FE Mechanical Study Path
A 12-week plan through 14 topics, with the guides, tools and practice for each.
The FE and PE exams are written and run by NCEES. Engineer Underground is not affiliated with NCEES. Exam formats, topics, calculator rules and the reference material change, so always check the current exam specifications on the NCEES website. Everything on this page is general study help, and the practice problems are original and not NCEES questions.
This is a study path for the Fundamentals of Engineering (FE) exam, Mechanical discipline: the order I would study the topics in, what each topic covers, and where the free guides, calculators and tables on this site fit. Reading everything on the site is free. The practice sets and printable formula sheets are for members, with one free sample for any account.
How the path works
- Work through the topics in order: each section lists what to know, the guides to read, the calculators to try, the tables you will want to find quickly, and the practice set and formula sheet for that topic.
- Read a guide, then do its practice problems on paper before looking at the answers. The answers show every step so you can see where a mistake started.
- Keep a short list of every mistake and what caused it. It is the best revision material you will have.
- Learn where things are in the NCEES FE Reference Handbook (the exam gives you a copy as a searchable PDF) so you are not hunting for a formula under time pressure. Our How to study page has more.
A 12-week schedule
A common plan is about 10 hours a week for 12 weeks. Move weeks around to match your strong and weak topics: spend more time on the subjects you studied longest ago.
| Week | Topics |
|---|---|
| 1 | Mathematics |
| 2 | Probability and Statistics, Engineering Economics |
| 3 | Statics |
| 4 | Dynamics, Kinematics and Vibrations |
| 5 | Mechanics of Materials |
| 6 | Material Properties and Processing, Ethics and Professional Practice |
| 7 | Fluid Mechanics |
| 8 | Thermodynamics |
| 9 | Heat Transfer |
| 10 | Electricity and Magnetism, Measurements, Instrumentation and Controls |
| 11 | Mechanical Design and Analysis |
| 12 | Review: mixed practice, your error list, and reference handbook drills |
The topics
- Mathematics
- Probability and Statistics
- Engineering Economics
- Ethics and Professional Practice
- Electricity and Magnetism
- Statics
- Dynamics, Kinematics and Vibrations
- Mechanics of Materials
- Material Properties and Processing
- Fluid Mechanics
- Thermodynamics
- Heat Transfer
- Measurements, Instrumentation and Controls
- Mechanical Design and Analysis
Mathematics
What it covers
- Algebra, trigonometry and analytic geometry
- Calculus: derivatives, integrals, series
- Vectors, matrices and linear algebra
- Ordinary differential equations
- Numerical methods
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Practice and formula sheets (members)
FORMULA SHEET · MEMBERS
Statistics and Engineering Math Formula Sheet
Descriptive statistics, the normal distribution, regression, calculus, trigonometry and algebra.
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Probability and Statistics
What it covers
- Mean, median, standard deviation and variance
- Normal distribution and z-scores
- Confidence intervals and hypothesis tests
- Regression and process capability
Read
Try
Practice and formula sheets (members)
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.
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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.
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Engineering Economics
What it covers
- Time value of money: present, future and annual worth
- Loan payments and interest
- Break-even and cost comparison
- Depreciation and rate of return
Read
Ethics and Professional Practice
What it covers
- Codes of ethics (for example the NSPE Code of Ethics)
- Public safety, honesty, conflicts of interest and confidentiality
- Licensure, intellectual property and professional liability
This topic is about reading a short scenario and applying a code of ethics. Read the NSPE code and your state board’s rules once, then practice with a few sample scenarios.
Electricity and Magnetism
What it covers
- DC circuits, Ohm’s law, Kirchhoff’s laws, equivalent resistance
- Capacitors, inductors and RC and RL transients
- AC power: real, reactive and apparent power, power factor
- Three-phase power, transformers and motors
- Op-amp and measurement basics
Read
Try
- Ohm’s Law and Power Calculator
- Three-Phase Power and Power Factor Calculator
- RC Time Constant and Filter Calculator
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Practice and formula sheets (members)
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.
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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.
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Electrical and Electronics Formula Sheet
Ohm’s law, networks, capacitors, filters, AC power, three-phase and wire sizing.
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Statics
What it covers
- Force and moment equilibrium, free-body diagrams
- Trusses, frames and machines
- Friction, centroids and moments of inertia
- Distributed loads and cables
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Practice and formula sheets (members)
EXAM PREP · MEMBERS
FE practice set 1: Statics
Beam reactions, cables, friction, centroids, moments and a hinged beam: 6 problems with worked answers.
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Statics and Dynamics Formula Sheet
Equilibrium, friction, centroids, kinematics, Newton’s laws, work and energy, momentum and rotation.
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Dynamics, Kinematics and Vibrations
What it covers
- Particle and rigid-body kinematics, projectiles
- Newton’s second law, work and energy, impulse and momentum
- Rotation, gears, belts and linkages
- Free and forced vibration, natural frequency, damping
Read
- Kinematics: Motion of Particles and Bodies
- Dynamics: Force, Energy and Momentum
- Linkages and Mechanisms
- Vibration, Isolation and Noise
Try
Practice and formula sheets (members)
EXAM PREP · MEMBERS
FE practice set 2: Dynamics
Kinematics, projectiles, energy, rotation, vibration and impact: 6 problems with worked answers.
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Mechanics of Materials
What it covers
- Stress and strain, Hooke’s law, thermal stress
- Bending, shear and deflection of beams
- Torsion of shafts and combined loading, Mohr’s circle
- Column buckling and pressure vessels
- Fatigue and stress concentration
Read
- Stress, Strain and Safety Factors
- Beam Bending and Deflection
- Torsion, Shear and Combined Loads
- Columns and Buckling
- Fatigue and Stress Concentration
- Section Properties and Structural Profiles
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Practice and formula sheets (members)
EXAM PREP · MEMBERS
FE practice set 3: Mechanics of Materials
Axial, bending, torsion, Mohr’s circle, buckling and pressure vessels: 6 problems with worked answers.
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Mechanical Formula Sheet
Stress, section properties, beams, torsion, columns, bolts, gears, springs and vibration.
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Material Properties and Processing
What it covers
- Properties of metals, plastics and ceramics: strength, hardness, ductility
- Heat treatment of steel and phase diagrams
- Corrosion and material selection
- Welding, casting, forming and machining processes
Read
- Steels and Heat Treatment
- Welding Processes and Weld Design
- Corrosion and Protection
- Material Selection, Testing and Failure
- Material Properties
Try
Look up
- Material Properties Table
- Steel Grade Cross Reference
- Aluminum Alloys and Tempers
- Stainless Steel Grades
Practice and formula sheets (members)
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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.
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Welding and Joining Formula Sheet
Weld strength, heat input, joint design, rivets and adhesives.
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Fluid Mechanics
What it covers
- Fluid properties, hydrostatics and buoyancy
- Continuity and Bernoulli, energy equation
- Pipe flow: Reynolds number, friction factor, minor losses
- Pumps, system curves and NPSH
- Flow measurement and momentum
Read
- Fluid Properties and Fluid Statics
- Continuity, Bernoulli and the Energy Equation
- Pipe Friction and the Moody Diagram
- Fittings, Valves and Minor Losses
- Pumps, Pump Curves and NPSH
- Flow Measurement
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- Water Properties vs Temperature
- Steel Pipe Sizes (NPS and DN, Schedule 40 and 80)
- Pipe Roughness Values
- Fitting and Valve Loss Coefficients (K Factors)
Practice and formula sheets (members)
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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.
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FE practice set 12: Pumps and Piping
Pipe friction, pump power, affinity laws, NPSH, fitting losses and water hammer: 6 problems with worked answers.
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Piping and Pipe Flow Formula Sheet
Continuity, Reynolds number, friction factor, Darcy-Weisbach, minor losses, Hazen-Williams, pump power, NPSH, wall thickness and surge.
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Thermodynamics
What it covers
- First law for closed and open systems
- Ideal gases and processes
- Second law, entropy and Carnot
- Steam tables, Rankine and gas power cycles
- Refrigeration, psychrometrics and combustion
Read
- Properties, State and the First Law
- Ideal Gases and Processes
- The Second Law, Entropy and Carnot
- Steam, Water and Property Tables
- Steam Power Cycles: Rankine
- Gas Cycles: Otto, Diesel and Brayton
- Refrigeration and Heat Pumps
- Moist Air and the Psychrometric Chart
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Practice and formula sheets (members)
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FE practice set 5: Thermodynamics and Heat Transfer
Ideal gas, isothermal work, Carnot, refrigeration, conduction and water heating: 6 problems with worked answers.
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Thermodynamics Formula Sheet
First and second laws, ideal gas processes, cycles, efficiency and refrigeration.
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Heat Transfer
What it covers
- Conduction through walls, cylinders and composite layers
- Convection and heat transfer coefficients
- Radiation and view factors
- Fins, transient heating and heat exchangers
Read
- Conduction: Walls, Pipes and Insulation
- Convection and Heat Transfer Coefficients
- Thermal Radiation
- Fins and Extended Surfaces
- Heat Exchangers: LMTD and NTU
- Transient Heating and Cooling
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Practice and formula sheets (members)
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Heat Exchangers Formula Sheet
Energy balance, LMTD and effectiveness-NTU methods, overall coefficient, fouling and typical U values.
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Measurements, Instrumentation and Controls
What it covers
- Sensors, signal conditioning and uncertainty
- Strain gauges, thermocouples, RTDs and bridges
- Sampling, aliasing and data acquisition
- Feedback control, transfer functions and stability
- PID controllers and step response
Read
- Sensor Basics and Selection
- Feedback Control Basics
- Laplace Transforms and Transfer Functions
- Time Response and Specifications
- Stability: Routh, Root Locus and Margins
- PID Control and Tuning
Try
Practice and formula sheets (members)
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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.
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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.
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Control Tuning Formula Sheet
PID forms, Ziegler-Nichols and lambda tuning rules, second-order response relations and sampling guidance.
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Mechanical Design and Analysis
What it covers
- Bolted joints, preload and threaded fasteners
- Springs, gears, shafts, keys and bearings
- Fatigue design and failure theories
- Welded joints, power screws, brakes and clutches
- Tolerances, fits and GD&T basics
Read
- Bolted and Welded Joints
- Springs: Design, Stress and Fatigue
- Bearings and Bearing Selection
- Power Screws and Lead Screws
- Clutches, Brakes and Couplings
- How Fits Work
Try
- Bolt Torque & Thread Engagement Tool
- Compression Spring Design Calculator
- Spur Gear Pair Designer
- Bearing Life (L10) Calculator
- Shaft and Key Sizing Calculator
Look up
- Bolt Strength Grades and Property Classes
- Deep-Groove Ball Bearing Dimensions
- Metric Parallel Keys and Keyways
- O-Ring Cross-Sections and Groove Depths
Practice and formula sheets (members)
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FE practice set 6: Machine Design
Bolts, gears, bearing life, fatigue, keys and springs: 6 problems with worked answers.
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Machine Design and Fatigue Formula Sheet
Combined stress, failure theories, fatigue, pressure vessels, bolts, bearings and keys.
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Bolted Joints Formula Sheet
Proof load and preload, tightening torque, joint stiffness, external load sharing, separation, shear and thread engagement.
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Gears, Belts and Chains Formula Sheet
Ratios, speeds, center distances, tooth forces, belts, chains and efficiency.
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Bearings and Lubrication Formula Sheet
Rolling bearing life, equivalent load, reliability factors, speed limits, viscosity ratio, friction and shaft fits.
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