Authoritative Data Source and Methodology
Primary Standard: IET Wiring Regulations — BS 7671:2018+A2:2022 (18th Edition, Amendment 2), Institution of Engineering and Technology (IET), 2022. Official IET page.
All calculations are based strictly on the formulas and methods provided by this source. Users must obtain tabulated values (It and mV/A/m) from their licensed copy of BS 7671 and apply them here.
The Formulas Explained
Minimum tabulated current-carrying capacity:
$$ I_{z,\min} = \frac{I_b}{C_a \cdot C_g \cdot C_i \cdot C_f} $$
Thermal compliance (device and cable):
$$ I_b \leq I_n \leq I_z $$
Voltage drop:
$$ \Delta V = I \cdot m \cdot L \,/\, 1000 \qquad \text{and} \qquad \%\Delta V = 100 \cdot \frac{\Delta V}{V_n} $$
where m is the tabulated coefficient in mV/A/m selected from Appendix 4 for the chosen cable/system.
Adiabatic short-circuit equation:
$$ S_{\min} = \frac{I_{sc} \cdot \sqrt{t}}{k} $$
with k taken from BS 7671 for the conductor material and insulation.
Glossary of Variables
- I_b — Design current of the load (A).
- I_n — Protective device rated current (A).
- I_z — Cable current-carrying capacity under installation conditions (A).
- I_{z, min} — Minimum tabulated capacity required before factors (A).
- C_a, C_g, C_i, C_f — Correction factors for ambient temperature, grouping, thermal insulation, and other conditions (dimensionless).
- m — Voltage drop coefficient from Appendix 4 (mV/A/m).
- L — Circuit length (m).
- V_n — Nominal system voltage (V): typically 230 V (single-phase) or 400 V (three-phase).
- I_sc — Prospective short-circuit current at the cable location (A).
- t — Disconnection time for the protective device (s).
- k — Material/insulation factor for the adiabatic check (A·s0.5/mm²).
- CSA — Conductor cross-sectional area (mm²).
How It Works: A Step-by-Step Example
Suppose a single-phase 230 V circuit has design current I_b = 32 A. The installation yields factors C_a = 1.00, C_g = 0.80, C_i = 1.00, and no additional factor (C_f = 1.00). Then:
$$ F = C_a \cdot C_g \cdot C_i \cdot C_f = 1.00 \cdot 0.80 \cdot 1.00 \cdot 1.00 = 0.80 $$
$$ I_{z,\min} = \frac{I_b}{F} = \frac{32}{0.80} = 40 \text{ A} $$
From BS 7671 tables, choose a cable with tabulated current capacity It ≥ 40 A for the installation method. For voltage drop, if length L = 30 m and the selected cable has m = 18 mV/A/m (from Appendix 4 for the appropriate arrangement):
$$ \Delta V = \frac{I \cdot m \cdot L}{1000} = \frac{32 \cdot 18 \cdot 30}{1000} = 17.28 \text{ V} $$
$$ \%\Delta V = 100 \cdot \frac{17.28}{230} \approx 7.5\% $$
If the permitted drop is 5%, the selected size fails on voltage drop; increase CSA or shorten the run until the percentage falls at or below 5%. Finally, if I_sc = 6 kA, t = 0.4 s, and k = 143 (Cu/XLPE):
$$ S_{\min} = \frac{6000 \cdot \sqrt{0.4}}{143} \approx 26.3 \text{ mm}^2 $$
Ensure the chosen line and CPC conductors meet or exceed the adiabatic requirement (note: CPC sizing may differ when using the adiabatic method versus table method).
Frequently Asked Questions (FAQ)
Does this calculator include the BS 7671 tables?
No. Those tables are copyrighted by the IET. This tool applies the official formulas and lets you input tabulated values from your licensed copy.
Which correction factors should I use?
Use the factors for your installation method and conditions directly from BS 7671 (ambient, grouping, thermal insulation, etc.). If manufacturer data specify additional derating, include it as Cf.
How do I select the correct mV/A/m value?
Appendix 4 provides mV/A/m values by conductor size, type, and system arrangement. Choose the row that matches your cable construction and whether it is single- or three-phase.
What is the relationship among Ib, In, and Iz?
Ensure Ib ≤ In ≤ Iz. That is, the device rating should be at least the design current and not exceed the cable’s capacity under installation conditions.
Do I need to consider temperature rise and installation method?
Yes. Installation method, ambient temperature, and thermal insulation all affect the cable’s capacity and are captured via the correction factors.
Is the adiabatic check for the line conductor or CPC?
The adiabatic equation is commonly applied to verify the CPC. Designers may also verify the line conductor thermal withstand for worst-case faults. Always apply the method relevant to your design and protective arrangements.
Does power factor affect voltage drop?
The tabulated mV/A/m already incorporates resistance and reactance under typical conditions. If your load has significant reactive component, select the appropriate table entry or apply manufacturer data.