AC Voltage Drop Calculator
Calculate single-phase or three-phase AC voltage drop from current, length, conductor size, power factor and reactance, with the formula and worked example.
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Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
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About this calculator
Use this when the circuit carries AC and the power factor and cable reactance matter, so a simple resistive estimate is not good enough. It takes the conductor size as an area, AWG number or diameter, and corrects the resistance for conductor temperature.
Limits of this calculator
Skin and proximity effect are not included, and they matter above about 150 mm². Reactance is the per-conductor value you enter from the data sheet. Compare the drop with the limit in your standard or specification.
Cross-check: 22 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed.
What this calculator checks
- AC voltage drop from conductor material, size, length and temperature, with the reactance you enter, for lagging or leading load.
What remains unverified
- Skin and proximity effect (they matter above about 150 mm²).
- Ampacity, installation method and grouping.
- Manufacturer AC resistance and reactance for the real cable.
- The permitted drop for your circuit type.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | IEC 60364-5-52; IEC 60228, IEC 60364-5-52:2009 + A1:2024 Ed 3.1; IEC 60228:2023 Ed 4.0 |
| Standard review state | Public-scope screened; licensed clause review still pending |
| Scope-screening note | AC wiring-system voltage-drop and conductor resistance context are relevant. The calculator uses a simplified R/X equation; verify the conductor operating temperature, reactance, circuit layout and permitted drop. |
| Cross-check test cases | 22 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; licensed clause-by-clause standard review; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Load current | 50 A |
| One-way length | 50 m |
| Conductor material | Copper |
| Conductor size given as | Cross-section (area) |
| Conductor cross-section | 10 mm² |
| AWG number | 8 |
| Wire diameter | 3.264 mm |
| Custom resistivity at 20 °C | 1.7241 × 10⁻⁸ Ω·m |
| Custom temperature coefficient (per °C) | 0 |
| Conductor temperature (°C) | 70 |
| Cable reactance | 0.08 Ω/km |
| Power factor | 0.9 |
| System voltage (line-to-line for three-phase) | 400 V |
| Circuit | Three-phase balanced |
| Load power factor | Lagging (inductive load, the usual case) |
| Conductors per phase in parallel | One (single set) |
- A = 10 mm² (given)
- ρ(70 °C) = 1.724e-8 × (1 + 0.00393 × 50) = 2.063e-8 Ω·m
- R = ρ L / A = 0.10314 Ω (one way)
- X = 0.08 Ω/km × 0.05 km = 0.004 Ω, sin φ = 0.4359
- Vd = √3 × 50 × (0.10314 × 0.9 + 0.004 × 0.4359) = 8.1903 V
- Vd % = 8.1903 / 400 × 100 = 2.048 %
Assumptions
- Balanced load, sinusoidal currents; choose leading only for a capacitive load, where the reactive term reduces the drop
- Resistance from material, size and temperature; skin and proximity effect are not included (they matter above about 150 mm²)
- Reactance is the per-conductor value you enter from the data sheet
- Single-phase uses the out-and-return path
- Parallel conductors (1 to 9 per phase) are identical, the same length and share the current equally; resistance and reactance are divided by the number in parallel, and mutual effects are ignored
For a resistive estimate set the power factor to 1 or the reactance to 0. Compare the result with the limit in your standard or specification.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Load current | A | greater than 0 A | |
| One-way length | m | greater than 0 m | |
| Conductor material | (choice) | Copper; Aluminium; Silver; Gold; Nickel; Nichrome; Custom (enter resistivity below) | |
| Conductor size given as | (choice) | Cross-section (area); AWG number; Wire diameter | |
| Conductor cross-section | mm² | greater than 0 mm² | |
| AWG number | (number) | -3 or more, up to 40 | |
| Wire diameter | mm | greater than 0 mm | |
| Custom resistivity at 20 °C | Ω·m | greater than 0 Ω·m | Starts at the Copper preset, 1.7241e-8 (aluminium preset 2.8264e-8). Pure-metal handbook values are lower: copper about 1.68e-8, aluminium about 2.65e-8. Carbon steel is about 1.43e-7. Take the value from your material data sheet |
| Custom temperature coefficient (per °C) | (number) | 0 or more, up to 0.01 | 0 uses the resistivity as given at every temperature. Used only when material is Custom |
| Conductor temperature (°C) | (number) | -50 or more, up to 250 | Operating temperature of the conductor: 70 °C for PVC, 90 °C for XLPE at full load. 20 °C gives the cold value, which understates the drop of a loaded cable. |
| Cable reactance | Ω/km | 0 Ω/km or more | Per conductor, from the cable data sheet. About 0.08 Ω/km is commonly quoted for LV multicore cable (indicative only). Use 0 for a resistive estimate. |
| Power factor | (number) | greater than 0, up to 1 | Rough starting point only. Resistive heating and incandescent loads are 1.0; a fully loaded induction motor is typically 0.8 to 0.88 and falls sharply when lightly loaded; discharge lighting depends on its ballast or driver. For real work use the nameplate or a measured value. |
| System voltage (line-to-line for three-phase) | V | greater than 0 V | |
| Circuit | (choice) | Single-phase (out and return); Three-phase balanced | |
| Load power factor | (choice) | Lagging (inductive load, the usual case); Leading (capacitive load) | |
| Conductors per phase in parallel | (choice) | One (single set); 2 in parallel; 3 in parallel; 4 in parallel; 5 in parallel; 6 in parallel; 7 in parallel; 8 in parallel; 9 in parallel |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Voltage drop | V | Shown to 3 decimal places | |
| Drop as % of system voltage | (number) | Shown to 2 decimal places | |
| Conductor resistance (one way, at temperature) | Ω | Shown to 5 decimal places | |
| Cross-section used | mm² | Shown to 4 decimal places | |
| Resistivity used (at conductor temperature) | Ω·m | Shown to 5 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
Typical values
| One-way length (m) | Voltage drop (V) | Drop as % of system voltage |
|---|---|---|
| 10 | 1.638 | 0.41 |
| 25 | 4.095 | 1.02 |
| 50 | 8.19 | 2.05 |
| 100 | 16.381 | 4.1 |
| 150 | 24.571 | 6.14 |
| 200 | 32.761 | 8.19 |
Other inputs are the same as in the worked example above.
Standards and further reading
- IEC 60364-5-52 (selection and erection of wiring systems, current-carrying capacity)
- IEC 60364-4-43 (protection against overcurrent, short-circuit withstand k factors)
- IEC 60228 (conductor sizes)
- IEC 60287 (calculation of cable current rating)
Ampacity and grouping factors come from your cable data sheet or your licensed copy of the standard; see STANDARDS.md for the method constants Elecmetric does use. These are named as background reading. Elecmetric does not embed clause text or rating tables, and the reviewer record for this calculator is separate from this list.
Frequently asked questions
What do I need to enter?
Enter load current, one-way length, conductor material, conductor size given as, conductor cross-section, aWG number, wire diameter, custom resistivity at 20 °C, conductor temperature (°C), cable reactance, power factor, system voltage (line-to-line for three-phase), circuit and load power factor. Change the unit of a value with its selector and the result stays the same.
How is this different from the voltage drop calculator for DC?
An AC circuit has reactance as well as resistance, and the power factor decides how much of each counts. The formula uses R cos φ plus X sin φ; the DC calculator uses resistance alone.
Why is the single-phase drop calculated over the out-and-return path?
Current flows out on one conductor and back on the other, so the drop is over twice the one-way length. Three-phase uses √3 with the line-to-line voltage instead.
When is the load power factor leading?
Only for a capacitive load. A leading current makes the reactive term reduce the drop. For the usual inductive load keep lagging.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 22 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Voltage Drop Formulas for Cables: Voltage drop formulas for single-phase and three-phase cables, percentage drop
- AC Circuit Formulas: Reactance and Impedance: AC circuit formulas: RMS and peak, frequency and period, inductive and capacitive reactance
- Conductor Resistance Formulas and Temperature: Conductor resistance formulas: resistance from length, area and resistivity, correction for temperature
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