# Wire Voltage Drop Calculator

> Computes the resistance of a copper or aluminium conductor from its AWG gauge or cross-section and one-way length, then the voltage drop, percentage drop, voltage at the load and power lost for DC, single-phase or three-phase circuits.

- Calculator id: `wire-voltage-drop` · Category: Engineering & Automotive (`engineering`) · Tool name: `calculate_wire_voltage_drop`
- Canonical page: https://tttkmbb.com/engineering/wire-voltage-drop · This document: https://tttkmbb.com/engineering/wire-voltage-drop.md · JSON definition: https://tttkmbb.com/engineering/wire-voltage-drop.json

## Purpose

Computes the resistance of a copper or aluminium conductor from its AWG gauge or cross-section and one-way length, then the voltage drop, percentage drop, voltage at the load and power lost for DC, single-phase or three-phase circuits.

**Use when:** You are sizing a cable run (solar, automotive, 12 V LED, branch circuit) and need to know whether the voltage drop stays within a limit such as 3 %.

**Do not use when:** You need ampacity (heating limits, which depend on insulation and installation method, not covered here), or the conductor is not copper or aluminium.

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `voltage_v` | number | V | required | Supply voltage (line-to-line for three-phase). (> 0, max 100000) |
| `current_a` | number | A | required | Current carried by the conductor in amperes. (min 0, max 100000) |
| `length_m` | number | m | required | Distance from source to load in metres (1 ft = 0.3048 m); the return conductor is accounted for automatically. (> 0, max 100000) |
| `awg` | integer |  | optional | American Wire Gauge number. Use 0 for 1/0, −1 for 2/0, −2 for 3/0, −3 for 4/0. Give either awg or cross_section_mm2. (min -3, max 40) |
| `cross_section_mm2` | number | mm² | optional | Conductor cross-sectional area in mm² (metric cable sizes 1.5, 2.5, 4, 6, 10 …). Give either awg or cross_section_mm2. (> 0, max 2000) |
| `material` | enum: copper \| aluminium |  | optional, default "copper" | Conductor material; resistivity at 20 °C. |
| `phase` | enum: dc \| single_phase \| three_phase |  | optional, default "dc" | DC and single-phase count the outgoing and return conductor (×2); balanced three-phase uses ×√3. |
| `conductor_temperature_c` | number | °C | optional, default 20 | Operating temperature of the conductor; resistance rises about 0.4 % per °C above 20 °C (use 75 for a fully loaded cable). (min -50, max 200) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `conductor_diameter_mm` | number | mm | Bare conductor diameter (from AWG or derived from the area). |
| `cross_section_mm2` | number | mm² | Conductor area. |
| `resistance_per_km_ohm` | number | Ω/km | ρ / A at the given temperature, per conductor. |
| `conductor_resistance_ohm` | number | Ω | Resistance of one conductor over length_m. |
| `voltage_drop_v` | number | V | 2 × I × R (DC, single-phase) or √3 × I × R (three-phase). |
| `voltage_drop_percent` | number | % | voltage_drop_v / voltage_v × 100. |
| `voltage_at_load_v` | number | V | voltage_v − voltage_drop_v. |
| `power_loss_w` | number | W | 2 × I² × R (DC, single-phase) or 3 × I² × R (three-phase). |
| `assessment` | string |  | Comparison with the common 3 % (branch circuit) and 5 % (total) voltage-drop recommendations (NEC informational note). |

## Formula

`d_mm = 0.127 × 92^((36 − awg) / 39); A = π d² / 4; R = ρ × (1 + α (T − 20)) × length_m / A; voltage_drop_v = k × current_a × R with k = 2 (dc, single_phase) or √3 (three_phase); ρ_copper = 1.724e-8 Ω·m, ρ_aluminium = 2.65e-8 Ω·m`

Resistive (DC) drop only; conductor reactance and power factor are ignored, which is accurate for cables up to about 25 mm² / 4 AWG at 50–60 Hz. The 3 %/5 % limits follow NEC 210.19(A) and 215.2(A) informational notes and similar rules in IEC 60364-5-52.

## Data Sources

- Wikipedia – American wire gauge — https://en.wikipedia.org/wiki/American_wire_gauge (reference, retrieved 2026-09-24)
- Wikipedia – Electrical resistivity and conductivity — https://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity (reference, retrieved 2026-09-24)
- NFPA 70 – National Electrical Code (voltage drop informational notes 210.19(A), 215.2(A)) — https://www.nfpa.org/codes-and-standards/nfpa-70-standard-development/70 (standard, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/wire-voltage-drop?voltage_v=…&current_a=…&length_m=…`
- `POST https://tttkmbb.com/api/v1/calculate/wire-voltage-drop` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/wire-voltage-drop · OpenAPI operationId `calculate_wire_voltage_drop` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "wire-voltage-drop", "inputs": {…}}`

## Example

- 12 V, 10 A, 5 m of 12 AWG copper: inputs `{"voltage_v":12,"current_a":10,"length_m":5,"awg":12}` → `{"conductor_diameter_mm":2.053,"cross_section_mm2":3.309,"resistance_per_km_ohm":5.2104,"conductor_resistance_ohm":0.02605,"voltage_drop_v":0.521,"voltage_drop_percent":4.34,"voltage_at_load_v":11.479,"power_loss_w":5.21}`
- 230 V single-phase, 16 A, 30 m of 2.5 mm² copper: inputs `{"voltage_v":230,"current_a":16,"length_m":30,"cross_section_mm2":2.5,"phase":"single_phase"}` → `{"resistance_per_km_ohm":6.896,"conductor_resistance_ohm":0.20688,"voltage_drop_v":6.62,"voltage_drop_percent":2.88,"voltage_at_load_v":223.38,"power_loss_w":105.923}`

```
GET https://tttkmbb.com/api/v1/calculate/wire-voltage-drop?voltage_v=12&current_a=10&length_m=5&awg=12
```

## Limitations

You need ampacity (heating limits, which depend on insulation and installation method, not covered here), or the conductor is not copper or aluminium. Resistive (DC) drop only; conductor reactance and power factor are ignored, which is accurate for cables up to about 25 mm² / 4 AWG at 50–60 Hz. The 3 %/5 % limits follow NEC 210.19(A) and 215.2(A) informational notes and similar rules in IEC 60364-5-52. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Is the length one-way or round trip?**

Enter the one-way distance from source to load; the calculator doubles it for DC and single-phase circuits and uses √3 for balanced three-phase.

**How much drop is acceptable?**

The NEC recommends at most 3 % on a branch or feeder and 5 % overall for efficiency; low-voltage systems (12 V solar or automotive) often need thicker cable than the current alone suggests to stay under 3 %.

## Related

- [Ohm's Law Calculator](https://tttkmbb.com/physics/ohms-law.md) — V = I·R for the conductor resistance.
- [Electric Power Calculator](https://tttkmbb.com/physics/electric-power.md) — Load current from power and voltage.
- [LED Resistor Calculator](https://tttkmbb.com/engineering/led-resistor.md) — Low-voltage LED circuits where drop matters.