Maps for Math

How do I size a wire? From the load to the voltage drop, step by step

Sizing a wire takes three linked calculations. First, the load’s watts divided by the voltage give the current. Second, the wire’s length, gauge, and metal give its resistance. Third, current times resistance is the voltage lost in the wire. If that drop is over about 3 percent, choose a thicker gauge or a shorter run.

3 steps · 2 links. Change any value that isn’t linked. Everything after it updates.

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  1. Step 1 · LIN-0003

    How many amps does it draw?

    15 A breaker80%: loads running 3 h or more (NEC)12.5 A · over 80%at 120 V
    Current
    12.5 A
    Power
    1.5 kW
    Supply voltage
    120 V

    12.5 A is over 80% of a 15 A breaker. That’s fine for short use, but for a load running 3 hours or more, the NEC calls for a larger circuit. This assumes a resistive load, like a heater, kettle, or toaster. Motors and compressors (fridges, air conditioners, pumps, power tools) draw several times this for a moment at startup, and somewhat more while running.

    On the label or the nameplate, in watts.
    More settings
    Under the NEC, a continuous load (one running 3 hours or more) should stay under 80% of this.
    Show the work
    1. Power = voltage × currentP = VI ;\Rightarrow; I = \frac{P}{V}
    2. With your numbersI = \frac{1500\,\mathrm{W}}{120\,\mathrm{V}} = 12.5\,\mathrm{A}
    3. 80% breaker check0.8 \times 15\,\mathrm{A} = 12\,\mathrm{A}

  2. Step 2 · RAT-0002

    Wire resistance: longer and thinner resist more

    18 AWG16 AWG14 AWG12 AWG10 AWG0.504 Ωcopper at 75 °C · out and back
    Wire resistance
    0.504 Ω
    Total conductor
    50 m
    Cross-section
    2.08×10^-6 m²
    More settings
    Current heats a wire, and hot copper resists about 22% more than cool copper. Code tables for voltage drop use 75 °C.
    Show the work
    1. Resistance of a wireR = \frac{\rho L}{A}
    2. Area of 14 AWGA = \frac{\pi d^2}{4} = \frac{\pi (1.628\,\mathrm{mm})^2}{4} = 2.081\,\mathrm{mm^2}
    3. Warm wire resists more: copper at 75 °C\rho_{75} = \rho_{20}\,(1 + \alpha\,\Delta T) = 1.724\times 10^{-8} \times (1 + 0.00393 \times 55) = 2.097\times 10^{-8}\,\Omega\cdot\mathrm{m}
    4. With your numbersR = \frac{2.097\times 10^{-8}\,\Omega\cdot\mathrm{m} \times 50\,\mathrm{m}}{2.081\times 10^{-6}\,\mathrm{m^2}} = 0.5038\,\Omega

  3. Step 3 · LIN-0004

    Voltage drop: what the wire takes before the load gets it

    supply120 Vat load113.7 V reaches the load3% targetlost in the wire: 6.3 V (5.2%) · 78.7 W of heatOver 3%: consider thicker or shorter wire.12.5 A through 0.504 Ω of wire
    Voltage drop
    6.3 V
    Drop (% of supply)
    5.25%
    Power lost as heat
    78.7 W
    Voltage at the load
    114 V
    Current (I)12.5 A
    from LIN-0003 · Current ·
    Wire resistance, out and back (two wires) (R)0.504 Ω
    from RAT-0002 · Wire resistance ·
    For three-phase, use the voltage between two lines, such as 208, 400, or 480 V.
    More settings
    Show the work
    1. Ohm’s law on the wire\Delta V = IR = 12.5 \times 0.5038 = 6.297\,\mathrm{V}
    2. As a percent of supply\frac{6.297}{120} \times 100 = 5.248\%
    3. Heat in the wireP = I^2R = (12.5)^2 \times 0.5038 = 78.72\,\mathrm{W}

Final results

Voltage drop (LIN-0004)
6.3 V
Drop (% of supply) (LIN-0004)
5.25%
Power lost as heat (LIN-0004)
78.7 W
Voltage at the load (LIN-0004)
114 V

Current from LIN-0003 feeds Current in LIN-0004. Wire resistance from RAT-0002 feeds Wire resistance, out and back (two wires) in LIN-0004.

Step by step

  1. Find the current the appliance draws: I = P / V.
  2. Check the breaker: a heater runs for hours, so the NEC wants it under 80% of the breaker. 12.5 A is over 80% of 15 A (12 A), so this heater belongs on a 20 A circuit, which needs 12 AWG wire anyway.
  3. Find the resistance of the wire run, counting both conductors, at 75 °C as code tables do: R = ρL / A.
  4. Multiply them to get the voltage drop: ΔV = I × R. Compare it with the supply voltage.
  5. If the drop is over 3%, try the next thicker gauge (a smaller AWG number) and watch every step update.

Each step is a full exhibit: How many amps does it draw?, Wire resistance: longer and thinner resist more, Voltage drop: what the wire takes before the load gets it.

Questions people ask

How much voltage drop is acceptable?

A common guideline is 3% on a branch circuit and 5% total. Motors and electronics may need less.

Why does the gauge change the voltage drop?

A thicker wire has more cross-section, so less resistance. Less resistance means less voltage lost for the same current.

Can I change the steps?

Yes. Change the load, the length, or the gauge and every later step recalculates. Open it as a board to add or remove links.

Updated : Wire resistance at 75 °C (drop now 5.25%), and a breaker step flagging 12.5 A over 80% of 15 A.

Change history (2 revisions)
  1. · rev 2: Wire resistance at 75 °C (drop now 5.25%), and a breaker step flagging 12.5 A over 80% of 15 A.
  2. · rev 1: Initial curated chain.

See everything that’s new on Maps for Math

CHN-001 · rev 2 · LIN-0003 r3 → RAT-0002 r3 → LIN-0004 r2 · updated 2026-10-02