Electrical Calculations Practice

The formulas worth knowing cold

At roughly two to four minutes per question, there is no time to derive these. The candidates who pass have them automatic.

Core electrical formulas for licensing exams
To find	Single phase	Three phase
Volt-amperes	VA = V × I	VA = 1.732 × V × I
Watts	W = V × I × PF	W = 1.732 × V × I × PF
Current	I = VA ÷ V	I = VA ÷ (1.732 × V)
Voltage drop	VD = 2 × K × I × L ÷ CM	VD = 1.732 × K × I × L ÷ CM

And the rest of the toolkit

Ohm's law: V = I × R, and the twelve forms derived from it with P = V × I
Power from resistance: P = I² × R and P = V² ÷ R
Series resistance: Rt = R1 + R2 + ... + Rn
Parallel resistance, two branches: Rt = (R1 × R2) ÷ (R1 + R2)
Parallel resistance, equal branches: Rt = R ÷ N
Wye system: Vline = 1.732 × Vphase, Iline = Iphase
Delta system: Vline = Vphase, Iline = 1.732 × Iphase
Transformer: Vp ÷ Vs = Np ÷ Ns, and VA in = VA out
Power factor: PF = W ÷ VA
Horsepower: 1 hp = 746 W of mechanical output
Resistivity constants: K = 12.9 for copper, 21.2 for aluminium

The percentage multipliers that run through everything

A surprising share of calculation questions reduce to knowing which multiplier applies. These are the ones worth memorising, with the article they come from.

Common percentage multipliers
Multiplier	Applies to
125%	Continuous load, for both conductor ampacity and device rating (210.19(A)(1)(a), 210.20(A))
125%	Single-motor branch-circuit conductors, from table full-load current (430.22)
125% / 115%	Motor overload device, from nameplate current — 125% with a 1.15 service factor or 40 °C rise, otherwise 115% (430.32(A)(1))
115%	Motor-circuit disconnecting means ampere rating (430.110(A))
175% / 250% / 300% / 800%	Motor branch-circuit device maximum: time-delay fuse, inverse time breaker, nontime-delay fuse, instantaneous trip breaker (Table 430.52)
100% then 35% then 25%	Dwelling lighting demand: first 3,000 VA, 3,001 to 120,000 VA, remainder (Table 220.42)
75%	Four or more appliances fastened in place on one feeder or service (220.53)
100% then 40%	Dwelling optional method general load: first 10 kVA, then the remainder (220.82(B))
70%	Additional neutral demand factor for ranges and dryers (220.61(B)(1))
80% / 70% / 50%	Ampacity adjustment for 4-6, 7-9 and 10-20 current-carrying conductors (Table 310.15(B)(3)(a))
53% / 31% / 40%	Conduit fill for 1, 2 and over 2 conductors (Chapter 9, Table 1)
60%	Conduit nipple not over 24 inches between enclosures (Chapter 9, Note 4)

Article references are to the 2017 NEC, cited from Public.Resource.Org's publication of incorporated standards. Verify against the edition your jurisdiction has adopted.

A worked service calculation, start to finish

This is the shape of the calculation that carries the most marks on the master exam. Follow the order; it is the order the article sets out.

Scenario: a 2,000 square foot dwelling with two small-appliance branch circuits, one laundry circuit, a 12 kW range, a 4.8 kW dryer, and a 240-volt single-phase service. Find the calculated load by the standard method.

General lighting: 2,000 ft² × 3 VA = 6,000 VA
Small-appliance circuits: 2 × 1,500 VA = 3,000 VA
Laundry circuit: 1,500 VA
Subtotal subject to demand factors: 6,000 + 3,000 + 1,500 = 10,500 VA
Apply the lighting demand factors: 3,000 at 100% plus 7,500 at 35% = 3,000 + 2,625 = 5,625 VA
Range, from Column C for one appliance not over 12 kW = 8,000 VA
Dryer: nameplate is 4,800 VA but the minimum is 5,000 VA, so use 5,000 VA
Total calculated load: 5,625 + 8,000 + 5,000 = 18,625 VA
Service current: 18,625 ÷ 240 = 77.6 A, so a 100-ampere service is the smallest standard size that serves it

Note the two traps in steps 5 and 7. The demand factors apply only to the lighting, small-appliance and laundry subtotal, not to the range and dryer. And the dryer is calculated at the 5,000 VA floor rather than its smaller nameplate rating.

Practise this calculation and its variations on the load calculations page, or check your working with the load calculation calculator.

Calculation topics

Each page explains the method, then puts you into exercises on it.

Questions about electrical calculations

Why do these exercises make me type the answer instead of choosing one?

Because picking from four options lets you work backwards. If you can eliminate three answers you never have to do the calculation, which is fine on exam day but useless for learning. Typing a number means you either did the arithmetic or you did not.

How much tolerance is allowed on a numeric answer?

Each exercise states its tolerance beneath the input box, and it is set to the precision the calculation actually warrants. A current answer might allow 0.1 amperes while a conductor area allows 0.0005 square inches. Answers are graded against that stated tolerance, so sensible rounding is accepted and a genuinely wrong method is not.

What answer formats are accepted?

Plain decimals, thousands separators such as 1,500, and fractions including mixed numbers such as 1 1/2. If you type a unit it is checked against the expected unit and its common spellings rather than being rejected outright, so "12.5 A", "12.5 amps" and "12.5" are all read the same way.

Which calculations appear most often on the exam?

Dwelling service load calculations, conductor sizing with correction and adjustment factors, the four motor circuit calculations, overcurrent device selection, conduit fill and voltage drop. On the Texas master exam, services and service equipment alone accounts for 8 of 30 scored calculations items.

Do I need a calculator for the exam?

North Carolina states that calculators are provided at the test center. Texas says electronic notepads are provided and directs candidates to its candidate bulletin for the full reference list. Check your own bulletin, and in either case practise with a basic calculator rather than a programmable one, since graphing and programmable calculators are commonly prohibited.

How are the answers to these exercises verified?

Every numeric answer carries an arithmetic expression that reproduces it from the question's own figures, and a validation script evaluates all of them and fails the build if any disagrees with the answer key. That catches a typed digit or a transposed number mechanically rather than relying on proofreading.

What is the most common arithmetic mistake on electrician exams?

Omitting the square root of 3 from a three-phase calculation, which produces an answer about 73 percent of the correct one — and that wrong value is usually among the offered options. Close behind it is applying the 125 percent continuous-load multiplier to the whole load instead of just the continuous portion.