BS 7671 Adiabatic Calculator
Determine the minimum protective conductor size (CPC) using the BS 7671 adiabatic equation. Calculate required CSA based on prospective fault current, disconnection time, and conductor material constants.
BS 7671 Adiabatic Calculator
How to Use BS 7671 Adiabatic Calculator
Verifying protective conductor sizing is key to electrical safety under standard UK wiring regulations. Follow these steps to calculate the required protective conductor cross-sectional area (CSA) for your circuit:
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1Enter prospective fault current. Input the maximum prospective fault current (I) in Amps at the relevant point in the installation.
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2Enter protective device disconnection time. Input the operating time (t) of the protective device (fuse or circuit breaker) in seconds.
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3Select conductor material insulation type. Select the conductor material (Copper, Aluminium, or Steel) and its insulation standard (PVC, XLPE, or EPR) to apply the correct k constant.
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4Choose optional safety margin. Apply an optional safety margin (0% to 20%) to account for potential variations in ambient parameters or fault parameters.
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5Click calculate. The engine computes the minimum required protective size and matches it to standard UK cable sizes.
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6Review calculated minimum conductor size and recommended standard cable size. Check the recommended standard size to complete the design phase.
Practical UK Installation Example
Consider a sub-main circuit supplying a distribution board in a UK commercial facility. The prospective fault current at the board is measured at 3,200 A, and the circuit breaker is rated to trip in 0.1 seconds. The protective conductor (CPC) is copper with thermoplastic PVC insulation (k = 115). Applying a 10% safety margin yields a minimum required CSA of 9.68 mm². This leads to selecting a standard commercial protective cable size of 10 mm², ensuring full thermal protection during faults without excessive material expenditure.
How to Calculate BS 7671 Adiabatic Calculator
The calculation of protective conductor size utilizes the standard adiabatic equation, assuming zero heat dissipation from the conductor to its surroundings during the very short duration of an electrical fault (less than 5 seconds). This calculation guarantees compliance with standard BS 7671 and IEC 60364 guidelines.
The Adiabatic Equation Formula
The standard formula for calculating the minimum cross-sectional area is defined as:
Where:
- S = minimum conductor cross-sectional area (mm²)
- I = prospective fault current (A)
- t = disconnection time of the protective device (s)
- k = conductor material constant (e.g., 115 for Copper PVC, 143 for Copper XLPE, 76 for Aluminium PVC, 50 for Steel)
Worked Engineering Example
Suppose you need to size the protective conductor with the following design parameters:
- Prospective Fault Current (I): 5000 A
- Disconnection Time (t): 0.4 s (standard for socket outlets under BS 7671)
- Conductor material: Copper PVC (constant k = 115)
Step 1 — Calculate the Square Root of Disconnection Time
Step 2 — Multiply by Fault Current
Step 3 — Divide by Conductor Material Constant (k)
Result and Cable Selection
The calculated minimum conductor size is 27.5 mm². Under standard commercial practices in the UK, conductors are manufactured in specific standard sizes. Since a conductor of exactly 27.5 mm² is not commercially available, you must round the result upward to select the next higher standard cable size, which is 35 mm².
Standard Selection and Regulations
According to BS 7671 Regulation 543.1.3 and IEC 60364 principles, using the adiabatic equation allows installers to select smaller protective conductors than the standard selection tables (such as Table 54.7) would suggest, provided the calculated value is met. This reduces raw material costs while maintaining full safety compliance. Note that this must be evaluated alongside loop impedance checks using our BS 7671 Earth Fault Loop Impedance Calculator to ensure the protective device actually trips within the specified time, and verified against overall voltage drops using the BS 7671 Voltage Drop Calculator.
BS 7671 Adiabatic Calculator Chart
This reference table details minimum calculated conductor sizes and recommended standard cable sizes based on a disconnection time of 0.4 seconds for standard copper PVC cables under BS 7671. Sizing checks can be compared against these figures when planning circuit designs.
| Fault Current (I) (A) | Disconnection Time (t) (s) | Material | k Factor | Calculated Size (mm²) | Recommended Cable Size (mm²) |
|---|---|---|---|---|---|
| 2,000 A | 0.4 s | Copper PVC | 115 | 11.00 mm² | 16 mm² |
| 3,000 A | 0.4 s | Copper PVC | 115 | 16.50 mm² | 25 mm² |
| 5,000 A | 0.4 s | Copper PVC | 115 | 27.50 mm² | 35 mm² |
| 7,000 A | 0.4 s | Copper PVC | 115 | 38.50 mm² | 50 mm² |
| 10,000 A | 0.4 s | Copper PVC | 115 | 55.00 mm² | 70 mm² |
| 15,000 A | 0.4 s | Copper PVC | 115 | 82.49 mm² | 95 mm² |
Note: Values are illustrative examples based on the BS 7671 adiabatic equation and should be verified against actual installation conditions and prospective device curves.
BS 7671 Adiabatic Calculator Frequently Asked Questions
The adiabatic equation in BS 7671 (Regulation 543.1.3) is S = √(I² × t) ÷ k. It determines the minimum cross-sectional area (S) of a protective conductor required to withstand thermal stress during a fault, assuming zero heat loss to the surroundings during rapid disconnection.
The k factor is a constant representing the material properties of the conductor and its insulation. It is determined by the material's resistivity, temperature coefficient of resistance, thermal capacity, and the initial and final limits of temperature, specified in BS 7671 Chapter 54 tables.
The adiabatic equation can be used when the disconnection time is less than 5 seconds. It applies to fault currents of short duration where heat dissipation from the conductor is negligible. It must not be used for sustained overload conditions or where disconnection exceeds 5 seconds.
The Circuit Protective Conductor (CPC) size can be calculated using the adiabatic equation S = I × √t ÷ k, where I is the prospective fault current, t is the operating time of the protective device, and k is the constant. Alternatively, selection can be made using the standard table method in BS 7671.
Under BS 7671, the minimum size for a protective conductor depends on installation conditions. For copper CPCs incorporated in a cable or tract, it can be 1.5 mm². For separate earthing conductors, the absolute minimum is 2.5 mm² if mechanically protected, and 4.0 mm² if not protected.
No, the adiabatic equation is not used to size main protective bonding conductors. Bonding conductors are sized based on the cross-sectional area of the main protective earthing conductor and the incoming neutral conductor, in accordance with BS 7671 Regulations 544.1 and 544.2.
Fault energy is represented by the term I²t (amperes squared seconds), which measures the thermal energy let-through of a protective device during a short circuit. The cable must have a thermal withstand capacity (represented by k²S²) greater than or equal to this let-through energy to prevent damage.
Yes, BS 7671 allows downsizing the protective conductor (CPC) compared to the line conductor, provided the calculated minimum size from the adiabatic equation is met. This often allows installers to use smaller CPCs than those selected via the standard selection table, saving cost.