The Calculations You Must Be Able to Do Before Exam Day
A checklist of the eight calculation families on journeyman and master exams, what each one needs from the code book, and the mistake that costs the most points in each.
Calculations are a quarter of a journeyman exam and up to a third of a master exam, and they are where scores separate. Not because the maths is hard, but because each problem needs the right table and the right rule, in the right order, under a clock. Here are the families, what each needs, and where candidates go wrong.
1. Conductor ampacity with correction and adjustment
What it asks. The allowable ampacity of a conductor after accounting for ambient temperature and the number of current-carrying conductors in a raceway or cable.
Where it lives. Table 310.16 for the base ampacity. 310.15(B) for temperature correction. 310.15(C) for adjustment when more than three current-carrying conductors share a raceway. 310.15(E) for which conductors count as current-carrying.
The method. Start at the conductor's insulation temperature column (90 degrees for THHN), multiply by the correction factor, multiply by the adjustment factor, then check that the result does not exceed the 75 degree (or 60 degree) value required by the terminations under 110.14(C).
The mistake. Applying the 75 degree termination limit before correction instead of after, or forgetting that the neutral counts as current-carrying in a 3-wire single-phase circuit from a 4-wire wye system.
2. Voltage drop
What it asks. The drop on a circuit of given length and load, or the conductor size needed to stay within 3 percent.
Where it lives. Chapter 9 Table 8 for circular mils. Informational notes to 210.19 and 215.2 for the 3 and 5 percent recommendations.
The method. Single phase: VD = 2 × K × I × L ÷ CM. Three phase: VD = 1.732 × K × I × L ÷ CM. K is about 12.9 for copper and 21.2 for aluminium; L is one-way length in feet.
The mistake. Using the round-trip length with the 2 already in the formula, or forgetting to switch from 2 to 1.732 for three phase.
3. Box fill
What it asks. Whether a given box is large enough, or the minimum box for a set of conductors, clamps and devices.
Where it lives. 314.16(B) for the counting rules. Table 314.16(B) for cubic inches per conductor. Table 314.16(A) for standard box volumes.
The method. Count every conductor that originates outside the box and terminates or is spliced inside. Count all equipment grounding conductors as one, all internal clamps as one, each device yoke as two of the largest conductor connected to it. Multiply by the volume per conductor and compare.
The mistake. Counting each ground separately, or forgetting the two-conductor allowance for a device.
4. Conduit fill
What it asks. How many conductors of a given type fit in a raceway, or the minimum raceway for a set of conductors.
Where it lives. Chapter 9 Table 1 (40 percent for three or more conductors, 31 percent for two, 53 percent for one). Table 4 for raceway areas. Table 5 for conductor areas. Annex C for the shortcut when all conductors are the same size and type.
The method. Add the conductor areas from Table 5, then find the raceway in Table 4 whose fill column meets or exceeds the total. For same-size conductors go straight to Annex C.
The mistake. Using the total area of the raceway instead of the percent-fill column, or looking up the wrong conductor type.
5. Motor circuits
What it asks. Conductor size, overload setting, branch-circuit short-circuit protection, or the feeder for a group of motors.
Where it lives. Tables 430.247 to 430.250 for full-load current. 430.22 for conductors. 430.32 for overloads. 430.52 and its table for short-circuit and ground-fault protection. 430.24 for feeders.
The method. Take full-load current from the table, not the nameplate. Conductors at 125 percent of that. Overloads from the nameplate at 115 or 125 percent depending on the motor's service factor and temperature rise. Branch-circuit protection from the table percentage (250 percent for an inverse-time breaker), rounded up to the next standard size if the exception allows.
The mistake. Nameplate current for conductors, table current for overloads: it is the other way round.
6. Dwelling load calculations
What it asks. The service or feeder size for a dwelling using the standard method or the optional method.
Where it lives. 220.12 for general lighting at 3 VA per square foot. 220.52 for small-appliance and laundry at 1500 VA each. Table 220.42 for the lighting demand factors. Table 220.55 for ranges, 220.54 for dryers. 220.82 for the optional method.
The method, standard. Lighting plus small-appliance plus laundry, with the first 3000 VA at 100 percent and the rest at 35 percent. Add range from Table 220.55, dryer at 5000 VA or nameplate if larger, fixed appliances with the 75 percent factor for four or more, the larger of heating or air conditioning. Divide by voltage.
The method, optional. Everything except heating and cooling added at nameplate, first 10 kVA at 100 percent and the rest at 40 percent, plus the heating or cooling load from 220.82(C).
The mistake. Applying the 35 percent demand factor to the range and dryer, or using the optional method's 40 percent on the standard calculation.
7. Transformer protection
What it asks. Primary and secondary current, and the maximum overcurrent device for each side.
Where it lives. Table 450.3(B). 240.6 for standard sizes. 240.21(C) for secondary conductors.
The method. I = kVA × 1000 ÷ V for single phase, ÷ (V × 1.732) for three phase. Primary only: 125 percent (with the next-size-up note for 9 amperes and over). Primary and secondary: 250 percent primary, 125 percent secondary.
The mistake. Forgetting the 1.732 on three-phase, or using the next-size-up allowance where the table's note does not grant it.
8. Conductor sizing for continuous loads
What it asks. The minimum conductor and overcurrent device for a load that runs three hours or more.
Where it lives. 210.19(A), 210.20(A), 215.2, 215.3.
The method. 125 percent of the continuous load plus 100 percent of the non-continuous load, then choose the conductor from the 75 degree column with at least that ampacity and the overcurrent device at the same figure.
The mistake. Applying 125 percent to the non-continuous portion too.
How to practise
Take one family a day for eight days, ten problems each, with the study guide open. Then start mixing: ten problems a day drawn at random from all eight, with the guide closed and a timer running. Log every miss by family and by the step where it went wrong. After two weeks the log tells you which two families still need work, and those get the remaining time. On exam day you should recognise every calculation question as one of these eight within a few seconds of reading it.