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Voltage Drop Calculator

Estimate the voltage lost along a copper or aluminum wire run from its gauge or area, length and current.

Level: Grades 11–12

Printable worksheet

Voltage Drop Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Circuit type
Conductor
Wire size given as

Distance from the source to the load, not the total wire used.

For three-phase, the line-to-line voltage.

Result

Voltage drop

4.7644 V

12 AWG copper carrying 15 A loses about 4.764 V (3.97%) over a 100 ft run.

Voltage drop (%)
3.97%Above the common 3% guideline for one circuit, but within the 5% often suggested for the feeder and branch circuit together. Consider a larger wire.
Voltage at the load
115.2356 V
Power lost in the wire
71.4657 W
Conductor resistance
5.2104 Ω/km
Conductor resistance
1.5881 Ω/1000 ft
Conductor area
3.3088 mm²

See the step-by-step solution ↓

Step-by-step solution

  1. Find the wire's thickness (diameter d) from its gauge number n = 12, using the standard AWG formula

    d=0.127×92(36−1239)=2.052525 mm

  2. Work out the area of the round wire's cut end (A). A bigger area means less resistance

    A=π4×2.0525252=3.308773 mm²

  3. Resistance per meter of copper at 20 °C: divide the metal's resistivity ρ (how strongly it resists current, 1.724e-8 Ω·m or 0.01724 Ω·mm²/m) by the area

    R/m=0.017243.308773=0.00521039 Ω/m

  4. Change the length to meters to match the resistance per meter (1 ft = 0.3048 m)

    100 ft×0.3048=30.48 m

  5. The current flows out and back, so the drop covers twice the one-way length: 2 × length × resistance per meter × current

    Vd=2×30.48×0.00521039×15=4.764381 V

  6. Divide the drop by the source voltage to see what share of it is lost, as a percent

    4.764381120×100=3.9703%

  7. Take the drop away from the source voltage to get what is left at the load

    120−4.764381=115.235619 V

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find out how much voltage your wire loses on the way to whatever it powers. Every wire has some resistance. So when current flows through it, a little voltage is lost along the way, and less reaches the load (the device at the end). On a short run of thick wire, the loss is tiny. But long runs, thin wire, high currents and low voltages can lose enough to dim lights, slow motors or stop electronics from working. The calculator estimates that loss for copper or aluminum wire.

Enter the wire size as an AWG gauge or as the area of its cut end. Then enter the one-way length of the run, the current and the source voltage. You get the drop in volts and as a percent of the supply. You also see the voltage left at the load and the power wasted as heat in the wire. The percent is compared with common design guidelines. Those are rules of thumb, not a check against any electrical code.

Where it's used

Why this math matters outside the classroom:

  • Long runs. Electricians check that a long run to a detached garage won't lose so much voltage that tools run poorly.
  • Upsizing wire. Moving from 14 AWG to 12 AWG copper cuts resistance by about 37%, which reduces voltage drop by the same share.
  • Low-voltage lighting. Landscape lighting installers keep 12 V runs short because the same drop is a bigger share of a low voltage.
  • Solar wiring. Solar installers size the wire from panels to inverter so the drop stays within a small percent of system voltage.
  • Worked example. A 30 m round trip of copper at 0.0052 Ω per meter carrying 15 A loses about 30 × 0.0052 × 15 ≈ 2.3 V.

How to use it

  1. Choose the circuit type (DC, single-phase AC or three-phase AC) and the wire's metal.
  2. Give the wire size as an AWG gauge from the list, or as an area in mm² or kcmil.
  3. Enter the one-way distance from the source to the load, in feet or meters. Then enter the current the load draws.
  4. Enter the source voltage (line-to-line for three-phase). Then read the drop, the percent and the voltage at the load.

What the inputs mean

Wire gauge
AWG sizes run from 0000 (4/0, the thickest listed) to 40 (very fine). Smaller numbers mean thicker wires with less resistance.
Conductor area
Use mm² for metric cable sizes such as 2.5 mm² or 16 mm². Use kcmil (thousands of circular mils, a North American size unit) for large wires above 4/0, such as 250 kcmil.
One-way length of the run
Measure the path the cable really takes from the panel, battery or supply to the load, one way. The calculator doubles it for the return path on DC and single-phase circuits. So don't double it yourself.
Load current
Use the current the load really draws. Or use the circuit's rated current for a worst-case estimate.
Source voltage
For three-phase, the line-to-line voltage.

Formula and method

AWG diameter:  d = 0.127 mm × 92^((36 − n) ÷ 39)
Area:          A = π ÷ 4 × d²
Resistance:    R/m = ρ ÷ A
DC and single-phase:  Vd = 2 × L × R/m × I
Three-phase:          Vd = √3 × L × R/m × I
Percent drop = Vd ÷ V × 100
ρ(copper) = 1.724e-8 Ω·m,  ρ(aluminum) = 2.82e-8 Ω·m  (at 20 °C)

In the formulas, n is the gauge number and d is the wire's diameter. A is the area of its cut end, and R/m is resistance per meter. ρ (the Greek letter rho) is resistivity, how strongly the metal resists current. L is the one-way length, I is the current, V is the source voltage and Vd is the voltage drop. The AWG formula gives a gauge's diameter, and the area of the round wire follows. Resistance per meter is the resistivity divided by that area. The resistivity values are the standard 20 °C figures for annealed (heat-softened) copper and for typical electrical-grade aluminum.

On DC and single-phase circuits, the current goes out on one wire and back on another. So the loop holds twice the one-way length of wire. On a balanced three-phase circuit, the return currents mostly cancel out. There, the drop between two lines works out to √3 times the drop along one wire.

Worked example

A 120 V single-phase circuit uses 12 AWG copper wire to feed a 15 A load 100 ft away.

  1. Diameter of 12 AWG: 0.127 × 92^((36 − 12) ÷ 39) = 2.052525 mm, giving an area of 3.308773 mm².
  2. Resistance: 0.01724 ÷ 3.308773 = 0.00521039 Ω per meter (about 1.588 Ω per 1000 ft).
  3. Length: 100 ft × 0.3048 = 30.48 m one way.
  4. Drop: Vd = 2 × 30.48 × 0.00521039 × 15 = 4.764381 V.
  5. Percent: 4.764381 ÷ 120 × 100 = 3.9703%, leaving about 115.24 V at the load.

Result: The run loses about 4.76 V (3.97%), above the common 3% guideline for a single circuit. Moving up to 10 AWG would cut the drop to about 3.0 V (2.5%).

Understanding the result

A widely used design guideline is to keep the drop on one branch circuit or feeder to about 3%. A branch circuit feeds outlets or devices, and a feeder carries power to a panel. The total from the service to the load should stay around 5%. These figures come from advisory notes, not required rules. Local codes and equipment makers may set their own limits.

Low-voltage DC systems include 12 V solar, car and boat wiring. There, the same percent is only a fraction of a volt. So designers often aim lower, sometimes 2 to 3%, especially for sensitive equipment.

If the drop is too high, use a thicker wire (a smaller AWG number) or shorten the run. You can also raise the supply voltage, so the same power needs less current.

Assumptions and limitations

  • Wire resistance is the DC value of a solid round wire at 20 °C. Stranded wire and wire running hot have somewhat higher resistance.
  • The current is steady. For AC, the load is treated as resistive, meaning it acts like a heater. Three-phase loads are balanced.
  • Only the wire's own resistance is counted. Terminals, breakers and connections add a little more drop.
  • Wire carrying current warms up, and copper's resistance rises about 0.4% per °C. So a wire at 75 °C has roughly 20% more resistance than the figure used here.
  • It ignores AC inductive reactance, an extra push-back that matters for large wires and low power factors.
  • This estimates voltage drop only. It doesn't check ampacity (how much current a wire can safely carry), insulation rating, conduit fill or any other code requirement. Wire sizes for real installations must follow your local electrical code. The work should be done or checked by a licensed electrician.

Frequently asked questions

Is the length one way or round trip?

Enter the one-way distance from the source to the load. For DC and single-phase circuits, the calculator multiplies by 2 for the return wire. For three-phase, it uses √3 instead.

How much voltage drop is acceptable?

Common guidance is about 3% for a single branch circuit or feeder, and 5% overall. These are guidelines for good performance, not code limits. Some equipment, such as motors starting under load, may need tighter figures.

Why does aluminum wire drop more voltage than copper?

Aluminum resists current about 64% more than copper does. So the same size wire has about 1.64 times the resistance and the drop. Aluminum wires are usually chosen one or two sizes larger to make up for it.

Does a higher voltage reduce voltage drop?

For the same power, yes. Doubling the voltage halves the current. That halves the drop in volts and cuts it to a quarter as a percent of the supply. That's why long runs and large loads use higher voltages.

How this calculator is checked

Method: AWG definition d = 0.127 mm × 92^((36 − n)/39); R = ρL/A with ρ = 1.724e-8 Ω·m (copper) and 2.82e-8 Ω·m (aluminum) at 20 °C; round-trip (×2) and three-phase (×√3) drop. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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