PE Mechanical Roadmap
The three depth areas, what is in each, and the resources that support them.
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.
The PE exam tests depth in one area of practice, after you have passed the FE and gained several years of supervised experience. This page is a roadmap, not a course: it lists the three depth areas for the Mechanical PE, the engineering topics inside each, and the guides, calculators, tables and formula sheets on this site that support them. Check the NCEES exam specifications for the current list of topics, the number of questions and the permitted references.
Planning your preparation
- Choose your depth area early, based on the work you do. Spend most of your time there.
- Plan for 3 to 4 months of steady study alongside a job. Most of the time goes on practice problems, not reading.
- Practice with the reference material you will be allowed in the exam, so you can find the formula, table or chart you need quickly.
- Work problems by hand with the calculator model you will use on the day. Check the NCEES calculator policy.
- Keep an error log. In the last weeks, rework your mistakes and time yourself on mixed sets.
Machine Design and Materials
Topics
- Stress, strain and failure theories, fatigue and fracture
- Springs, fasteners, shafts, keys, bearings, gears, belts and chains
- Power screws, brakes, clutches, couplings and flywheels
- Vibration, balancing and noise
- Materials selection, heat treatment, welding and corrosion
- Tolerances, fits and stack-ups
Guides on this site
- Machine Design
- Structures and Strength of Materials
- Materials and Processes
- Gears and Power Transmission
- Fits & Tolerances
- GD&T
Calculators
- Bearing Life (L10) Calculator
- Compression Spring Design Calculator
- Spur Gear Pair Designer
- Bolt Torque & Thread Engagement Tool
- Fit Calculator (ISO 286)
Reference tables
- Bolt Strength Grades and Property Classes
- Steel Grade Cross Reference
- Deep-Groove Ball Bearing Dimensions
- Metric Parallel Keys and Keyways
- O-Ring Cross-Sections and Groove Depths
Formula sheets and practice (members)
FORMULA SHEET · MEMBERS
Machine Design and Fatigue Formula Sheet
Combined stress, failure theories, fatigue, pressure vessels, bolts, bearings and keys.
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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.
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FORMULA SHEET · MEMBERS
Gears, Belts and Chains Formula Sheet
Ratios, speeds, center distances, tooth forces, belts, chains and efficiency.
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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.
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FORMULA SHEET · MEMBERS
Welding and Joining Formula Sheet
Weld strength, heat input, joint design, rivets and adhesives.
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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.
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HVAC and Refrigeration
Topics
- Psychrometrics and air-conditioning processes
- Heating and cooling loads, ventilation and indoor air quality
- Ducts, fans, coils, chillers and cooling towers
- Refrigeration cycles and heat pumps
- Hydronic systems, controls and energy use
Guides on this site
Calculators
- Psychrometric Calculator and Chart
- Pipe Flow and Pressure Drop Calculator
- Pump Power and Sizing Calculator
Reference tables
Formula sheets and practice (members)
FORMULA SHEET · MEMBERS
Fluids and Thermal Formula Sheet
Pipe flow, pumps, pneumatics, heat transfer and moist air.
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FORMULA SHEET · MEMBERS
Thermodynamics Formula Sheet
First and second laws, ideal gas processes, cycles, efficiency and refrigeration.
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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.
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Thermal and Fluid Systems
Topics
- Pipe and duct flow, pumps, fans and compressors
- Power cycles: Rankine, Brayton, Otto and Diesel; combustion
- Heat exchangers, conduction, convection and radiation
- Hydraulic and pneumatic systems
- Steam systems and boilers
Guides on this site
Calculators
- Pipe Flow and Pressure Drop Calculator
- Pump Power and Sizing Calculator
- Compressed Air Consumption Calculator
- Pneumatic and Hydraulic Cylinder Force and Speed Calculator
Reference tables
- Water Properties vs Temperature
- Steel Pipe Sizes (NPS and DN, Schedule 40 and 80)
- Pipe Roughness Values
- Fitting and Valve Loss Coefficients (K Factors)
- Thermal Conductivity of Materials
Formula sheets and practice (members)
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.
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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.
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FORMULA SHEET · MEMBERS
Hydraulics and Pneumatics Formula Sheet
Pressure, force, flow, speed, power, orifices, accumulators and air consumption.
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FORMULA SHEET · MEMBERS
Pneumatics and Compressed Air Formula Sheet
Cylinder force, air consumption, receiver sizing, compression, choked flow, valve flow coefficients and typical pressures.
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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.
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EXAM PREP · MEMBERS
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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The practice sets on this site are written at FE level. They are a good warm-up for the calculations behind PE problems, but they are not PE-level questions. For PE practice, use the sample questions and practice exams published by NCEES and the reference material for your depth area.