Revision Volt

Electrical Formulas

A clear formula guide for electrical revision. Each formula shows what the symbols mean, when to use it and a quick worked example so learners understand the method instead of just memorising it.

key formulas

resistance, Zs and PFC

voltage drop made simple

BS 7671

useful for exam revision

Formula 01

Power Triangle

⚡

Formula

P = V × I | S² = P² + Q² | pf = P ÷ S

What the values mean

P = real power in watts (W) or kilowatts (kW)
V = voltage in volts (V)
I = current in amps (A)
S = apparent power in volt-amperes (VA) or kilovolt-amperes (kVA)
Q = reactive power in VAr or kVAr
pf = power factor

Used for

Used when calculating real power, apparent power, reactive power or power factor.

Quick example

A 230 V load draws 10 A. P = 230 × 10 = 2300 W, or 2.3 kW.

Revision tip

Remember: watts are the useful power doing the work.

Formula 02

Ohm’s Law Triangle

🔺

Formula

V = I × R | I = V ÷ R | R = V ÷ I

What the values mean

V = voltage in volts (V)
I = current in amps (A)
R = resistance in ohms (Ω)

Used for

Used to calculate voltage, current or resistance when two values are known.

Quick example

A 230 V load has a resistance of 46 Ω. I = 230 ÷ 46 = 5 A.

Revision tip

Cover the value you want in the triangle to see the formula.

Formula 03

Voltage Drop Formula

📉

Formula

Vd = (mV/A/m × Ib × L) ÷ 1000

What the values mean

Vd = voltage drop in volts (V)
mV/A/m = voltage drop value from cable tables
Ib = design current in amps (A)
L = route length of the circuit in metres (m)
1000 = converts millivolts to volts

Used for

Used to calculate how much voltage is lost along a cable run.

Quick example

A 40 A circuit is 25 m long with a cable factor of 11 mV/A/m. Vd = 11 × 40 × 25 ÷ 1000 = 11 V.

Revision tip

Longer cable, higher current or higher mV/A/m all increase voltage drop.

Formula 04

Voltage Drop Percentage

✅

Formula

%Vd = (Vd ÷ Vsupply) × 100

What the values mean

%Vd = voltage drop as a percentage
Vd = calculated voltage drop in volts (V)
Vsupply = nominal supply voltage, usually 230 V or 400 V

Used for

Used to check whether the voltage drop is within the permitted percentage.

Quick example

A 9.8 V drop on a 230 V circuit gives 9.8 ÷ 230 × 100 = 4.26%.

Revision tip

Lighting circuits usually have a lower permitted voltage drop than other final circuits.

Formula 05

PFC / PEFC / PSCC

💥

Formula

Ipf = V ÷ Z

What the values mean

Ipf = prospective fault current in amps (A) or kiloamps (kA)
V = voltage in volts (V)
Z = impedance in ohms (Ω)
PEFC = prospective earth fault current
PSCC = prospective short-circuit current
PFC = highest value between PEFC and PSCC

Used for

Used to check the maximum fault current that could flow and whether protective devices have enough breaking capacity.

Quick example

230 V with Ze of 0.18 Ω gives Ipf = 230 ÷ 0.18 = 1277.7 A, or 1.28 kA.

Revision tip

Record the highest measured value between PEFC and PSCC.

Formula 06

Zs Formula

🧲

Formula

Zs = Ze + (R1 + R2)

What the values mean

Zs = total earth fault loop impedance in ohms (Ω)
Ze = external earth fault loop impedance in ohms (Ω)
R1 = resistance of the line conductor
R2 = resistance of the circuit protective conductor (CPC)
R1 + R2 = resistance of the circuit line and CPC path

Used for

Used to calculate or verify earth fault loop impedance for a final circuit.

Quick example

Ze = 0.28 Ω and R1 + R2 = 0.37 Ω. Zs = 0.28 + 0.37 = 0.65 Ω.

Revision tip

Zs must be low enough to allow the protective device to disconnect in time.

Formula 07

Ib Design Current

🧠

Formula

Ib = P ÷ V

What the values mean

Ib = design current in amps (A)
P = power of the load in watts (W)
V = supply voltage in volts (V)

Used for

Used to calculate the current a circuit is expected to carry before selecting protective devices and cables.

Quick example

A 9.2 kW cooker on 230 V gives Ib = 9200 ÷ 230 = 40 A.

Revision tip

Convert kW to W before calculating. 9.2 kW = 9200 W.

Formula 08

Energy kWh Formula

Formula

Energy (kWh) = Power (kW) × Time (h)

What the values mean

Energy = electricity used in kilowatt-hours (kWh)
Power = load power in kilowatts (kW)
Time = running time in hours (h)
Cost = kWh × tariff

Used for

Used to work out energy use and running cost of electrical appliances.

Quick example

A 2 kW heater runs for 3.5 h. Energy = 2 × 3.5 = 7 kWh. At £0.28/kWh, cost = £1.96.

Revision tip

Minutes must be converted into hours before using the formula.

Formula 09

Three-Phase Current Formula

🔌

Formula

I = P ÷ (√3 × VL × pf)

What the values mean

I = line current in amps (A)
P = three-phase power in watts (W)
√3 = 1.732
VL = line voltage, usually 400 V
pf = power factor

Used for

Used to calculate the line current of a balanced three-phase load.

Quick example

An 18 kW motor at 400 V and pf 0.86 gives I = 18000 ÷ (1.732 × 400 × 0.86) = 30.2 A.

Revision tip

Use 400 V for UK three-phase line voltage unless the question states otherwise.

Formula 10

Correction Factor Formula

🧮

Formula

It = In ÷ (Ca × Cg × Ci × ...)

What the values mean

It = required tabulated current-carrying capacity of the cable
In = rating of the protective device in amps (A)
Ca = ambient temperature correction factor
Cg = grouping correction factor
Ci = thermal insulation correction factor
Other factors may apply depending on the installation method

Used for

Used when choosing a cable size after correction factors have reduced its current-carrying capacity.

Quick example

A 32 A device with Ca 0.87 and Cg 0.80 gives It = 32 ÷ (0.87 × 0.80) = 46 A.

Revision tip

Correction factors usually mean you need a larger cable, not a smaller one.

Formula 11

Ring Final R1 + R2

🔁

Formula

R1 + R2 ≈ (r1 + r2) ÷ 4

What the values mean

R1 + R2 = expected resistance at socket outlets
r1 = end-to-end resistance of the line conductor
r2 = end-to-end resistance of the CPC
÷ 4 = approximate relationship used for a ring final circuit

Used for

Used during continuity testing of ring final circuits to estimate the expected R1 + R2 value.

Quick example

If r1 = 0.64 Ω and r2 = 1.04 Ω, R1 + R2 ≈ (0.64 + 1.04) ÷ 4 = 0.42 Ω.

Revision tip

This is for ring final circuits, not normal radial circuits.

Formula 12

Adiabatic Equation

🟩

Formula

S = √(I² × t) ÷ k

What the values mean

S = minimum protective conductor size in mm²
I = fault current in amps (A)
t = disconnection time in seconds (s)
k = factor based on conductor material, insulation and temperature limits

Used for

Used to check whether a CPC is large enough to withstand fault current until the protective device disconnects.

Quick example

I = 1000 A, t = 0.1 s and k = 115. S = √(1000² × 0.1) ÷ 115 = 2.75 mm².

Revision tip

Higher fault current or longer disconnection time increases the required CPC size.