Adiabatic Equation Calculator

The minimum csa of a cpc can be selected from the appropriate table in BS 7671. In certain circumstances the cpc csa can be calculated using the adiabatic equation for a specific circuit, this will determine the actual minimum csa of a cpc required for the specific circuit in question.

The calculation to calculate an earthing cable size (circuit protective conductor size) is the Adiabatic Equation. Earthing cable size selection charts can also be found in BS7671.

The Adiabatic Equation is the mathematical equation / formula used to calculate the minimum cpc size, if a non standard cable size is calculated then the next available larger size shall be used.

The preferred method for selecting a circuit protective conductor size is by selecting from the appropriate table in BS 7671.

The Adiabatic Equation might be used to calculate the absolute minimum size of a cpc for an existing installed cpc should that be smaller than that required of the appropriate table.

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

1. Enter a measured voltage value Uo = 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 = BS EN 60898 Type B.

4. Select a protective device rating = 10 Amps.

5. Select a conductor type = Single cable not bunched.

6. Select a conductor material = 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.

Our Adiabatic Equation Calculator works online and offline, so it is always available when you need it.

This Adiabatic Equation calculator uses the Adiabatic Equation formula from BS 7671.

The k factor for copper cables tables can be found in the wiring regulations. The actual k factor table to use depends on the cable conductor type,

• Single cable not bunched
• Incorporated in a cable or run with cables

Other Conductor Types:

• Sheath or armour of cable
• Steel conduit or trunking

Then there is the specification of the conductor material:

• Copper 70°C Thermoplastic
• Copper 90°C Thermoplastic
• Copper 90°C Thermosetting

Other Conductor Materials:

• Aluminium 70°C Thermoplastic
• Aluminium 90°C Thermoplastic
• Aluminium 90°C Thermosetting
• Steel 70°C Thermoplastic
• Steel 90°C Thermoplastic
• Steel 90°C Thermosetting
• Lead 70ºC Thermoplastic
• Lead 90ºC Thermoplastic
• Lead 90ºC Thermosetting

To calculate the cpc csa size using the Adiabatic Equation Calculator is fairly simple.

The required tables, times and k factors are already programmed and will auto calculate the values depending on your selections.

1. Input a measured voltage value
2. Input a measured Zs value
3. Select a protective device
4. Select a protective device rating
5. Select a conductor type
6. Select a conductor material
7. Tap Calculate

The Adiabatic Equation Calculator will then calculate fault current, conductor size mm, k value and disconnection time (s).