What maths do I need as an electrical apprentice?

Electrical apprentices need to be confident with basic arithmetic (add, subtract, multiply, divide), fractions and decimals, percentages, powers and roots (especially square roots for AC calculations), and basic algebra for transposing formulae. You will use these skills to apply Ohm's Law, calculate power, work out voltage drop, check circuit impedance, and calculate fault current. Trigonometry (sine, cosine, tangent) and Pythagoras' theorem become important for AC power factor calculations from Year 2 onwards. You do not need A-level maths — a solid GCSE Maths foundation is sufficient.

How do I transpose Ohm's Law to find resistance?

Start with V = I × R. To find R, you need to isolate it by dividing both sides by I. This gives V/I = R, or more neatly, R = V ÷ I. Example: if the voltage across a resistor is 24V and the current through it is 3A, then R = 24 ÷ 3 = 8Ω. The golden rule of transposition is: whatever you do to one side of the equation, you must do the same to the other side.

What is voltage drop and why does it matter?

Voltage drop is the reduction in voltage that occurs along a cable due to its resistance. In a circuit, every metre of cable has a resistance that causes a small voltage drop when current flows through it. If too much voltage is lost in the cables, the load at the end of the circuit receives less voltage than it needs — lights will dim, motors will overheat, and equipment may malfunction. BS 7671 Table 4Ab sets the maximum permitted voltage drop: 3% for lighting circuits (6.9V on a 230V system) and 5% for power circuits (11.5V on 230V).

What is power factor and do I need to understand it in Year 1?

Power factor is the ratio of true (real) power (watts) to apparent power (volt-amperes) in an AC circuit. It arises because inductors and capacitors cause current to be out of phase with voltage. In Year 1, you are primarily working with resistive DC and simple AC circuits where power factor = 1, so P = V × I is straightforward. Power factor becomes important from Year 2 when you study inductive loads like motors and fluorescent lighting. However, knowing the concept exists — and that the power triangle uses true power (W), reactive power (VAr), and apparent power (VA) — is useful background.

How do I calculate percentage voltage drop?

Percentage voltage drop = (Vd ÷ Vn) × 100, where Vd is the actual voltage drop in volts and Vn is the nominal supply voltage (230V for single-phase UK). Example: if a circuit has a voltage drop of 8V, percentage Vd = (8 ÷ 230) × 100 = 3.48%. This exceeds the 3% limit for lighting circuits but is within the 5% limit for power circuits. You can also calculate voltage drop directly using the formula: Vd = (mV/A/m × I × L) ÷ 1000, using the millivolt per ampere per metre values from BS 7671 Appendix 4.

What is Pythagoras' theorem used for in electrical work?

In AC circuits, voltage, current, and impedance are not always in phase. When a circuit contains both resistance (R) and reactance (X — from inductors or capacitors), they combine at right angles in a phasor diagram. Pythagoras' theorem (Z² = R² + X²) gives us the impedance Z from the resistance and reactance: Z = √(R² + X²). Similarly, apparent power (VA) = √(true power² + reactive power²). In Year 1 you mainly deal with resistive circuits, but understanding that Pythagoras applies to AC quantities prepares you for Year 2 and the C&G 2365 Unit 204.

What scientific notation values come up most in electrical work?

The most common SI prefixes you will use daily are: kilo (k) = ×1,000 — kilowatts (kW), kilohms (kΩ), kilovolt-amperes (kVA); mega (M) = ×1,000,000 — megohms (MΩ) used in insulation resistance testing; milli (m) = ÷1,000 — milliamps (mA) for RCD ratings (30mA trip), millivolts (mV) in voltage drop tables; micro (μ) = ÷1,000,000 — microfarads (μF) for capacitors. You must be comfortable converting between these. For example, 250mA = 0.25A; 2.5kΩ = 2,500Ω; 100μF = 0.0001F.

APPRENTICE MATHS GUIDE

Maths for Electrical Apprentices: Essential Electrical Calculations

Every electrical maths skill you need as an apprentice — Ohm's Law, the power triangle, voltage drop, percentage voltage drop, transposition of formulae, Pythagoras for AC circuits, SI prefixes, and practical worked examples.

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13 min readUpdated 2026-05-18Andrew Moore, Founder of Elec-Mate

Written and reviewed by Andrew Moore, founder of Elec-Mate, against BS 7671:2018+A4:2026, IET Guidance Note 3 and the IET On-Site Guide.

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Key Takeaways

1Ohm's Law (V = IR) is the starting point for almost every electrical calculation — master transposition and you can find any unknown.
2The power triangle (P = IV, P = I²R, P = V²/R) gives you three ways to calculate power — use whichever two quantities you already know.
3Voltage drop is calculated using the formula: Vd = (mV/A/m × I × L) / 1000, where mV/A/m values come from BS 7671 Appendix 4 tables.
4Percentage voltage drop must not exceed 3% for lighting circuits or 5% for power circuits under normal BS 7671 conditions.
5Transposition of formulae is a core maths skill — always perform the same operation to both sides of the equation to isolate the unknown.

01 · Apprentice Maths Guide

Ohm's Law Calculations

Ohm's Law is V = I × R. The three variables — voltage (V), current (I), and resistance (R) — are related such that if you know any two, you can calculate the third. This is the foundation of every electrical calculation you will do throughout your career.

Find V: V = I × R. Example: I = 5A, R = 10Ω → V = 5 × 10 = 50V.
Find I: I = V ÷ R. Example: V = 230V, R = 46Ω → I = 230 ÷ 46 = 5A.
Find R: R = V ÷ I. Example: V = 12V, I = 0.4A → R = 12 ÷ 0.4 = 30Ω.
Series circuit example: Three resistors of 4Ω, 6Ω, and 10Ω in series on a 20V supply. Rt = 4 + 6 + 10 = 20Ω. I = V ÷ Rt = 20 ÷ 20 = 1A. Vd across 6Ω resistor = 1 × 6 = 6V.

Use the Elec-Mate Study Centre calculation tools to generate random Ohm's Law problems and check your working. Repeated practice is the only reliable way to build calculation speed for exams.

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02 · Apprentice Maths Guide

Power Triangle (P = IV)

The power triangle gives you three equivalent formulae for calculating electrical power. By combining P = IV with Ohm's Law (V = IR), you get two additional forms that allow you to calculate power from any pair of known quantities.

P = I × V — use when you know current and voltage. Example: a kettle draws 10A on a 230V supply. P = 10 × 230 = 2,300W = 2.3kW.
P = I² × R — use when you know current and resistance. Example: 5A through a 20Ω resistor. P = 5² × 20 = 25 × 20 = 500W. This formula also shows why cable sizing matters — doubling the current quadruples the power dissipated as heat.
P = V² ÷ R — use when you know voltage and resistance. Example: 230V across a 529Ω load. P = 230² ÷ 529 = 52,900 ÷ 529 = 100W.
Transposing for current: If P and V are given: I = P ÷ V. Example: a 3kW shower on 230V draws I = 3,000 ÷ 230 ≈ 13A. This tells you the minimum circuit current rating required.

These three forms of the power formula are all you need for DC and resistive AC power calculations. The formulae also appear in design work — calculating the current demand of a circuit before selecting the correct cable and protective device.

03 · Apprentice Maths Guide

Voltage Drop Formula

Every cable has resistance. When current flows through a cable, the resistance causes a voltage drop — a reduction in voltage between the supply and the load. BS 7671 requires you to calculate voltage drop to ensure the load receives adequate voltage. The standard formula uses millivolt per ampere per metre (mV/A/m) values from BS 7671 Appendix 4.

Formula: Vd = (mV/A/m × I × L) ÷ 1000. Where: mV/A/m = the millivolt drop per ampere per metre for your cable (from BS 7671 Appendix 4 Table 4Ab or 4D2B), I = design current in amps, L = one-way cable length in metres.
Worked example: A 2.5mm² twin and earth cable (mV/A/m = 18) runs 20m to supply a 13A socket. Vd = (18 × 13 × 20) ÷ 1000 = 4,680 ÷ 1000 = 4.68V.
Maximum permitted voltage drop: BS 7671 Table 4Ab allows 3% for lighting (6.9V) and 5% for other circuits (11.5V) on a 230V supply. 4.68V = 2.03%, which is within both limits. The circuit is acceptable.
When voltage drop is too high: Select a larger cable with a lower mV/A/m value, reduce the circuit length (use a sub-distribution board closer to the load), or reduce the current demand. Recalculate until Vd is within limits.

04 · Apprentice Maths Guide

Percentage Voltage Drop

Once you have calculated the actual voltage drop in volts, you need to express it as a percentage of the nominal supply voltage to compare against the BS 7671 limits.

Formula: % Vd = (Vd ÷ Vn) × 100. Where Vd = actual voltage drop (V) and Vn = nominal supply voltage (230V for single-phase UK).
Example: Actual Vd = 8.5V on a 230V power circuit. % Vd = (8.5 ÷ 230) × 100 = 3.7%. This is within the 5% limit for power circuits but would exceed the 3% limit for a lighting circuit.
Three-phase circuits: Use the line voltage (400V) as Vn for three-phase calculations. The mV/A/m values for three-phase cables are listed separately in BS 7671 Appendix 4 tables.

Voltage drop calculation is a compulsory element of the design section of your Level 3 qualification and appears in the City & Guilds 2365 Unit 305 (Electrical Systems Design) exam. Practise with the Elec-Mate calculation tools to build speed and accuracy.

05 · Apprentice Maths Guide

Transposition of Formulae

Transposition means rearranging a formula to make a different variable the subject. In electrical work you constantly need to find a different unknown from the same relationship — for example, finding current from a power and voltage, or finding resistance from a voltage drop and current. The rules are straightforward but require practice.

Rule 1 — Do the same to both sides: To isolate a variable, perform the inverse operation on both sides. If a variable is multiplied, divide both sides. If it is divided, multiply both sides.
Example — find R from P = V²/R: Multiply both sides by R → P × R = V². Divide both sides by P → R = V² ÷ P. Example: P = 100W, V = 230V → R = 230² ÷ 100 = 52,900 ÷ 100 = 529Ω.
Example — find L from voltage drop formula: From Vd = (mV/A/m × I × L) ÷ 1000, multiply both sides by 1000 → Vd × 1000 = mV/A/m × I × L. Divide both sides by (mV/A/m × I) → L = (Vd × 1000) ÷ (mV/A/m × I).
Rule 2 — Handle square roots and squares carefully: To isolate a squared variable, take the square root of both sides. To isolate a square-rooted variable, square both sides.

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06 · Apprentice Maths Guide

Pythagoras' Theorem for AC Circuits

In AC circuits containing inductance or capacitance, resistance (R) and reactance (X) are out of phase with each other. They cannot simply be added — instead they are combined using Pythagoras' theorem because they are at 90° to each other on a phasor diagram.

Impedance formula: Z = √(R² + X²). Impedance (Z, measured in ohms) is the total opposition to current flow in an AC circuit — the AC equivalent of resistance.
Worked example: A circuit has R = 3Ω and inductive reactance XL = 4Ω. Z = √(3² + 4²) = √(9 + 16) = √25 = 5Ω. Current I = V ÷ Z = 230 ÷ 5 = 46A.
Power triangle: True power (P, watts), reactive power (Q, VAr), and apparent power (S, VA) follow the same Pythagorean relationship: S = √(P² + Q²). Power factor = P ÷ S.
When this appears in exams: Impedance calculations with Pythagoras appear in C&G 2365 Unit 204 (Electrical Installations Technology) and again in Unit 304. Recognising a 3-4-5 triangle (and its multiples: 6-8-10, 5-12-13) saves calculation time in exams.

07 · Apprentice Maths Guide

Scientific Notation and SI Prefixes

Electrical values span an enormous range — from picofarads (millionths of millionths of a farad) to megawatts (millions of watts). Scientific notation and SI prefixes let you express these values conveniently and without ambiguity.

Mega (M) = ×10⁶: 1MΩ = 1,000,000Ω. Insulation resistance is measured in megohms — a healthy insulation resistance for a new installation is typically greater than 1MΩ, and often several hundred megohms.
Kilo (k) = ×10³: 2.5kΩ = 2,500Ω; 3kW = 3,000W; 400kV = 400,000V (grid transmission voltage). Used for larger, practical values.
Milli (m) = ×10⁻³: 30mA = 0.03A — the standard RCD tripping current for protection against electric shock. 100mV = 0.1V. mV/A/m values in voltage drop tables are in millivolts.
Micro (μ) = ×10⁻⁶: 100μF = 0.0001F. Motor start capacitors are typically 4μF to 70μF. Power factor correction capacitors in commercial installations may be hundreds of μF.

Converting between units: to convert from milli to base unit, divide by 1,000. To convert from kilo to base unit, multiply by 1,000. Get comfortable doing this without a calculator — some multi-choice exam questions catch apprentices who convert the wrong way.

08 · Apprentice Maths Guide

Practical Worked Examples

The best way to consolidate electrical maths is to work through realistic examples that combine multiple calculation types, just as exam questions do. Here are three examples that represent the style of question you will encounter.

Example 1 — Cable sizing and voltage drop:
A 32A ring final circuit is wired in 2.5mm² twin and earth. The longest radial distance from the consumer unit to the furthest socket is 22m. The mV/A/m value for 2.5mm² in a ring circuit = 7.3mV/A/m (half the tabulated value because of the ring). Design current (Ib) = 20A (typical). Vd = (7.3 × 20 × 22) ÷ 1000 = 3,212 ÷ 1000 = 3.21V. % Vd = (3.21 ÷ 230) × 100 = 1.4%. Well within the 5% limit.
Example 2 — Power and current:
An immersion heater is rated 3kW at 230V. What current does it draw and what is its resistance? I = P ÷ V = 3,000 ÷ 230 = 13.04A. R = V ÷ I = 230 ÷ 13.04 = 17.64Ω (or R = V² ÷ P = 52,900 ÷ 3,000 = 17.63Ω — same answer). The circuit requires a 16A MCB and 2.5mm² cable.
Example 3 — Series circuit with voltage drops:
Three lamps of 20Ω, 30Ω, and 50Ω are connected in series across a 200V supply. Rt = 20 + 30 + 50 = 100Ω. I = V ÷ Rt = 200 ÷ 100 = 2A. Vd across 30Ω lamp = 2 × 30 = 60V. P dissipated by 50Ω lamp = I² × R = 4 × 50 = 200W.

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Frequently Asked Questions About Maths for Electrical Apprentices

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Maths for Electrical Apprentices: Essential Electrical Calculations

Key Takeaways

Ohm's Law Calculations

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Power Triangle (P = IV)

Voltage Drop Formula

Percentage Voltage Drop

Transposition of Formulae

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Pythagoras' Theorem for AC Circuits

Scientific Notation and SI Prefixes

Practical Worked Examples

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Frequently Asked Questions About Maths for Electrical Apprentices

What maths do I need as an electrical apprentice?

How do I transpose Ohm's Law to find resistance?

What is voltage drop and why does it matter?

What is power factor and do I need to understand it in Year 1?

How do I calculate percentage voltage drop?

What is Pythagoras' theorem used for in electrical work?

What scientific notation values come up most in electrical work?

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