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MasterMath

Wire Size Calculator

What size of cable keeps the voltage drop within the limit, given the run, the current and the conductor material.

Currency and number format for

Standard size

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Standard size—
Theoretical minimum—
Drop at that size—
As a percentage—
Maximum drop allowed—
Power of the circuit—
Conductor—

How this was worked out

    Indicative result. The sum is the physics of voltage drop and is for sizing and checking. The minimum size required for each circuit, the protective device that goes with it and the installation method are set by the wiring regulations of each country, which also cap the current-carrying capacity according to how the cable is run. An electrical installation is signed off by a professional.

    The formula

    S = factor × ρ × length × current ÷ allowed drop

    Where it comes from

    A cable has resistance, and that resistance eats part of the voltage along the way. The drop is proportional to the length and the current, and inversely proportional to the size: more metres or more amps call for more copper. The factor in the formula is 2 for single phase, because the current goes and returns along two conductors, and √3 for balanced three phase. On that basis, a 16 A circuit over 25 metres calls for 2.03 mm² in theory, which rounded to a standard size is the familiar 2.5 mm².

    How to work it out by hand

    1. Work out the allowed drop: the voltage times the maximum percentage
    2. Multiply the system factor by the resistivity, the length and the current
    3. Divide by the allowed drop: that is the theoretical size
    4. Step up to the next standard size

    What is worth knowing

    Voltage drop is not the only criterion, and on short runs it is rarely the one that governs: over small distances the deciding factor is usually the current-carrying capacity of the cable, which depends on how it is installed — in free air, in conduit, buried, bunched with others — and is set out in regulation tables. This calculator solves the drop; current capacity is looked up separately. Aluminium needs around 60 % more cross-section than copper for the same job, because it conducts less well, and in exchange it weighs and costs less: that is why it is used on long supply runs and not in interior wiring.

    Frequently asked questions

    What size cable do I need?

    It depends on the length, the current and the drop you allow. A 16 A single-phase circuit over 25 metres at 3 % drop calls for 2.5 mm².

    How is voltage drop calculated?

    Multiply the system factor (2 single phase, √3 three phase) by the resistivity, the length and the current, then divide by the cross-section.

    How much voltage drop is allowed?

    Regulations typically limit it to 3 % for lighting and 5 % for other uses, measured from the board. Check the rules where you are.

    Why does a long cable need a bigger size?

    Because the drop grows in proportion to the length: twice the metres is twice the drop at the same cross-section.

    Copper or aluminium?

    Aluminium needs about 60 % more cross-section for the same job, but weighs and costs less. It is used on long supply runs, not interior wiring.

    Is voltage drop enough to choose a cable?

    No. On short runs the current-carrying capacity governs, and that depends on how the cable is installed and comes from regulation tables.