BS 7671 Earth Fault Loop Impedance (Zs) Calculator

Professional BS 7671 Zs Calculator for UK electricians. Compute Earth Fault Loop Impedance (Zs), maximum permissible Zs, and fault current per IET Wiring Regulations (BS 7671:2018+A2:2022). Fully accessible, mobile-first, and optimized for speed.

BS 7671 Earth Fault Loop Impedance (Zs) Calculator

This professional-grade calculator helps UK electricians and engineers verify earth fault loop impedance (Zs), estimate fault current, and check compliance against maximum Zs derived from protective device characteristics under BS 7671:2018+A2:2022. It is optimized for mobile use, fully accessible, and designed for high accuracy and speed.

Data Source and Methodology

Authoritative reference: IET Wiring Regulations — BS 7671:2018+A2:2022, including Section 41 (Protection against electric shock), Tables 41.3–41.6, and Appendix 3 (Time–current characteristics). Official publisher: The IET and BSI. See: IET BS 7671 and BSI publications.

All calculations follow standard BS 7671 design assumptions: fault current estimated from nominal voltage reduced by Cmin, loop impedance obtained from Ze and R1+R2 with temperature correction, and device instantaneous multiples for conservative checks where manufacturer curves or tabulated values are not consulted.

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

The Formulas Explained

Loop impedance from components and temperature:

$$ Z_s \;=\; Z_e \;+\; (R_1 + R_2)_{20^\circ\!C}\,\big[\,1 + \alpha\,(T - 20^\circ\!C)\,\big] $$

Prospective earth fault current (conservative):

$$ I_f \;=\; \frac{C_{\min}\,U_0}{Z_s} $$

Maximum permissible Zs based on instantaneous operation:

$$ Z_{s,\text{max}} \;=\; \frac{C_{\min}\,U_0}{I_a}, \qquad I_a = k\,I_n $$

with typical conservative multipliers for MCBs: \(k = 5\) (Type B), \(10\) (Type C), \(20\) (Type D). For precise values use BS 7671 tables or manufacturer curves.

Glossary of Variables

    - U0: Nominal phase-to-earth voltage (V).
    - Cmin: Minimum voltage factor (dimensionless, typically 0.95).
    - Ze: External earth fault loop impedance (Ω).
    - R1 + R2: Line plus CPC resistance at 20 °C (Ω).
    - T: Estimated operating temperature of conductors (°C).
    - α: Temperature coefficient of copper ≈ 0.004/°C.
    - Zs: Total earth fault loop impedance (Ω).
    - If: Prospective earth fault current to earth (A).
    - In: Protective device rated current (A).
    - Ia: Fault current ensuring automatic disconnection (A).
    - Zs,max: Maximum permissible loop impedance (Ω).

How It Works: A Step-by-Step Example

Suppose U0 = 230 V, Cmin = 0.95, Ze = 0.35 Ω, R1+R2 at 20 °C = 0.40 Ω, and T = 70 °C. Device is MCB Type B with In = 32 A.

  1. Temperature-correct R1+R2: α = 0.004/°C, ΔT = 50 °C ⇒ factor = 1 + 0.004×50 = 1.2. Thus (R1+R2)T = 0.40 × 1.2 = 0.48 Ω.
  2. Total Zs: Zs = Ze + (R1+R2)T = 0.35 + 0.48 = 0.83 Ω.
  3. Fault current: If = (Cmin × U0) / Zs = (0.95 × 230) / 0.83 ≈ 263 A.
  4. Ia for Type B: k = 5 ⇒ Ia = 5 × 32 = 160 A.
  5. Max Zs: Zs,max = (0.95 × 230) / 160 ≈ 1.366 Ω.
  6. Compliance: 0.83 Ω ≤ 1.366 Ω ⇒ Pass.

Frequently Asked Questions (FAQ)

Do I need the BS 7671 tables if I use this calculator?

Yes. This tool implements the core formulas but does not replace official tables, correction notes, or manufacturer time–current data. Always verify final designs against BS 7671 and the On-Site Guide.

Why is Cmin set to 0.95?

It provides a conservative allowance for supply voltage variations under fault conditions, as commonly adopted in BS 7671 design calculations.

What if I only have a measured Zs?

Enter it directly in “Measured Zs”. The tool will prioritise it for fault current and compliance checks and ignore Ze/R1+R2 unless measured Zs is empty.

How accurate is the temperature correction?

It uses a standard linear copper coefficient (α ≈ 0.004/°C). This is appropriate for design estimates. For critical cases, consult detailed cable data and installation conditions.

Can I use this for RCBOs?

Yes, if the RCBO’s instantaneous characteristics are equivalent to the selected MCB type. For exact verification, consult the device’s time–current curves.

What if Zs is very low and If is extremely high?

That typically improves disconnection but ensure the device and conductors can withstand the thermal and mechanical stress (check PFC/PEFC and device breaking capacity).

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[Z_s \;=\; Z_e \;+\; (R_1 + R_2)_{20^\circ\!C}\,\big[\,1 + \alpha\,(T - 20^\circ\!C)\,\big]\]
Z_s \;=\; Z_e \;+\; (R_1 + R_2)_{20^\circ\!C}\,\big[\,1 + \alpha\,(T - 20^\circ\!C)\,\big]
Formula (extracted LaTeX)
\[I_f \;=\; \frac{C_{\min}\,U_0}{Z_s}\]
I_f \;=\; \frac{C_{\min}\,U_0}{Z_s}
Formula (extracted LaTeX)
\[Z_{s,\text{max}} \;=\; \frac{C_{\min}\,U_0}{I_a}, \qquad I_a = k\,I_n\]
Z_{s,\text{max}} \;=\; \frac{C_{\min}\,U_0}{I_a}, \qquad I_a = k\,I_n
Formula (extracted text)
Loop impedance from components and temperature: $ Z_s \;=\; Z_e \;+\; (R_1 + R_2)_{20^\circ\!C}\,\big[\,1 + \alpha\,(T - 20^\circ\!C)\,\big] $ Prospective earth fault current (conservative): $ I_f \;=\; \frac{C_{\min}\,U_0}{Z_s} $ Maximum permissible Zs based on instantaneous operation: $ Z_{s,\text{max}} \;=\; \frac{C_{\min}\,U_0}{I_a}, \qquad I_a = k\,I_n $ with typical conservative multipliers for MCBs: \(k = 5\) (Type B), \(10\) (Type C), \(20\) (Type D). For precise values use BS 7671 tables or manufacturer curves.
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Full original guide (expanded)

BS 7671 Earth Fault Loop Impedance (Zs) Calculator

This professional-grade calculator helps UK electricians and engineers verify earth fault loop impedance (Zs), estimate fault current, and check compliance against maximum Zs derived from protective device characteristics under BS 7671:2018+A2:2022. It is optimized for mobile use, fully accessible, and designed for high accuracy and speed.

Data Source and Methodology

Authoritative reference: IET Wiring Regulations — BS 7671:2018+A2:2022, including Section 41 (Protection against electric shock), Tables 41.3–41.6, and Appendix 3 (Time–current characteristics). Official publisher: The IET and BSI. See: IET BS 7671 and BSI publications.

All calculations follow standard BS 7671 design assumptions: fault current estimated from nominal voltage reduced by Cmin, loop impedance obtained from Ze and R1+R2 with temperature correction, and device instantaneous multiples for conservative checks where manufacturer curves or tabulated values are not consulted.

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

The Formulas Explained

Loop impedance from components and temperature:

$$ Z_s \;=\; Z_e \;+\; (R_1 + R_2)_{20^\circ\!C}\,\big[\,1 + \alpha\,(T - 20^\circ\!C)\,\big] $$

Prospective earth fault current (conservative):

$$ I_f \;=\; \frac{C_{\min}\,U_0}{Z_s} $$

Maximum permissible Zs based on instantaneous operation:

$$ Z_{s,\text{max}} \;=\; \frac{C_{\min}\,U_0}{I_a}, \qquad I_a = k\,I_n $$

with typical conservative multipliers for MCBs: \(k = 5\) (Type B), \(10\) (Type C), \(20\) (Type D). For precise values use BS 7671 tables or manufacturer curves.

Glossary of Variables

    - U0: Nominal phase-to-earth voltage (V).
    - Cmin: Minimum voltage factor (dimensionless, typically 0.95).
    - Ze: External earth fault loop impedance (Ω).
    - R1 + R2: Line plus CPC resistance at 20 °C (Ω).
    - T: Estimated operating temperature of conductors (°C).
    - α: Temperature coefficient of copper ≈ 0.004/°C.
    - Zs: Total earth fault loop impedance (Ω).
    - If: Prospective earth fault current to earth (A).
    - In: Protective device rated current (A).
    - Ia: Fault current ensuring automatic disconnection (A).
    - Zs,max: Maximum permissible loop impedance (Ω).

How It Works: A Step-by-Step Example

Suppose U0 = 230 V, Cmin = 0.95, Ze = 0.35 Ω, R1+R2 at 20 °C = 0.40 Ω, and T = 70 °C. Device is MCB Type B with In = 32 A.

  1. Temperature-correct R1+R2: α = 0.004/°C, ΔT = 50 °C ⇒ factor = 1 + 0.004×50 = 1.2. Thus (R1+R2)T = 0.40 × 1.2 = 0.48 Ω.
  2. Total Zs: Zs = Ze + (R1+R2)T = 0.35 + 0.48 = 0.83 Ω.
  3. Fault current: If = (Cmin × U0) / Zs = (0.95 × 230) / 0.83 ≈ 263 A.
  4. Ia for Type B: k = 5 ⇒ Ia = 5 × 32 = 160 A.
  5. Max Zs: Zs,max = (0.95 × 230) / 160 ≈ 1.366 Ω.
  6. Compliance: 0.83 Ω ≤ 1.366 Ω ⇒ Pass.

Frequently Asked Questions (FAQ)

Do I need the BS 7671 tables if I use this calculator?

Yes. This tool implements the core formulas but does not replace official tables, correction notes, or manufacturer time–current data. Always verify final designs against BS 7671 and the On-Site Guide.

Why is Cmin set to 0.95?

It provides a conservative allowance for supply voltage variations under fault conditions, as commonly adopted in BS 7671 design calculations.

What if I only have a measured Zs?

Enter it directly in “Measured Zs”. The tool will prioritise it for fault current and compliance checks and ignore Ze/R1+R2 unless measured Zs is empty.

How accurate is the temperature correction?

It uses a standard linear copper coefficient (α ≈ 0.004/°C). This is appropriate for design estimates. For critical cases, consult detailed cable data and installation conditions.

Can I use this for RCBOs?

Yes, if the RCBO’s instantaneous characteristics are equivalent to the selected MCB type. For exact verification, consult the device’s time–current curves.

What if Zs is very low and If is extremely high?

That typically improves disconnection but ensure the device and conductors can withstand the thermal and mechanical stress (check PFC/PEFC and device breaking capacity).

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[Z_s \;=\; Z_e \;+\; (R_1 + R_2)_{20^\circ\!C}\,\big[\,1 + \alpha\,(T - 20^\circ\!C)\,\big]\]
Z_s \;=\; Z_e \;+\; (R_1 + R_2)_{20^\circ\!C}\,\big[\,1 + \alpha\,(T - 20^\circ\!C)\,\big]
Formula (extracted LaTeX)
\[I_f \;=\; \frac{C_{\min}\,U_0}{Z_s}\]
I_f \;=\; \frac{C_{\min}\,U_0}{Z_s}
Formula (extracted LaTeX)
\[Z_{s,\text{max}} \;=\; \frac{C_{\min}\,U_0}{I_a}, \qquad I_a = k\,I_n\]
Z_{s,\text{max}} \;=\; \frac{C_{\min}\,U_0}{I_a}, \qquad I_a = k\,I_n
Formula (extracted text)
Loop impedance from components and temperature: $ Z_s \;=\; Z_e \;+\; (R_1 + R_2)_{20^\circ\!C}\,\big[\,1 + \alpha\,(T - 20^\circ\!C)\,\big] $ Prospective earth fault current (conservative): $ I_f \;=\; \frac{C_{\min}\,U_0}{Z_s} $ Maximum permissible Zs based on instantaneous operation: $ Z_{s,\text{max}} \;=\; \frac{C_{\min}\,U_0}{I_a}, \qquad I_a = k\,I_n $ with typical conservative multipliers for MCBs: \(k = 5\) (Type B), \(10\) (Type C), \(20\) (Type D). For precise values use BS 7671 tables or manufacturer curves.
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

BS 7671 Earth Fault Loop Impedance (Zs) Calculator

This professional-grade calculator helps UK electricians and engineers verify earth fault loop impedance (Zs), estimate fault current, and check compliance against maximum Zs derived from protective device characteristics under BS 7671:2018+A2:2022. It is optimized for mobile use, fully accessible, and designed for high accuracy and speed.

Data Source and Methodology

Authoritative reference: IET Wiring Regulations — BS 7671:2018+A2:2022, including Section 41 (Protection against electric shock), Tables 41.3–41.6, and Appendix 3 (Time–current characteristics). Official publisher: The IET and BSI. See: IET BS 7671 and BSI publications.

All calculations follow standard BS 7671 design assumptions: fault current estimated from nominal voltage reduced by Cmin, loop impedance obtained from Ze and R1+R2 with temperature correction, and device instantaneous multiples for conservative checks where manufacturer curves or tabulated values are not consulted.

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

The Formulas Explained

Loop impedance from components and temperature:

$$ Z_s \;=\; Z_e \;+\; (R_1 + R_2)_{20^\circ\!C}\,\big[\,1 + \alpha\,(T - 20^\circ\!C)\,\big] $$

Prospective earth fault current (conservative):

$$ I_f \;=\; \frac{C_{\min}\,U_0}{Z_s} $$

Maximum permissible Zs based on instantaneous operation:

$$ Z_{s,\text{max}} \;=\; \frac{C_{\min}\,U_0}{I_a}, \qquad I_a = k\,I_n $$

with typical conservative multipliers for MCBs: \(k = 5\) (Type B), \(10\) (Type C), \(20\) (Type D). For precise values use BS 7671 tables or manufacturer curves.

Glossary of Variables

    - U0: Nominal phase-to-earth voltage (V).
    - Cmin: Minimum voltage factor (dimensionless, typically 0.95).
    - Ze: External earth fault loop impedance (Ω).
    - R1 + R2: Line plus CPC resistance at 20 °C (Ω).
    - T: Estimated operating temperature of conductors (°C).
    - α: Temperature coefficient of copper ≈ 0.004/°C.
    - Zs: Total earth fault loop impedance (Ω).
    - If: Prospective earth fault current to earth (A).
    - In: Protective device rated current (A).
    - Ia: Fault current ensuring automatic disconnection (A).
    - Zs,max: Maximum permissible loop impedance (Ω).

How It Works: A Step-by-Step Example

Suppose U0 = 230 V, Cmin = 0.95, Ze = 0.35 Ω, R1+R2 at 20 °C = 0.40 Ω, and T = 70 °C. Device is MCB Type B with In = 32 A.

  1. Temperature-correct R1+R2: α = 0.004/°C, ΔT = 50 °C ⇒ factor = 1 + 0.004×50 = 1.2. Thus (R1+R2)T = 0.40 × 1.2 = 0.48 Ω.
  2. Total Zs: Zs = Ze + (R1+R2)T = 0.35 + 0.48 = 0.83 Ω.
  3. Fault current: If = (Cmin × U0) / Zs = (0.95 × 230) / 0.83 ≈ 263 A.
  4. Ia for Type B: k = 5 ⇒ Ia = 5 × 32 = 160 A.
  5. Max Zs: Zs,max = (0.95 × 230) / 160 ≈ 1.366 Ω.
  6. Compliance: 0.83 Ω ≤ 1.366 Ω ⇒ Pass.

Frequently Asked Questions (FAQ)

Do I need the BS 7671 tables if I use this calculator?

Yes. This tool implements the core formulas but does not replace official tables, correction notes, or manufacturer time–current data. Always verify final designs against BS 7671 and the On-Site Guide.

Why is Cmin set to 0.95?

It provides a conservative allowance for supply voltage variations under fault conditions, as commonly adopted in BS 7671 design calculations.

What if I only have a measured Zs?

Enter it directly in “Measured Zs”. The tool will prioritise it for fault current and compliance checks and ignore Ze/R1+R2 unless measured Zs is empty.

How accurate is the temperature correction?

It uses a standard linear copper coefficient (α ≈ 0.004/°C). This is appropriate for design estimates. For critical cases, consult detailed cable data and installation conditions.

Can I use this for RCBOs?

Yes, if the RCBO’s instantaneous characteristics are equivalent to the selected MCB type. For exact verification, consult the device’s time–current curves.

What if Zs is very low and If is extremely high?

That typically improves disconnection but ensure the device and conductors can withstand the thermal and mechanical stress (check PFC/PEFC and device breaking capacity).

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[Z_s \;=\; Z_e \;+\; (R_1 + R_2)_{20^\circ\!C}\,\big[\,1 + \alpha\,(T - 20^\circ\!C)\,\big]\]
Z_s \;=\; Z_e \;+\; (R_1 + R_2)_{20^\circ\!C}\,\big[\,1 + \alpha\,(T - 20^\circ\!C)\,\big]
Formula (extracted LaTeX)
\[I_f \;=\; \frac{C_{\min}\,U_0}{Z_s}\]
I_f \;=\; \frac{C_{\min}\,U_0}{Z_s}
Formula (extracted LaTeX)
\[Z_{s,\text{max}} \;=\; \frac{C_{\min}\,U_0}{I_a}, \qquad I_a = k\,I_n\]
Z_{s,\text{max}} \;=\; \frac{C_{\min}\,U_0}{I_a}, \qquad I_a = k\,I_n
Formula (extracted text)
Loop impedance from components and temperature: $ Z_s \;=\; Z_e \;+\; (R_1 + R_2)_{20^\circ\!C}\,\big[\,1 + \alpha\,(T - 20^\circ\!C)\,\big] $ Prospective earth fault current (conservative): $ I_f \;=\; \frac{C_{\min}\,U_0}{Z_s} $ Maximum permissible Zs based on instantaneous operation: $ Z_{s,\text{max}} \;=\; \frac{C_{\min}\,U_0}{I_a}, \qquad I_a = k\,I_n $ with typical conservative multipliers for MCBs: \(k = 5\) (Type B), \(10\) (Type C), \(20\) (Type D). For precise values use BS 7671 tables or manufacturer curves.
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn
Formulas

(Formulas preserved from original page content, if present.)

Version 0.1.0-draft
Citations

Add authoritative sources relevant to this calculator (standards bodies, manuals, official docs).

Changelog
  • 0.1.0-draft — 2026-01-19: Initial draft (review required).