What is the adiabatic equation used for?

The adiabatic equation S = sqrt(I squared t) / k calculates the minimum cross-sectional area of a protective conductor (CPC) that can withstand fault current without overheating. It ensures the CPC can carry the fault energy until the protective device disconnects. The 'k' value depends on the conductor material and insulation type — 115 for PVC/copper and 143 for XLPE/copper.

How do I calculate three-phase power?

For balanced three-phase loads: P = sqrt(3) x VL x IL x cos(phi), where VL is line voltage (400V), IL is line current, and cos(phi) is the power factor. For resistive loads (heaters, kettles), power factor is 1.0. For motors, typical power factor is 0.8 to 0.85. For single-phase power: P = V x I x cos(phi) where V is 230V.

What is the voltage drop formula for cables?

Voltage drop = (mV/A/m x Ib x L) / 1000, where mV/A/m is the cable's millivolt drop per amp per metre (from BS 7671 tables), Ib is the design current, and L is the cable length in metres. The result must not exceed 5% (11.5V single-phase at 230V, 23V three-phase at 400V) from the origin of the installation.

How do I calculate parallel resistance?

For two resistors in parallel: Rt = (R1 x R2) / (R1 + R2) — the product-over-sum formula. For three or more: 1/Rt = 1/R1 + 1/R2 + 1/R3 + ... The result is always less than the smallest individual resistance. This applies to parallel cable runs, lamp arrays, and understanding why adding parallel loads reduces circuit impedance.

What is impedance and how does it differ from resistance?

Resistance (R) opposes DC current flow and is constant. Impedance (Z) opposes AC current flow and includes both resistance and reactance. Reactance comes from inductors (XL = 2 pi f L) and capacitors (XC = 1 / (2 pi f C)). Total impedance is Z = sqrt(R squared + X squared). In AC circuits, impedance determines current flow, not resistance alone.

How do I use correction factors for cable sizing?

The minimum tabulated current rating is It = Ib / (Ca x Cg x Ci x Cc), where Ib is design current, Ca is ambient temperature correction (from Table 4B1), Cg is grouping factor (from Table 4C1), Ci is thermal insulation factor, and Cc is the semi-enclosed fuse factor (0.725 for BS 3036 fuses, 1.0 otherwise). Select the cable from the appropriate table whose rating equals or exceeds It.

Electrical Formulas Reference

Complete formula reference — Ohm's law, AC impedance, parallel resistance, star-delta, three-phase power, cable sizing corrections, and adiabatic equation

AC impedanceStar-deltaThree-phaseAdiabatic

Ohm's Law

The fundamental relationship between voltage, current, and resistance. Every electrical calculation builds on this.

V = I x R

V: = Voltage in volts (V)
I: = Current in amps (A)
R: = Resistance in ohms (Ω)

Fundamental electrical law

Ohm's Law transpositions

Ohm's Law

To Find	Formula	Example
Voltage (V)	V = I x R	5A through 46Ω = 230V
Current (I)	I = V / R	230V across 46Ω = 5A
Resistance (R)	R = V / I	230V at 5A = 46Ω

Power Formulas

Power is the rate of energy transfer. These formulas link power to voltage, current, and resistance.

P = V x I

P: = Power in watts (W)
V: = Voltage in volts (V)
I: = Current in amps (A)

Basic power formula

P = I\u00B2 x R

P: = Power in watts (W)
I: = Current in amps (A)
R: = Resistance in ohms (Ω)

Power dissipated in a resistance

P = V\u00B2 / R

P: = Power in watts (W)
V: = Voltage in volts (V)
R: = Resistance in ohms (Ω)

Power from voltage and resistance

Power formula applications

Power triangle derivations

Formula	Best Used When
P = V x I	You know the supply voltage and measured current
P = I² x R	You know the current and conductor resistance (e.g. calculating heat loss in cables)
P = V² / R	You know the voltage across a fixed resistance (e.g. heater element rating)

AC Impedance and Reactance

In AC circuits, impedance replaces resistance as the opposition to current flow. It combines resistance and reactance.

Z = \u221A(R\u00B2 + X\u00B2)

Z: = Impedance in ohms (Ω)
R: = Resistance in ohms (Ω)
X: = Reactance in ohms (Ω) — either X_L or X_C

Impedance triangle

X_L = 2\u03C0fL

X_L: = Inductive reactance in ohms (Ω)
f: = Frequency in hertz (50Hz in UK)
L: = Inductance in henrys (H)

Inductive reactance

X_C = 1 / (2\u03C0fC)

X_C: = Capacitive reactance in ohms (Ω)
f: = Frequency in hertz (50Hz in UK)
C: = Capacitance in farads (F)

Capacitive reactance

Practical Application

In most power installation work, reactance is significant only in long cable runs (above 16mm\u00B2) and motor circuits. For cables up to 16mm\u00B2 at typical domestic run lengths, the reactive component is negligible and voltage drop tables based on resistance alone are sufficient. BS 7671 tables include separate columns for resistance and reactance components of voltage drop for larger cables.

Parallel Resistance

Resistances in parallel reduce the total resistance. This applies to parallel cable runs, lamp arrays, and understanding fault current paths.

1/R_t = 1/R_1 + 1/R_2 + 1/R_3 + ...

R_t: = Total parallel resistance in ohms (Ω)
R_1, R_2, R_3: = Individual resistances in ohms (Ω)

General parallel resistance formula

R_t = (R_1 x R_2) / (R_1 + R_2)

R_t: = Total resistance of two parallel resistors (Ω)
R_1: = First resistance (Ω)
R_2: = Second resistance (Ω)

Product-over-sum (two resistors only)

Parallel resistance examples

Ohm's Law

R1	R2	Result (R_t)	Application
1.0Ω	1.0Ω	0.5Ω	Two identical parallel cable runs — halves the resistance
10Ω	10Ω	5Ω	Two identical heating elements in parallel
100Ω	200Ω	66.7Ω	Unequal parallel loads — result is less than smaller value
0.8Ω	0.2Ω	0.16Ω	Earth fault paths — parallel paths reduce Zs

Star-Delta Transformation

Star-delta (Y-\u0394) conversion formulas are used in three-phase circuit analysis and motor starting calculations.

Delta to Star conversion

Network analysis — delta to star

Star Resistance	Formula	Description
R_a	R_a = (R_ab x R_ca) / (R_ab + R_bc + R_ca)	Star resistance at node A from adjacent delta resistances
R_b	R_b = (R_ab x R_bc) / (R_ab + R_bc + R_ca)	Star resistance at node B from adjacent delta resistances
R_c	R_c = (R_bc x R_ca) / (R_ab + R_bc + R_ca)	Star resistance at node C from adjacent delta resistances

Star to Delta conversion

Network analysis — star to delta

Delta Resistance	Formula	Description
R_ab	R_ab = R_a + R_b + (R_a x R_b) / R_c	Delta resistance between nodes A and B
R_bc	R_bc = R_b + R_c + (R_b x R_c) / R_a	Delta resistance between nodes B and C
R_ca	R_ca = R_c + R_a + (R_c x R_a) / R_b	Delta resistance between nodes C and A

When You Need This

Star-delta conversion is primarily used in three-phase motor starting calculations and complex network analysis. For a balanced load where all three resistances are equal (R), the conversion simplifies to: R_star = R_delta / 3 and R_delta = 3 x R_star.

Three-Phase Power

Three-phase power calculations for balanced star and delta connected loads.

P = \u221A3 x V_L x I_L x cos\u03C6

P: = Total three-phase active power in watts (W)
V_L: = Line voltage (400V in UK)
I_L: = Line current in amps (A)
cosφ: = Power factor (1.0 for resistive, 0.8-0.85 for motors)

Three-phase power formula

Star and delta voltage/current relationships

BS 7671 and IET Guidance

Configuration	Voltage Relationship	Current Relationship	Common Use
Star (Y)	V_L = √3 x V_P (400V line = 230V phase)	I_L = I_P (line current equals phase current)	Distribution systems, motor starting (reduced voltage)
Delta (Δ)	V_L = V_P (line voltage equals phase voltage)	I_L = √3 x I_P (line current = 1.732 x phase current)	Motor running, heating elements, balanced industrial loads

Neutral Current in Three-Phase

In a perfectly balanced three-phase star system, the neutral current is zero. In practice, single-phase loads create imbalance and the neutral carries the out-of-balance current. In systems with significant non-linear loads (LED drivers, switch-mode power supplies), third harmonic currents add in the neutral rather than cancelling. The neutral current can exceed the line current — size the neutral conductor accordingly.

Cable Sizing with Correction Factors

The fundamental cable sizing formula accounts for all derating factors that reduce a cable's current-carrying capacity.

I_t \u2265 I_b / (C_a x C_g x C_i x C_c)

I_t: = Minimum tabulated current rating from BS 7671 tables (A)
I_b: = Design current of the circuit (A)
C_a: = Ambient temperature correction factor (Table 4B1)
C_g: = Grouping correction factor (Table 4C1)
C_i: = Thermal insulation correction factor (Table 52.2)
C_c: = Semi-enclosed fuse factor (0.725 for BS 3036, otherwise 1.0)

BS 7671 Appendix 4

Common ambient temperature correction factors (Table 4B1)

BS 7671 Table 4B1

Ambient Temp	PVC (70°C)	XLPE (90°C)
25°C	1.03	1.02
30°C (reference)	1.00	1.00
35°C	0.94	0.96
40°C	0.87	0.91
45°C	0.79	0.87
50°C	0.71	0.82

Values shown for conductors rated at 70 degrees C (PVC) and 90 degrees C (XLPE/SWA).

Cumulative Derating

Correction factors are multiplied together, so their cumulative effect can be severe. A cable at 35 degrees ambient (Ca=0.94) in a group of 4 (Cg=0.65) with a BS 3036 fuse (Cc=0.725) has a combined factor of 0.94 x 0.65 x 0.725 = 0.443. The cable must have a tabulated rating of more than double the design current. Always calculate the combined factor before selecting a cable size.

Voltage Drop

Voltage drop must be calculated for every circuit to ensure equipment receives adequate supply voltage.

V_d = (mV/A/m x I_b x L) / 1000

V_d: = Voltage drop in volts
mV/A/m: = Millivolt drop per amp per metre from BS 7671 tables
I_b: = Design current in amps (A)
L: = Cable length in metres (one-way)

BS 7671 Tables 4D1B to 4J4B

Maximum permitted voltage drop

BS 7671 Appendix 12

Supply	Maximum VD (5%)	Notes
Single-phase 230V	11.5V	From origin to furthest point of utilisation
Three-phase 400V	20V	Line-to-line voltage drop limit
Lighting circuits	3% (6.9V at 230V)	Recommended limit for lighting to prevent visible flicker

The 5% limit can be split between sub-main and final circuit as the designer sees fit.

Adiabatic Equation

The adiabatic equation determines the minimum protective conductor size to withstand fault current.

S = \u221A(I\u00B2t) / k

S: = Minimum CPC cross-sectional area in mm²
I: = Fault current in amps (A)
t: = Disconnection time of protective device in seconds
k: = Material factor from Table 54.4

BS 7671 Regulation 543.1, Table 54.4

k-values for protective conductors (Table 54.4)

BS 7671 Table 54.4

Conductor Material	Insulation Type	k Value
Copper	PVC (70°C)	115
Copper	XLPE (90°C)	143
Copper	Bare (exposed to touch)	159
Copper	Bare (not exposed to touch)	200
Aluminium	PVC (70°C)	76
Aluminium	XLPE (90°C)	94
Steel	PVC (70°C)	51

Using the Adiabatic Equation

The adiabatic equation assumes that all fault energy is absorbed by the conductor without any heat dissipation — a worst-case assumption valid for short disconnection times (under 5 seconds). For longer disconnection times, the assumption is less conservative. Calculate I from Uo/Zs (prospective earth fault current) and t from the protective device time-current characteristic at that fault level. If the calculated S exceeds the installed CPC size, you must increase the CPC or change the protective device.

Frequently Asked Questions

Related Calculators

Ohm's Law

Calculate voltage, current, resistance or power

Cable Size

Calculate the correct cable size for any circuit

Voltage Drop

Check voltage drop against BS 7671 limits

Three Phase Balance

Balance loads across three phases