FE and PE Exam

NCEES FE and PE exams · independent study site · checked Oct 29, 2026

The FE exam, discipline by discipline

The FE (Fundamentals of Engineering) exam is generally the first step toward a professional engineer license. NCEES writes it in seven disciplines, each a computer-based test of 110 questions in 5 h 20 min, given year-round in Pearson VUE test centers. This site has worked problems for five of them and for the PE Mechanical HVAC & Refrigeration exam that can follow, and each table cites the NCEES document behind it, with the day we read it.

All practice tests FE vs PE

Updated Oct 29, 2026 · Not affiliated with NCEES.

Exams with practice sets

FE Civil

NCEES

Fourteen sections; Structural, Geotechnical and Water Resources run 10–15 questions each

  • Questions110
  • Exam time5 h 20 min
  • Exam fee$225

FE Mechanical

NCEES

Home of the mechanics on this site: statics, dynamics, mechanics of materials, thermodynamics, heat transfer

  • Questions110
  • Exam time5 h 20 min
  • Exam fee$225

FE Electrical and Computer

NCEES

Seventeen sections, and the widest math range of any FE: 11–17 questions

  • Questions110
  • Exam time5 h 20 min
  • Exam fee$225

FE Environmental

NCEES

Water and wastewater, and fluid mechanics and hydraulics, are the two largest sections at 12–18 each

  • Questions110
  • Exam time5 h 20 min
  • Exam fee$225

FE Chemical

NCEES

The chemical engineering FE: balances, thermodynamics, mass transfer and reactor design

  • Questions110
  • Exam time5 h 20 min
  • Exam fee$225

PE Mechanical HVAC & Refrigeration

NCEES

The licensing exam after the FE, for HVAC&R engineers: 80 questions, USCS only

  • Questions80
  • Exam time8 h
  • Exam fee$400

One problem from each exam

0 / 6 answered · 0 correct
Question 1 of 6 · FE Civil · Structural Engineering · 10–15 items

Which LRFD load combination (ASCE 7 strength design) would typically govern the gravity design of a roof framing system in a region with high snow loads and minimal seismic activity?

Solution

The governing strength combination carries the 1.6 factor on the dominant variable load. Snow dominates here:

U = 1.2D + 1.6S + L

FE Reference Handbook, Structural Design — load combinations (ASCE 7).

This combination checks uplift and overturning with minimum dead load; it governs anchorage, not gravity framing under heavy snow.
With snow as the principal variable load, this is the combination that puts the 1.6 factor on S, so it produces the largest factored gravity demand.
This combination makes occupancy live load the principal load; snow rides along at only 0.5, which under-represents a heavy-snow site.
This is the seismic combination; with minimal seismic activity E is small and snow is cut to 0.2S, so it does not govern.
Question 2 of 6 · FE Mechanical · Mechanics of Materials · 9–14 items

A stress element has σx = 80 MPa, σy = 20 MPa, and τxy = 40 MPa. What is the maximum principal stress?

Given
  • Normal stress σx = 80 MPa
  • Normal stress σy = 20 MPa
  • Shear stress τxy = 40 MPa
FindMaximum principal stress σ1 (MPa)

Solution

σ1 = (80 + 20)/2 + √(((80 − 20)/2)2 + 402) = 50 + 50 = 100 MPa

FE Reference Handbook, Mechanics of Materials: principal stresses.

80 MPa is σx; shear stress raises the maximum normal stress above it.
This adds τxy directly to the average stress and leaves out the ((σx − σy)/2)2 term.
σ1 = (σx + σy)/2 + √(((σx − σy)/2)2 + τxy2) = 50 + √(900 + 1600) = 100 MPa.
This uses σx − σy = 60 instead of half of it under the square root.
Question 3 of 6 · FE Electrical and Computer · Properties of Electrical Materials · 4–6 items

The resistivity of copper at 20 °C is 1.68 × 10−8 Ω·m. What is the resistance of a 100 m copper wire with a cross-sectional area of 2 mm2?

Given
  • Resistivity ρ = 1.68 × 10−8 Ω·m
  • Length L = 100 m
  • Cross-sectional area A = 2 mm2
FindResistance R (Ω)

Solution

R = ρL/A

R = (1.68 × 10−8 Ω·m × 100 m)/(2 × 10−6 m2) = 0.84 Ω

This converts 2 mm2 as 2 × 10−3 m2; 1 mm2 = 10−6 m2.
This treats 2 mm as a diameter (A = π × 12 mm2); the stem gives the area directly.
R = ρL/A = 1.68 × 10−8 × 100/(2 × 10−6) = 0.84 Ω.
This converts 1 mm2 as 10−7 m2, ten times too small.
Question 4 of 6 · FE Environmental · Environmental Chemistry · 7–11 items

A groundwater contains 60 mg/L of calcium (Ca2+) and 24 mg/L of magnesium (Mg2+). What is its total hardness in mg/L as CaCO3?

Given
  • Ca2+ = 60 mg/L (equivalent weight 20.04)
  • Mg2+ = 24 mg/L (equivalent weight 12.15)
  • CaCO3 equivalent weight = 50.04
FindTotal hardness (mg/L as CaCO3)

Solution

Convert each divalent cation to CaCO3 equivalents and add (Environmental chemistry: hardness).

Ca: 60 × 50.04/20.04 = 150 mg/L; Mg: 24 × 50.04/12.15 = 99 mg/L

TH = 150 + 99 = 249 mg/L as CaCO3

84 mg/L adds the ion concentrations without converting them to CaCO3 equivalents.
99 mg/L is the magnesium hardness alone.
150 mg/L is the calcium hardness alone; magnesium is a hardness ion too.
199 mg/L converts magnesium with its molar mass (24.31) instead of its equivalent weight (12.15), halving its contribution.
Ca: 60 × 50.04/20.04 = 150; Mg: 24 × 50.04/12.15 = 99; total hardness = 249 mg/L as CaCO3.
Question 5 of 6 · FE Chemical · Mass Transfer and Separation · 8–12 items

In an absorption tower, the minimum liquid-to-gas ratio (L/G)min occurs when:

Solution

(L/G)min = (yin − yout)/(xout − xin), xout = yin/m

Pinch at the bottom: infinite stages; operation typically at 1.2–1.5 × (L/G)min.

Pressure drop depends on hydraulics (packing, flow rates), not on the minimum solvent rate.
Equal absorption and desorption rates describe local equilibrium, which at (L/G)min occurs only at the rich end, not along the whole tower.
At (L/G)min the operating line touches the equilibrium line at the rich (bottom) end: exit liquid in equilibrium with entering gas, which needs infinite height.
A pinch at the lean (top) end limits the purity of the exit gas, not the minimum solvent rate.
Question 6 of 6 · PE Mechanical HVAC & Refrigeration · HVAC Loads and Psychrometrics · 18–27 items

A space with a cooling load of 60,000 Btu/h has a sensible heat ratio of 0.65. What is the latent cooling load in Btu/h?

Given
  • Total cooling load = 60,000 Btu/h
  • Sensible heat ratio SHR = 0.65
FindLatent cooling load (Btu/h)

Solution

qL = qT(1 − SHR)

qL = 60,000 Btu/h × (1 − 0.65) = 21,000 Btu/h

21,000 Btu/h is the latent part: total minus the sensible share, 60,000 × (1 − 0.65).
32,300 Btu/h treats 60,000 Btu/h as the sensible load and backs out latent as S(1 − SHR)/SHR; the stem gives the total.
39,000 Btu/h is the sensible load, 0.65 × 60,000 — the SHR fraction itself, not the remainder.
60,000 Btu/h is the whole cooling load; no split by SHR has been made.

Answer every question to see your score

Each problem was set for this site against the current specification of its exam and is solved step by step; none comes from an NCEES exam. The full sets are on each exam’s practice test.

FE and PE problems on your phone

FE Civil app

FE Civil questions, answers and worked solutions in a study app.

Not affiliated with NCEES.

FE Mechanical app

FE Mechanical questions, answers and worked solutions in a study app.

Not affiliated with NCEES.

FE Electrical and Computer app

FE Electrical and Computer questions, answers and worked solutions in a study app.

Not affiliated with NCEES.

FE Environmental app

FE Environmental questions, answers and worked solutions in a study app.

Not affiliated with NCEES.

FE Chemical app

FE Chemical questions, answers and worked solutions in a study app.

Not affiliated with NCEES.

PE Mechanical HVAC & Refrigeration app

PE Mechanical HVAC & Refrigeration questions, answers and worked solutions in a study app.

Not affiliated with NCEES.

What is on the FE exam

Each discipline has its own specification, the NCEES list of sections with a question range for each, in force since July 2020. Four sections are common ground: mathematics, probability and statistics, ethics and engineering economics. They make up about a fifth of the Civil, Mechanical, Environmental and Chemical specifications, a quarter or more on Electrical and Computer and Other Disciplines, and close to a third on Industrial and Systems. These four get one shared treatment, on the FE practice test and engineering economics; the rest of each exam is the discipline itself.

You bring no books. Your one reference is the FE Reference Handbook, a searchable PDF on the exam screen, and the only calculator is one model from the approved list. Problems mix SI and US customary units. How the appointment runs, from the break to the pass/fail notice, is on FE exam format.

Seven FE disciplines, one half-year

Checked Oct 29, 2026. Sources are numbered and listed under Source notes. Jan–Jun 2026, counting first-time takers from EAC/ABET programs no more than 12 months past graduation. FE Industrial and Systems and FE Other Disciplines are tracked here with facts only for now. Other periods and repeat takers: FE pass rates.
ExamFirst-time pass rateFirst-time takersPracticeSourceChecked
FE Civil66%6,247Practice test
Exam facts
[1]
FE Mechanical73%5,153Practice test
Exam facts
[1]
FE Electrical and Computer70%1,782Practice test
Exam facts
[1]
FE Environmental71%1,063Practice test
Exam facts
[1]
FE Chemical68%743Practice test
Exam facts
[1]
FE Industrial and Systems67%259—[1]
FE Other Disciplines61%921—[1]

Which FE discipline should you take?

Take the one whose specification matches what you studied, since its sections are your coursework:

  • Civil, mechanical, environmental, or electrical and computer engineering: the FE of the same name. Chemical engineers take FE Chemical.
  • Industrial and systems engineering: FE Industrial and Systems, which gives probability and statistics 10–15 questions, the most of any FE. Listed below with facts only.
  • A program with no FE of its own: FE Other Disciplines, a broad exam with statics, dynamics, fluids, electrical and thermal sections. NCEES breaks its takers down by degree, among them naval architecture, nuclear, mining, materials, biological and architectural engineering, with first-time pass rates of 41–83% by program in Jan–Jun 2026.

When to sit it: early. First-time takers from ABET programs passed at 71% before graduation and 71% within 12 months of it, against 63% later, in NCEES data for 2014–25 with all disciplines pooled. Your state board decides when you may register: the requirements are on FE exam format.

After the FE

A pass makes you eligible for the intern certificate your state board issues (EIT certification). The license itself needs qualifying experience and the PE exam, and the board decides whether you may sit the PE before that experience is complete. Two boards, for example:

  • Texas: Yes (decoupled)
  • California: Yes (exam first)

Experience years under the Model Law, and other boards: how to become a PE. FE and PE compared: FE vs PE; the PE in general: PE exam overview.

  1. Degree

    EAC/ABET bachelor’s degree in engineering (the Model Law also counts ETAC/ABET, master’s and doctoral routes, with different experience years).

    Source: [2]

  2. FE exam

    Pass the FE in your discipline, usually near graduation.

    Source: [1]

  3. EI / EIT

    The state board certifies you as an engineer intern.

    Source: [2]

  4. Experience

    Four years of progressive engineering experience under the Model Law.

    Source: [2]

  5. PE exam

    Pass the PE in your field; some boards let you sit before the experience is done.

    Source: [2][3]

  6. License

    Apply to the board; some states add their own exams.

    Source: [2]

Next in line, with facts only

Checked Oct 29, 2026. Sources are numbered and listed under Source notes. Facts only so far, drawn from the same NCEES pages and guide. PE Structural is taken in sections, priced per section.
ExamQuestionsExam timeExam feeWhen you can testSourceChecked
FE Industrial and Systems1105 h 20 min$225Year-round[1][4][5]
FE Other Disciplines1105 h 20 min$225Year-round[1][4][5]
PE Civil808 h$400Year-round[4][5][6][7]
PE Mechanical Machine Design & Materials808 h$400Year-round[4][5][7][8]
PE Mechanical Thermal & Fluid Systems808 h$400Year-round[4][5][7][9]
PE Electrical Power808 h$400Year-round[4][5][7][10]
PE Structural55 / 605.5 h / 6 h$350 × 4Breadth year-round[4][5][11]

Checked against the current NCEES documents

Where older prep material is out of date:

  • Fee: $225 per attempt since 2024; a guide quoting $175 predates the change.
  • Specifications: July 2020 for every FE discipline, and the NCEES notice that lists exam changes through fall 2027 names none for the FE.
  • Handbook: no version number here. The exam uses the current version, which is in your MyNCEES account.
  • PE HVAC&R: since October 2025 its outline has four applied areas, so a guide that splits it into Principles and Applications describes the old exam.

FE guides

Source notes

  1. NCEES: FE exam ncees.org · checked Oct 29, 2026
  2. NCEES Model Law, 2026 (PDF) ncees.org
  3. NCEES Model Rules, 2026 (PDF) ncees.org
  4. NCEES Examinee Guide, May 2026 (PDF) ncees.org · checked Oct 29, 2026
  5. NCEES: new exam prices effective January 1, 2024 ncees.org · checked Oct 29, 2026
  6. NCEES: PE Civil specifications, April 2024 (Water Resources and Environmental module, PDF) ncees.org · checked Oct 29, 2026
  7. NCEES: PE pass-rate table and PE Mechanical exams page ncees.org · checked Oct 29, 2026
  8. NCEES: PE Mechanical Machine Design and Materials specifications, October 2025 (PDF) ncees.org · checked Oct 29, 2026
  9. NCEES: PE Mechanical Thermal and Fluid Systems specifications, October 2025 (PDF) ncees.org · checked Oct 29, 2026
  10. NCEES: PE Electrical and Computer: Power specifications, October 2025 (PDF) ncees.org · checked Oct 29, 2026
  11. NCEES: PE Structural exam ncees.org · checked Oct 29, 2026

Short answers on the FE

What is the FE exam?

The Fundamentals of Engineering exam, written and scored by NCEES. It is designed for students close to finishing an accredited engineering degree and for recent graduates, and passing it, with an accepted degree, leads to EI/EIT certification from your state board.

Is the FE exam hard?

First-time pass rates sit in the 60s and low 70s. In Jan–Jun 2026 they ran from 61% (FE Other Disciplines) to 73% (FE Mechanical), among EAC/ABET graduates of the past 12 months (all disciplines).

Which FE should a chemical, industrial or naval graduate pick?

Chemical engineers take FE Chemical, industrial and systems engineers take FE Industrial and Systems, and programs without an FE of their own, naval architecture among them, take FE Other Disciplines. The last two have facts here but no practice set yet.

Is the EIT exam the same as the FE?

Yes: there is no separate EIT exam. EIT, or engineer intern, is the certificate a state board issues once you pass the FE and hold an accepted degree (Model Law: Degree + FE). Titles and fees vary by board: EIT certification.

When can I take the FE exam?

Year-round, in four quarterly windows. Who may register, and how early, is up to your state board (requirements).