f(x)

Key Formulas

Essential electrical formulas for BS 7671 design and verification calculations.

Ohm's Law & Power

Ohm's Law

V = I × R

V Voltage (Volts)

I Current (Amperes)

R Resistance (Ohms (Ω))

Variations

Current: I = V ÷ R

Resistance: R = V ÷ I

Power (Single Phase)

P = V × I × cosφ

P Power (Watts)

V Voltage (Volts)

I Current (Amperes)

cosφ Power factor

Variations

Resistive: P = I²R

Voltage form: P = V²/R

Power (Three Phase)

P = √3 × Vₗ × Iₗ × cosφ

Vₗ Line voltage (400V)

Iₗ Line current (A)

cosφ Power factor

Design & Sizing

Design Current

Ib = P / (V × cosφ)

Ib Design current (Amperes)

P Power (Watts)

V Voltage (Volts)

cosφ Power factor

Variations

Three Phase: Ib = P / (√3 × Vₗ × cosφ)

Single phase formula

Cable Sizing (Required It)

It = In / (Ca × Cg × Ci × Cc)

It Required tabulated current rating (Amperes)

In Rating of protective device (A)

Ca Ambient temperature correction factor

Cg Grouping correction factor

Ci Thermal insulation correction factor

Cc Semi-enclosed fuse correction factor

BS 7671: Reg 433

Voltage Drop

VD = (mV/A/m × Ib × L) / 1000

VD Voltage drop (Volts)

mV/A/m Table value for cable type/size (mV/A/m)

Ib Design current (Amperes)

L Cable length (metres)

BS 7671: Appendix 12

Protection

Earth Fault Loop

If = U₀ / Zs

U₀ Nominal voltage to earth (230V)

Zs Earth fault loop impedance (Ω)

For disconnection within required time, Zs must be ≤ max values in Table 41.2–41.4

BS 7671: Reg 411.4.5

Adiabatic Equation

S = √(I²t) / k

S Minimum conductor cross-sectional area (mm²)

I Fault current (Amperes)

t Disconnection time (seconds)

k Factor from Tables 54.2–54.6

BS 7671: Reg 543.1.3

Prospective Fault Current

Ipf = U₀ / Ze

Ipf Prospective fault current (Amperes)

U₀ Nominal voltage to earth (230V)

Ze External earth fault loop impedance (Ω)

Variations

At any point: Ipf = U₀ / Zs

At origin of installation

BS 7671: Reg 434.5.1

Zs Values

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