Nobody failed the journeyman exam because they couldn't do algebra.

Why trade math trips people who are good at the work

You can be excellent on the tools and still lose an exam on paper, because exam math has constraints the job doesn't:

• Mixed units, every question. Feet and inches, fractional inches, decimal feet, metric on imported gear — converted mid-problem, under time.
• Formulas that look alike. Ohm's law and the power formulas share letters; single-phase and three-phase differ by a √3 that is easy to leave out.
• Table lookups feeding the math. Get the right number out of the wrong column and perfect arithmetic produces a wrong answer with nothing to flag it.
• Rounding rules that matter. Round a conduit bend to the nearest sixteenth in the wrong direction and the pipe doesn't fit.

What gets tested, by trade

Electrical

Ohm's law and the power triangle; series and parallel resistance; voltage drop over a run; conductor ampacity with derating for temperature and fill; box and conduit fill; motor full-load current; single- vs three-phase power, where the √3 lives; transformer turns and kVA; and conduit bending — offsets, saddles, and concentric bends with their multipliers and shrink.

HVAC/R

Airflow and duct sizing, CFM against static pressure, the sensible heat equation, superheat and subcooling, refrigerant pressure-temperature relationships, heat load estimation, and belt-and-pulley ratios.

Plumbing & pipefitting

Offsets with the standard travel multipliers (45°, 22.5°, 60°), rolling offsets, pipe volume and fill, fixture unit counts to pipe size, slope and fall over a run, and pressure loss from friction and elevation.

Machining & fabrication

Feeds and speeds, SFM to RPM, bend allowance and K-factor, bolt-circle coordinates, taper calculations, and tolerance stack-up.

The offset multiplier, as an example of the real failure

Every apprentice learns that a 45° offset uses a multiplier of 1.414 and a 30° offset uses 2. Almost nobody gets that part wrong. What goes wrong is what it multiplies: the multiplier applies to the offset distance to give travel, and then shrink has to come off the measurement to the bend mark. Mix the order and the arithmetic is flawless and the pipe is short.

That is a setup error, and it is invisible to any check that only looks at your final number. A step-level check reads the working and says which line stopped following — which is the only feedback that stops it happening again.

How to study for a licensing exam

1. Work on paper, units on every line. Same discipline as the job: if the units don't cancel to what the question asked for, the setup is wrong before the arithmetic starts.
2. Learn where the number comes from, not just the formula. Most exams are open-code; knowing which table and which column beats memorising a value.
3. Sanity-check against the physical world. You know what a plausible run, load or bend looks like. If the number would be absurd on site, it's wrong on paper.
4. Check your working, not your answer. Photograph the calc sheet and get the first bad line named. Track categories — yours will cluster around two or three setups.
5. Practise under time. Licensing exams are timed and that changes which errors you make.

Straight talk

This checks your math. It is not a code reference, it does not know your jurisdiction's amendments, and nothing it says overrides the NEC, your local code, or an inspector. Use it the way you'd use a sharp second pair of eyes on a calc sheet — to find the line you got wrong while it's still on paper.

Related: fraction calculator for the sixteenths-and-thirty-seconds arithmetic, and the Pythagorean theorem calculator, which is doing most of the work behind every offset and diagonal run you'll ever calculate.