 |
| Gold | 2.44E-8 | 40.984 | 0.0034 |
| Aluminum | 2.65E-8 | 37.736 | 0.00429 |
Preview: first 4 of 15 rows and 4 of 5 columns.
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Bolt strength grades and property classes
ISO 898-1 classes 4.6 to 12.9 and SAE J429 grades 2, 5 and 8 with proof, yield and tensile strength in MPa and ksi.
| Standard | Grade or class | Size range | Proof strength (MPa) |
|---|---|---|---|
| ISO 898-1 | 4.6 | M5 to M100 | 225 |
| ISO 898-1 | 4.8 | M5 to M100 | 310 |
| ISO 898-1 | 5.6 | M5 to M100 | 280 |
| ISO 898-1 | 5.8 | M5 to M24 | 380 |
Preview: first 4 of 16 rows and 4 of 10 columns.
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Metric hex bolt, nut and washer dimensions
M3 to M36: wrench flats, head height, nut thickness and washer sizes (ISO 4017, 4032, 7089).
| Thread | Coarse pitch (mm) | Hex across flats (mm) | Hex across flats (in) |
|---|---|---|---|
| M3 | 0.5 | 5.5 | 0.217 |
| M4 | 0.7 | 7 | 0.276 |
| M5 | 0.8 | 8 | 0.315 |
| M6 | 1 | 10 | 0.394 |
Preview: first 4 of 13 rows and 4 of 9 columns.
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Socket head cap screw dimensions
M3 to M36: head diameter, head height, hex key size and counterbore sizes (ISO 4762).
| Thread | Coarse pitch (mm) | Head diameter dk (mm) | Head height k (mm) |
|---|---|---|---|
| M3 | 0.5 | 5.5 | 3 |
| M4 | 0.7 | 7 | 4 |
| M5 | 0.8 | 8.5 | 5 |
| M6 | 1 | 10 | 6 |
Preview: first 4 of 13 rows and 4 of 7 columns.
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Metric bolt clearance hole sizes
Fine, medium and coarse through holes for M3 to M36 (ISO 273), with the tap drill.
| Thread | Fine (close) hole (mm) | Medium (normal) hole (mm) | Coarse (loose) hole (mm) |
|---|---|---|---|
| M3 | 3.2 | 3.4 | 3.6 |
| M4 | 4.3 | 4.5 | 4.8 |
| M5 | 5.3 | 5.5 | 5.8 |
| M6 | 6.4 | 6.6 | 7 |
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Estimated bolt tightening torque (metric)
Preload and dry or lubricated torque for classes 8.8, 10.9 and 12.9, M5 to M36, computed from the proof strength.
| Thread | Stress area (mm2) | 8.8 preload (kN) | 8.8 torque dry (N m) |
|---|---|---|---|
| M5 | 14.2 | 6.2 | 6.2 |
| M6 | 20.1 | 8.8 | 10.5 |
| M8 | 36.6 | 15.9 | 25.5 |
| M10 | 58 | 25.2 | 50.5 |
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Hex bolt wrench size chart
Across-flats sizes for metric and inch bolts in millimeters and inches.
| Bolt size | Hex across flats (mm) | Hex across flats (in) | Note |
|---|---|---|---|
| M3 (metric) | 5.5 | 0.217 | |
| M4 (metric) | 7 | 0.276 | |
| M5 (metric) | 8 | 0.315 | |
| M6 (metric) | 10 | 0.394 |
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European I-beam and H-beam sections (IPE, HEA, HEB)
Dimensions, area, mass, second moments and section moduli of 40 rolled sections, computed from the dimensions.
| Section | Depth h (mm) | Width b (mm) | Web tw (mm) |
|---|---|---|---|
| IPE 80 | 80 | 46 | 3.8 |
| IPE 100 | 100 | 55 | 4.1 |
| IPE 120 | 120 | 64 | 4.4 |
| IPE 140 | 140 | 73 | 4.7 |
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Round steel tube (CHS) section properties
Mass, area, second moment and section modulus of 12 standard tube sizes.
| Outside diameter D (mm) | Wall t (mm) | Mass (kg/m) | Area (cm2) |
|---|---|---|---|
| 33.7 | 3.2 | 2.41 | 3.07 |
| 42.4 | 3.2 | 3.09 | 3.94 |
| 48.3 | 3.2 | 3.56 | 4.53 |
| 60.3 | 3.6 | 5.03 | 6.41 |
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Square hollow section (SHS) properties
Mass, area, second moment and section modulus of 17 square tubes, including the corner radii.
| Section (mm) | Side b (mm) | Wall t (mm) | Outside corner radius (mm) |
|---|---|---|---|
| 20 x 20 x 2 | 20 | 2 | 4 |
| 25 x 25 x 2.5 | 25 | 2.5 | 5 |
| 30 x 30 x 3 | 30 | 3 | 6 |
| 40 x 40 x 3 | 40 | 3 | 6 |
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Steel bar weight per meter
Round, square and hexagon steel and round aluminum bar from 5 to 100 mm, in kg/m and lb/ft.
| Size d or across flats (mm) | Round steel (kg/m) | Square steel (kg/m) | Hexagon steel (kg/m) |
|---|---|---|---|
| 5 | 0.154 | 0.196 | 0.17 |
| 6 | 0.222 | 0.283 | 0.245 |
| 8 | 0.395 | 0.502 | 0.435 |
| 10 | 0.617 | 0.785 | 0.68 |
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Rebar sizes (ASTM and metric)
US bar numbers #3 to #18 and metric 6 to 40 mm with diameter, area and mass.
| Bar size | Nominal diameter (mm) | Nominal diameter (in) | Area (mm2) |
|---|---|---|---|
| US #3 | 9.5 | 0.375 | 71 |
| US #4 | 12.7 | 0.5 | 127 |
| US #5 | 15.9 | 0.625 | 198 |
| US #6 | 19.1 | 0.75 | 285 |
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Metric parallel keys and keyways
Key width and height and the keyway depths in shaft and hub for shafts 6 to 130 mm (ISO 773).
| Shaft diameter (mm) | Key width b (mm) | Key height h (mm) | Keyway depth in shaft t1 (mm) |
|---|---|---|---|
| Over 6 to 8 | 2 | 2 | 1.2 |
| Over 8 to 10 | 3 | 3 | 1.8 |
| Over 10 to 12 | 4 | 4 | 2.5 |
| Over 12 to 17 | 5 | 5 | 3 |
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Inch square keys and keyseats
Square key sizes by shaft diameter, 5/16 to 4-1/2 in (ANSI B17.1).
| Shaft diameter | Square key size (in) | Square key size (decimal in) | Square key size (mm) |
|---|---|---|---|
| Over 5/16 to 7/16 in | 3/32 | 0.0938 | 2.38 |
| Over 7/16 to 9/16 in | 1/8 | 0.125 | 3.18 |
| Over 9/16 to 7/8 in | 3/16 | 0.1875 | 4.76 |
| Over 7/8 to 1-1/4 in | 1/4 | 0.25 | 6.35 |
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Steel grade cross reference
AISI/SAE, UNS, EN and JIS equivalents of 21 common carbon, alloy, tool and stainless steels.
| AISI / SAE grade | UNS number | European (EN) name | EN number |
|---|---|---|---|
| A36 | K02600 | S275JR (about) | 1.0044 |
| 1018 | G10180 | C15E / C16E (about) | 1.1141 |
| 1020 | G10200 | C22E | 1.1151 |
| 1045 | G10450 | C45E | 1.1191 |
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Aluminum alloys and tempers
Nine common alloys with composition, temper, strength, weldability and uses.
| Alloy | Series | Main alloying elements | Typical temper |
|---|---|---|---|
| 1100 | 1xxx | Pure aluminum (99.0 percent) | H14 |
| 3003 | 3xxx | Manganese | H14 |
| 5052 | 5xxx | Magnesium 2.5 percent | H32 |
| 5083 | 5xxx | Magnesium 4.5 percent, manganese | H116 |
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Stainless steel grades
Ten grades with composition, minimum strength, magnetism and corrosion resistance.
| Grade | Family | Chromium (percent) | Nickel (percent) |
|---|---|---|---|
| 304 | Austenitic | 18 | 8 |
| 304L | Austenitic | 18 | 8 |
| 316 | Austenitic | 16 to 18 | 10 to 14 |
| 316L | Austenitic | 16 to 18 | 10 to 14 |
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O-ring cross-sections and groove depths
AS568 series and common metric cross-sections with groove depth ranges from the usual squeeze.
| O-ring series or size | Cross-section (in) | Cross-section (mm) | Static groove depth, 15 to 30 percent squeeze: smallest (mm) |
|---|---|---|---|
| AS568 0xx (-001 to -050) | 0.07 | 1.78 | 1.24 |
| AS568 1xx (-102 to -178) | 0.103 | 2.62 | 1.83 |
| AS568 2xx (-201 to -284) | 0.139 | 3.53 | 2.47 |
| AS568 3xx (-309 to -395) | 0.21 | 5.33 | 3.73 |
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Properties of air vs temperature
Density, viscosity, specific heat, conductivity, Prandtl number and speed of sound from -20 to 400 C.
| Temperature (C) | Density (kg/m3) | Dynamic viscosity (micropascal seconds) | Kinematic viscosity (mm2/s) |
|---|---|---|---|
| -20 | 1.3944 | 16.153 | 11.584 |
| 0 | 1.2923 | 17.16 | 13.279 |
| 20 | 1.2041 | 18.133 | 15.059 |
| 40 | 1.1272 | 19.075 | 16.922 |
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Properties of common gases
Molar mass, gas constant, density, viscosity and speed of sound of nine gases at 20 C.
| Gas | Molar mass (g/mol) | Gas constant R (J/kg K) | Density at 20 C, 1 atm (kg/m3) |
|---|---|---|---|
| Air (dry) | 28.96 | 287.1 | 1.2039 |
| Nitrogen | 28.013 | 296.8 | 1.1645 |
| Oxygen | 31.999 | 259.8 | 1.3302 |
| Carbon dioxide | 44.01 | 188.9 | 1.8295 |
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Properties of common liquids
Density, viscosity, specific heat and conductivity of ten liquids at 20 C.
| Liquid | Density (kg/m3) | Dynamic viscosity (mPa s) | Kinematic viscosity (mm2/s) |
|---|---|---|---|
| Water | 998.2 | 1.002 | 1.004 |
| Seawater (3.5 percent salt) | 1025 | 1.08 | 1.054 |
| Ethanol | 789 | 1.2 | 1.521 |
| Methanol | 791 | 0.59 | 0.746 |
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Pipe roughness values
Absolute roughness of common pipe materials with relative roughness for three sizes.
| Pipe material | Roughness, lowest (mm) | Roughness, highest (mm) | Typical roughness (mm) |
|---|---|---|---|
| Drawn tubing: copper, brass, glass, plastic | 0.0015 | 0.0015 | 0.0015 |
| PVC and polyethylene pipe | 0.0015 | 0.007 | 0.0032 |
| Stainless steel, drawn | 0.015 | 0.015 | 0.015 |
| Commercial or welded steel, new | 0.045 | 0.046 | 0.0455 |
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Fitting and valve loss coefficients (K factors)
Typical K and equivalent length for 17 fittings and valves, screwed and flanged.
| Fitting or valve | Loss coefficient K, screwed | Loss coefficient K, flanged or welded | Equivalent length in diameters, screwed (L/D) |
|---|---|---|---|
| Standard 90 degree elbow | 0.9 | 0.3 | 45 |
| Long radius 90 degree elbow | 0.6 | 0.2 | 30 |
| 45 degree elbow | 0.4 | 0.2 | 20 |
| 180 degree return bend | 1.5 | 0.2 | 75 |
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Thermal conductivity of materials
Conductivity, density, specific heat and diffusivity of 20 solids, liquids and gases.
| Material | Thermal conductivity k (W/m K) | Density (kg/m3) | Specific heat (J/kg K) |
|---|---|---|---|
| Copper | 401 | 8960 | 385 |
| Aluminum, pure | 237 | 2700 | 903 |
| Brass | 109 | 8530 | 380 |
| Carbon steel (0.5 percent C) | 54 | 7833 | 465 |
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Emissivity of common surfaces
Total emissivity of 18 surfaces, with reflectivity and emitted radiation at 100 C.
| Surface | Total emissivity (near room temperature) | Reflectivity of an opaque surface (1 - emissivity) | Radiation emitted at 100 C (W/m2) |
|---|---|---|---|
| Aluminum, polished | 0.05 | 0.95 | 55 |
| Aluminum, commercial sheet | 0.09 | 0.91 | 98.9 |
| Aluminum, anodized | 0.77 | 0.23 | 846.5 |
| Copper, polished | 0.03 | 0.97 | 33 |
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Motor full-load current (three-phase)
Full-load amps for 1/2 to 100 hp at 208, 230, 460 and 575 V (NEC Table 430.250).
| Motor (hp) | Motor (kW) | 208 V (A) | 230 V (A) |
|---|---|---|---|
| 0.5 | 0.37 | 2.4 | 2.2 |
| 0.75 | 0.56 | 3.5 | 3.2 |
| 1 | 0.75 | 4.6 | 4.2 |
| 1.5 | 1.12 | 6.6 | 6 |
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Standard breaker and fuse sizes
Standard ampere ratings with the 80 percent continuous-load rule and the power they carry.
| Standard rating (A) | Largest continuous load: 80 percent of the rating (A) | Three-phase power at 400 V at that load, power factor 1 (kW) | Single-phase power at 120 V at that load (kW) |
|---|---|---|---|
| 15 | 12 | 8.3 | 1.44 |
| 20 | 16 | 11.1 | 1.92 |
| 25 | 20 | 13.9 | 2.4 |
| 30 | 24 | 16.6 | 2.88 |
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IP ratings explained
What each digit of an IP code means for solids, dust and water.
| Position in the code (IP + two digits) | Digit | What it means | Short description |
|---|---|---|---|
| First digit: solids | 0 | No protection | None |
| First digit: solids | 1 | Objects larger than 50 mm | Back of a hand |
| First digit: solids | 2 | Objects larger than 12.5 mm | A finger |
| First digit: solids | 3 | Objects larger than 2.5 mm | Tools and thick wires |
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Physical constants
Exact and measured values of c, h, e, k, N_A, G, R and 12 more (CODATA 2018).
| Quantity | Symbol | Value | Unit |
|---|---|---|---|
| Speed of light in vacuum | c | 299 792 458 | m/s |
| Planck constant | h | 6.62607015E-34 | J s |
| Elementary charge | e | 1.602176634E-19 | C |
| Boltzmann constant | k | 1.380649E-23 | J/K |
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Greek alphabet in engineering
The 24 letters with upper and lower case and the symbols they usually stand for.
| Name | Upper case | Lower case | Position in the alphabet |
|---|---|---|---|
| Alpha | Α | α | 1 |
| Beta | Β | β | 2 |
| Gamma | Γ | γ | 3 |
| Delta | Δ | δ | 4 |
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Deep-groove ball bearing dimensions
Bore, outside diameter and width for the 60, 62 and 63 series.
| Designation | Bore d (mm) | Outside diameter D (mm) | Width B (mm) |
|---|---|---|---|
| 6000 | 10 | 26 | 8 |
| 6001 | 12 | 28 | 8 |
| 6002 | 15 | 32 | 9 |
| 6003 | 17 | 35 | 10 |
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Unit conversion tables
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Pressure unit factors
Every pressure unit in the converter with its exact factor and where it is used.
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Density unit factors
Every density unit in the converter with its exact factor and where it is used.
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Temperature unit factors
Every temperature unit in the converter with its exact factor and where it is used.
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Angles unit factors
Every angles unit in the converter with its exact factor and where it is used.
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Flow rate unit factors
Every flow rate unit in the converter with its exact factor and where it is used.
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Time unit factors
Every time unit in the converter with its exact factor and where it is used.
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Stress unit factors
Every stress unit in the converter with its exact factor and where it is used.
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Strain unit factors
Every strain unit in the converter with its exact factor and where it is used.
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Velocity unit factors
Every velocity unit in the converter with its exact factor and where it is used.
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Volume unit factors
Every volume unit in the converter with its exact factor and where it is used.
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Length unit factors
Every length unit in the converter with its exact factor and where it is used.
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Mass unit factors
Every mass unit in the converter with its exact factor and where it is used.
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Force unit factors
Every force unit in the converter with its exact factor and where it is used.
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Torque unit factors
Every torque unit in the converter with its exact factor and where it is used.
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Power unit factors
Every power unit in the converter with its exact factor and where it is used.
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Energy unit factors
Every energy unit in the converter with its exact factor and where it is used.
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