Methodology

Scope

Wire Math is an estimator. Every calculator on the site converts between metric and imperial wire sizes or computes a single electrical quantity (voltage drop, resistance, indicative ampacity) from the inputs you provide. It does not perform a BS 7671 compliance check, and it does not replace design or verification work carried out by a competent person.

Formulas in use

• AWG ↔ mm²: d = 0.127 · 92^((36 − awg)/39)mm and area = π · (d/2)². The reverse direction inverts algebraically and snaps to the nearest integer AWG, with the residual delta reported.
• SWG: lookup table only, sourced from the legacy British Standard SWG values published in BS 3737. No interpolation between rows.
• Voltage drop: Vd = k · I · L · ρ(T) / A with k = 2 for single-phase and k = √3 for three-phase. Resistivity is temperature-adjusted as ρ(T) = ρ₂₀ · (1 + α · (T − 20)).
• Resistance: R = ρ(T) · L / A, with an optional power-loss helper P = I² · R.
• Ampacity helper: a filterable lookup over a reference table. Derating for grouping, ambient temperature, or installation method is out of scope and remains BS 7671 territory.

Constants

• Resistivity at 20 °C: copper ρ₂₀ = 1.724 × 10⁻⁸ Ω·m, aluminium ρ₂₀ = 2.82 × 10⁻⁸ Ω·m.
• Temperature coefficient: copper α = 0.00393 / °C, aluminium α = 0.00403 / °C.
• UK CSA ladder used in selectors: 1, 1.5, 2.5, 4, 6, 10, 16, 25, 35, 50, 70, 95, 120 mm².

Precision policy

Internal arithmetic uses IEEE 754 double precision and rounds only at the display layer, per the precision specified by each formula output. Conversion fixtures are validated to a relative tolerance of 1e-6; voltage-drop fixtures to an absolute tolerance of 0.5 %. NaN and Infinity are rejected at the validation boundary.

Build identity

When you report a result you disagree with, please include the two values below. Together they pin the exact code and formula versions that produced your number.

• Build SHA: 3150e0a6f096
• Formula registry checksum: a0471ccd8f3d

See sources for the standards we reference, and the disclaimer for the boundary between estimation and compliance.