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Adiabatic Equation Calculator


Easily calculate cpc sizes and sizing of earthing conductors

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Adiabatic Calculator



The Adiabatic Equation Calculator is for calculating the absolute minimum permitted circuit protective conductor size, or for verifying an existing protective conductor is adequately sized.


The current edition (at time of writing) of BS 7671 states:
The cross-sectional area of each protective conductor, other than a protective bonding conductor, shall be:

  1. (i) Calculated in accordance with regulation 543.1.3 or
  2. (ii) Selected in accordance with regulation 543.1.4

This Adiabatic Equation Calculator App is designed to assist in satisfying option (i) above.

- Calculating the Adiabatic Equation need not be daunting, get the app!


  • Conductor mm²
  • la = Fault current
  • I² = Fault current²
  • k = Conductor k value
  • t = Disconnection time

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Adiabatic Equation Formula

Adiabatic Calculator


The Adiabatic Equation Calculator couldn’t be any easier to use, just enter your voltage and Zs values, then select your choice from the following drop down options.


  1. Protective Device
  2. Protective Device Rating
  3. Protective Conductor Type
  4. Protective Conductor Material

Then tap the “Calculate” button to get the results, it is that simple!

Protective Device


We have pre-programmed in the operating time / current characteristics for the protective device circuit breakers, fuses and RCBO’s so you don’t need to look them up.

Protective Devices:

  • MCB’s
  • RCBO’s
  • Fuses

Device Ratings:

  • Depends on selected protective device

Protective Conductor


Select your choice of protective conductor type, then conductor material. The options available for protective conductor material depends on the selected conductor type.

Types of Protective Conductors:

  • Single cable not bunched
  • Incorporated in a cable or bunched with cables
  • Sheath or armour of cable
  • Steel conduit or trunking

Protective Conductor Material:

  • Copper
  • Aluminium
  • Steel
  • Lead

Protective Conductor k Values:

Conductor k values have already been set, your protective conductor type and conductor material selections will automatically set the values of k for you.

Adiabatic Calculation


Once you have completed the quick steps mentioned above, tap the calculate button to get the results.

In addition to calculating the protective conductor size the Adiabatic Equation calculator also displays all the other relevant calculation results associated with the final calculation of the earth / earthing conductor / protective conductor size.

Adiabatic Equation Calculation Results

Resulting Parameters:

  • Conductor size mm²
  • la
  • k
  • t
Adiabatic Equation Formula
Adiabatic Equation Results.

Tablets and Phones


Adiabatic Equation Calculator is optimised to work on all screen sizes and resolutions from the iPhone 5 up to large tablets such as the iPad Pro and all Android devices.


  • Easy to use
  • Preset data
  • Quick and instant results
  • Dedicated support team
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What is the minimum size of a circuit protective conductor (cpc)

The minimum size of a cpc can be selected from the appropriate table in BS 7671 or it can be calculated using the Adiabatic Equation, the later method will determine the minimum csa size (cross section area) of a cpc required, if the calculated minimum size of protective conductor does not exist, then the next larger size up shall be selected.

Maximum Operating Time Current Characteristic Tables

The maximum operating time current tables cable found in the following tables of BS 7671,

  • Fig 3A2 (a,b) – BS 3036 Semi-enclosed Fuse
  • Fig 3A3 (a,b) – BS 88-2.2
  • Fig 3A4 – BS EN 60898 / 61009-1 MCB/RCBO Type B
  • Fig 3A5 – BS EN 60898 / 61009-1 MCB/RCBO Type C
  • Fig 3A6 – BS EN 60898 / 61009-1 MCB/RCBO Type D
  • BS 1361 Fuse

The relevant fault current time curve values have been pre-set in the Adiabatic Equation App and are automatically applied to the Adiabatic calculation.

For cable limiting temperatures see Protection Against Exceeding Cable Limiting Temperatures

Conductor k Values

Conductor values of k can be found in the following tables of BS 7671,

  • Table 54.2 – Conductor not incorporated in a cable and not bunched with cables.
  • Table 54.3 – Conductor incorporated in a cable or bunched with cables.
  • Table 54.4 – Sheath or armour of a cable.
  • Table 54.5 – Steel conduit or trunking

The relevant conductor k values have been pre-set in the Adiabatic Equation App and are automatically applied to the Adiabatic calculation.

Adiabatic Calculation Example

Here we demonstrate an adiabatic equation calculation example, we will explain how the adiabatic equation calculator works.

1. Enter a measured voltage value Uo i.e. 230V.
The voltage value needs to be a measured value in-order to carry out an accurate calculation, Uo is the voltage to earth.

2. Enter a measured Zs value = 0.26 Ohms.
The Zs value needs to be a measured value in-order to carry out an accurate calculation, Zs is the earth (fault) loop impedance.

3. Select a protective device type i.e. BS EN 60898 Type B.
4. Select a protective device rating i.e. 10 Amps.
5. Select a conductor type i.e. Single cable not bunched.
6. Select a conductor material i.e Copper – 70°C Thermoplastic.

Adiabatic Calculation Results:

la (PEFC) = 884.62
I² = 782552.54
k = 143
t (s) = 0.1
Conductor csa = 1.956 mm²

As 1.956 mm is not a standard cable size the next available larger cable size shall be used.

la is the prospective earth fault current, I² is the fault current squared, k is the conductor k value, t is the disconnection time in seconds and conductor csa is the cpc earthing conductor size in millimetres.

The Adiabatic Equation

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