When designing electrical wiring, it is necessary to take into account the voltage drop in the cable. This is especially important in individual houses where the length of the wiring can be critical. To avoid making calculations for each wire separately, it is convenient to use an online calculator designed for this task.
Like this? Please share:
NOTE. The voltage drop calculated by the calculator is an approximate value and does not guarantee a 100% accurate result. The results may vary depending on the actual cables and wires, different resistivity of the material, number of cores in the cable, temperature and weather conditions, place of installation, etc.
Voltage Drop Calculations
DC / Single Phase Calculation
To find the voltage drop V in volts (V), multiply the wire current I in amps (A) by 2 and by the one way wire length L in feet (ft), then multiply by the wire resistance per 1000 feet R in ohms (Ω/kft), and then divide by 1000:
Vdrop (V) = Iwire (A) × Rwire(Ω) = Iwire (A) × (2 × L(ft) × Rwire(Ω/kft) / 1000(ft/kft))
To calculate the voltage drop V in volts (V), take the wire current I in amps (A) and multiply it by 2 and by the one way wire length L in meters (m), then multiply by the wire resistance per 1000 meters R in ohms (Ω/km), and then divide by 1000:
Vdrop (V) = Iwire (A) × Rwire(Ω) = Iwire (A) × (2 × L(m) × Rwire (Ω/km) / 1000(m/km))
3 Phase Calculation
To find the line to line voltage drop V in volts (V), multiply the wire current I in amps (A) by square root of 3 and by the one way wire length L in feet (ft), then multiply by the wire resistance per 1000 feet R in ohms (Ω/kft), and then divide by 1000:
Vdrop (V) = √3 × Iwire (A) × Rwire (Ω) = 1,732 × Iwire (A) × (L(ft) × Rwire (Ω/kft) / 1000(ft/kft))
To calculate the line to line voltage drop V in volts (V), take the wire current I in amps (A) and multiply it by square root of 3 and by the one way wire length L in meters (m), then multiply by the wire resistance per 1000 meters R in ohms (Ω/km), and then divide by 1000:
Vdrop (V) = √3 × Iwire (A) × Rwire (Ω) = 1,732 × Iwire (A) × (L(m) × Rwire (Ω/km) / 1000(m/km))
Wire Diameter Calculations
To find the wire diameter dn in inches (in) for n gauge wire, multiply 0.005in by 92 to the power of 36 minus the gauge number n, and then divide by 39:
dn (in) = 0,005 in × 92(36-n)/39
The n gauge wire diameter dn in millimeters (mm) is equal to 0,127mm times 92 raised to the power of 36 minus gauge number n, divided by 39:
dn (mm) = 0,127 mm × 92(36-n)/39
Wire Cross Sectional Area Calculations
To calculate the cross sectional area An in kilo-circular mils (kcmil) for n gauge wire, take the wire diameter d in inches (in) and square it, then multiply by 1000:
An (kcmil) = 1000×dn2 = 0,025 in2 × 92(36-n)/19,5
To find the cross sectional area An in square inches (in2) for n gauge wire, multiply the wire diameter d in inches (in) by itself, then multiply by pi and divide by 4:
An (in2) = (π/4)×dn2 = 0,000019635 in2 × 92(36-n)/19,5
The n gauge wire’s cross sercional area An in square millimeters (mm2) is equal to pi divided by 4 times the square wire diameter d in millimeters (mm):
An (mm2) = (π/4)×dn2 = 0,012668 mm2 × 92(36-n)/19,5
Wire Resistance Calculations
To calculate the wire resistance R in ohms per kilofeet (Ω/kft) for n gauge wire, take the wire’s resistivity ρ in ohm-meters (Ω·m) and multiply it by 0.3048×1000000000, then divide by 25.42 and by the cross sectional area An in square inches (in2):
Rn (Ω/kft) = 0,3048 × 109 × ρ(Ω·m) / (25,42 × An (in2))
To find the wire resistance R in ohms per kilometer (Ω/km) for n gauge wire, take the wire’s resistivity ρ in ohm-meters (Ω·m) and multiply it by 1000000000, then divide by the cross sectional area An in square millimeters (mm2):
Rn (Ω/km) = 109 × ρ(Ω·m) / An (mm2)
Example
For example: Calculate the voltage drop of a 240V AC single phase circuit drawing 20A using a 50′ long 12AWG copper conductor.
A 12 AWG wire has a cross-sectional area 3.308 mm2 per the table below. Recall that the resistivity of a copper conductor is 1.7241×10-8 Ω·m. You can convert the length in feet to meters by multiplying by 0.3048.
Vdrop (V) = Iwire (A) * (2 * L(m) * Rwire (Ω/km) / 1000(m/km)) = Iwire (A) * (2 * L(m) * ((109 * ρ(Ω·m) / An (mm2) ) / 1000(m/km))) = 20 A * (2 * 50 ft * 0.3048 m/ft * (109 * 1.7241×10-8 Ω·m / 3.308 mm2) / 1000(m/km) = 20 A * (30.48 m * 5.211 (Ω/km) / 1000 (m/km)) = 20 A * 0.1588 Ω = 3.1766 V .
