BS 7671 Adiabatic Equation Calculator

This professional-grade calculator helps UK electricians, designers, and inspectors apply the BS 7671 adiabatic equation to protective conductors. Instantly compute the minimum CPC size, the maximum disconnection time, or the permissible fault current, complete with clear pass/fail feedback and a rounded recommendation to standard sizes.

The adiabatic equation verifies that a protective conductor can thermally withstand the energy let-through during an earth fault. This tool supports multiple calculation modes and standard conductor size suggestions to accelerate compliant designs under UK BS 7671.

Authoritative Data Source and Methodology

Primary reference: BS 7671:2018+A2:2022 — Requirements for Electrical Installations (IET Wiring Regulations), Regulation 543.1.3 and Appendix 4, Table 54.3 (k-values). Official overview: IET — BS 7671.

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The calculator uses I²t = k²S² to solve for the requested variable. k-values are preloaded from Table 54.3 and may be overridden with manufacturer data. Results are rounded up to the next standard size for practical selection, and a pass/fail flag indicates compliance with the adiabatic criterion.

The Formula Explained

$$ I^2 \cdot t = k^2 \cdot S^2 $$
Solving for S: $$ S = \frac{I \cdot \sqrt{t}}{k} $$ Solving for t: $$ t = \left(\frac{k \cdot S}{I}\right)^2 $$ Solving for I: $$ I = \frac{k \cdot S}{\sqrt{t}} $$

Where S is in mm², I in A, t in seconds, and k is unitless as per BS 7671 Table 54.3.

Glossary of Variables

  • S (mm²): Cross-sectional area of the protective conductor (CPC) being sized or verified.
  • I (A): Fault current flowing for time t through the protective device and conductor.
  • t (s): Disconnection time at current I from the protective device’s actual time-current performance.
  • k (—): Thermal withstand constant from BS 7671 Table 54.3 (depends on material and insulation).
  • Rounded recommendation: Next standard size at or above the calculated S for practical selection.
  • Pass/Fail: Indicates whether the provided CPC size satisfies I²t ≤ k²S².

How It Works: A Step-by-Step Example

  1. Choose Copper (PVC) so k = 115 (from Table 54.3).
  2. Assume fault current I = 3000 A and disconnection time t = 0.4 s.
  3. Apply S = I·√t / k. Compute: √0.4 ≈ 0.6325; 3000 × 0.6325 ≈ 1897.5; 1897.5 / 115 ≈ 16.5 mm².
  4. Round up to the next standard size. Recommendation: 25 mm² copper CPC.
  5. Adiabatic criterion satisfied if the installed size ≥ 16.5 mm² (rounded selection ≥ 25 mm² passes).

Frequently Asked Questions (FAQ)

What is the adiabatic equation used for?

To ensure a protective conductor can thermally withstand an earth fault until the protective device disconnects, preventing insulation damage.

Which k-value should I select?

Use Table 54.3 in BS 7671 based on material and insulation. Common values: Copper PVC 115, Copper XLPE/EPR 143, Aluminium PVC 76, Aluminium XLPE/EPR 94.

Does this check replace disconnection-time requirements?

No. You must also verify fault loop impedance and disconnection times per Chapter 41 and device data.

Why does the tool round up the size?

Conductors are manufactured in standard sizes. Rounding up provides a realistic, compliant selection.

Can I enter k from a manufacturer?

Yes. Use the custom k override if validated manufacturer data differs from Table 54.3.

What if my fault current is given in kA?

Select kA in the unit dropdown; the calculator converts internally to amperes.

Is this applicable to PEN conductors or bonding?

Applicability depends on context and BS 7671 sections. Consult the regulations and guidance notes for specific cases.

Strumento sviluppato da Ugo Candido.
Contenuti verificati da Intrelec Technical Review Board.
Ultima revisione per l'accuratezza in data: .