Voltage Drop Calculator
How the formula works
Voltage drop is the voltage lost along a cable when current flows through it. Every cable has resistance, and AC cables also have a small reactance. If the drop is too large, motors run hot, lights dim and sensitive equipment can trip or fail. This calculator finds the drop for single phase AC, three phase AC and DC circuits, and also shows the receiving end voltage, the power lost in the cable and the smallest standard cable size that meets your limit.
Formulas
R = ρ × (1 + α × (T − 20)) ÷ A
Single phase AC: Vd = 2 × I × L × (R × cosφ + X × sinφ)
Three phase AC: Vd = √3 × I × L × (R × cosφ + X × sinφ)
DC: Vd = 2 × I × L × R
Voltage drop % = (Vd ÷ V) × 100
Receiving end voltage = V − Vd
Cable power loss (single phase and DC) = 2 × I² × R × L
Cable power loss (three phase) = 3 × I² × R × L
Where
- Vd = voltage drop in volts
- V = supply voltage in volts (line to line for three phase)
- I = load current in amperes
- L = one way cable length in metres
- A = conductor cross section in mm²
- R = conductor resistance in ohm per metre, corrected for temperature
- X = cable reactance, taken as 0.08 ohm per km (0.00008 ohm per metre) for AC cables
- ρ at 20 °C = 0.017241 ohm·mm²/m for copper and 0.028264 ohm·mm²/m for aluminium
- α = 0.00393 per °C for copper and 0.00403 per °C for aluminium
- T = conductor operating temperature in °C
- cosφ = power factor and sinφ = √(1 − cosφ²)
Commonly used limits
- Many standards and guides suggest about 3 % for lighting and branch circuits and about 5 % from the source to the farthest load.
- Your project specification, client requirement or local electrical code always has the final say.
The calculator picks the smallest size from the standard list (1.5 to 630 mm²) whose drop stays within the limit you select. This size is based on voltage drop only. You must still check the cable current carrying capacity, grouping and ambient factors, and short circuit withstand.
Worked example
Example 1: Three phase feeder
A three phase, 415 V copper XLPE cable of 35 mm² feeds a load of 70 A at 0.85 power factor. The cable is 80 m long. Find the voltage drop.
Step 1: Resistance at 90 °C
ρ = 0.017241 × (1 + 0.00393 × 70) = 0.02198 ohm·mm²/m
R = 0.02198 ÷ 35 = 0.000628 ohm/m
Step 2: Power factor terms
cosφ = 0.85, sinφ = 0.527, X = 0.00008 ohm/m
R × cosφ + X × sinφ = 0.000534 + 0.000042 = 0.000576 ohm/m
Step 3: Voltage drop
Vd = 1.732 × 70 × 80 × 0.000576 = 5.59 V
Voltage drop % = 5.59 ÷ 415 × 100 = 1.35 %
Result
Receiving end voltage = 409.4 V
Cable power loss = 3 × 70² × 0.000628 × 80 = about 739 W
For a 3 % limit, the minimum size by voltage drop is 16 mm². The 35 mm² cable is well within the limit.
Example 2: Single phase circuit
A single phase, 230 V copper PVC cable of 4 mm² supplies a 16 A load at 0.9 power factor over 25 m. The conductor temperature is 70 °C.
ρ = 0.017241 × (1 + 0.00393 × 50) = 0.02063 ohm·mm²/m, so R = 0.02063 ÷ 4 = 0.005157 ohm/m.
cosφ = 0.9, sinφ = 0.436
Vd = 2 × 16 × 25 × (0.005157 × 0.9 + 0.00008 × 0.436) = 3.74 V
Voltage drop % = 3.74 ÷ 230 × 100 = 1.63 %
Receiving end voltage = 226.3 V, cable loss = about 66 W. For a 3 % limit, the minimum size is 2.5 mm².
Common mistakes
- Using the total round trip length. Enter only the one way length. The formulas already include the return path.
- Using phase voltage for a three phase system. Use the line to line voltage, for example 415 V and not 240 V.
- Ignoring conductor temperature. Copper resistance at 90 °C is about 27 % higher than at 20 °C. Using cold values gives a drop that is too low.
- Forgetting the power factor. Motors and other inductive loads have a power factor below 1, and it changes the result.
- Choosing the cable only by voltage drop. A cable that passes the drop check may still be too small for the current. Always check the current rating as well.
- Using the starting current for the running check. Motor starting current is much higher, so check the starting voltage dip separately.
- Applying the limit to one cable only. The 5 % limit is usually for the whole path from the source to the load, so the feeder and the final circuit share it.
- Mixing units. Length must be in metres, size in mm² and current in amperes.
Frequently asked questions
What is a safe voltage drop percentage?
Many standards and design guides recommend about 3 % for branch and lighting circuits and about 5 % in total from the source to the final load. Some projects use tighter limits, so always follow your specification and local code.
Why is voltage drop important?
Too much drop reduces the voltage at the load. Motors draw more current and overheat, lamps become dim, and electronic equipment may reset or fail. It also wastes energy as heat in the cable.
How can I reduce voltage drop?
Use a larger conductor size, shorten the cable run, use copper instead of aluminium, improve the power factor, or raise the supply voltage level where the design allows it.
Is the drop higher in single phase or three phase?
For the same load power and voltage, three phase gives a lower drop because the current per conductor is smaller. In the formulas, the single phase factor is 2 and the three phase factor is 1.732.
Does this calculator include reactance?
Yes, for AC circuits. It uses a typical value of 0.08 ohm per km. The reactance of real cables depends on the cable type and laying method, so use the manufacturer value for final design.
Which temperature should I select?
Use 70 °C for PVC insulated cables and 90 °C for XLPE insulated cables when the cable carries its full rated current. Use 20 °C only for a quick cold estimate.
Can I use this for DC systems?
Yes. Select DC, enter the DC voltage as a custom value and the load current. Power factor is not used for DC.
Does the result replace a full cable sizing calculation?
No. It is a design aid. Cable sizing also needs the current rating, installation method, grouping, ambient temperature and short circuit checks, as required by your code.