Adiabatic Equation Calculator | BS 7671 CPC Sizing (UK)

What is the adiabatic equation in BS 7671?

The adiabatic equation is a fundamental calculation method specified in BS 7671 (UK Wiring Regulations) for determining the minimum cross-sectional area of circuit protective conductors (CPC) and earthing conductors. This electrical adiabatic equation ensures that protective conductors can safely withstand fault currents without thermal damage during the brief period before the protective device operates.

The adiabatic equation for CPC sizing is expressed as:

s = √(I² × t) / k

Where:

• s = minimum cross-sectional area of protective conductor in mm²
• I = fault current in Amps (prospective earth fault current)
• t = disconnection time in seconds (operating time of protective device)
• k = material and insulation factor from BS 7671 tables

This calculation is covered under Regulation 543.1.3 in BS 7671 Chapter 54 (Earthing arrangements and protective conductors). It provides a precise method for earthing conductor size BS 7671 compliance, particularly important where high fault currents or extended disconnection times are present.

How to use this adiabatic equation calculator

Basic Mode (Regulation 543.1.3 - Adiabatic Equation):

1. Enter fault current (I): Input the prospective earth fault current in Amps. This value is typically determined from earth fault loop impedance (Zs or Ze) calculations.
2. Enter disconnection time (t): Input the maximum disconnection time in seconds as required by BS 7671 for your circuit type (e.g., 0.4s for socket outlets, 5s for distribution circuits).
3. Select conductor material and insulation: Choose the appropriate combination from the dropdown menu. The calculator will automatically populate the correct k factor from BS 7671 tables.
4. Optional - Custom k factor: If you need to use a specific k value not listed, check the "Use custom k factor" box and enter your value.
5. Click Calculate: The calculator will compute the minimum CPC size in mm² and recommend the next standard conductor size.

Checking an Existing Conductor:

To verify if an existing protective conductor meets the adiabatic equation requirements:

1. Complete the basic inputs above to establish your fault current and disconnection time.
2. In the "Check Existing Protective Conductor" section, enter the size of your existing CPC.
3. Select the material and insulation type of the existing conductor.
4. Click Calculate to see a clear PASS or FAIL result with detailed I²t comparison.

Common Sizes Table:

After calculation, the tool displays a comprehensive table showing standard conductor sizes from 1.0 mm² to 300 mm². Each size shows its maximum I²t capacity and whether it passes or fails for your specific fault conditions. The smallest passing size is highlighted as the recommended option.

Using Regulation 543.1.4 Mode:

Select the "543.1.4 - Based on Line Conductor" option to determine CPC size based on the relationship to the line conductor size. This method is simpler but may result in larger conductors than the adiabatic method.

Typical k factors for copper and aluminium conductors

The k factor (sometimes called the k factor cable value) is a coefficient that accounts for the resistivity, temperature coefficient, and heat capacity of the conductor material and its insulation. These values are specified in BS 7671 Tables 54.2 to 54.6.

The k factor depends on:

• Conductor material (copper or aluminium)
• Insulation type and temperature rating
• Initial and final temperatures

Common k values (typical examples):

Higher k values indicate better thermal performance, resulting in smaller required conductor sizes for a given fault current and disconnection time. This is why copper conductors (with higher k values) generally allow smaller protective conductor sizes compared to aluminium for the same fault conditions.

Understanding I²t calculation and fault current

The I²t calculation (I squared t) is a measure of thermal energy let-through during a fault condition. It represents the heating effect of fault current over time and is fundamental to protective conductor sizing.

I²t = I² × t (expressed in A²s)

Where the fault current (I) comes from your prospective fault current calculation, which depends on:

• Zs (earth fault loop impedance) for final circuits
• Ze (external earth fault loop impedance) for main earthing conductors
• Supply voltage (typically 230V for single-phase, 400V for three-phase circuits)

The disconnection time (t) must comply with BS 7671 requirements:

• 0.4 seconds for final circuits supplying socket outlets and mobile equipment
• 5 seconds for distribution circuits and fixed equipment
• Refer to protective device time-current characteristics for actual operating times

This free adiabatic calculator for electricians automatically performs the I²t calculation and compares it against the thermal capacity of different conductor sizes, helping you select the minimum CPC size in mm² that satisfies both thermal and regulatory requirements.

Limitations and professional responsibilities

This circuit protective conductor calculator is provided as an educational and design aid tool. While it implements the BS 7671 adiabatic equation accurately, users must understand the following limitations and responsibilities:

Professional responsibility: Electrical installation design and verification must be carried out by qualified and competent persons. This electrician calculator UK tool should be used alongside:

• Complete fault level and Zs calculations
• Protective device coordination studies
• Manufacturer's cable data and installation methods
• BS 7671 requirements for earthing systems (TN-S, TN-C-S, TT, IT)
• Assessment of mechanical protection requirements