Cable Voltage Drop
Vdrop = 2 × I × R/m × L
Quick answer
This calculator solves Vdrop = 2 × I × R × L for Voltage Drop. With Current 2 A, Resistance per meter (Ω/m) 0.1 Ω/m, One-Way Length 1 m, the result is 0.4 V. It solves in 4 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The total voltage drop in a cable includes both the outgoing and return conductors, hence the factor of 2. This round-trip drop is the voltage difference between what leaves the source and what arrives at the load. Excessive voltage drop causes devices to malfunction, reduces motor torque, dims LED lighting, and wastes energy as heat in the cable. Industry standards typically require less than 3% voltage drop for branch circuits and less than 5% for combined feeder and branch circuits. For 12V DC systems, even a 0.5V drop represents a 4% loss.
Variables
- Vdrop — Total round-trip voltage drop (V)
- I — Load current (A)
- R — Resistance per meter of one conductor (Ω/m)
- L — One-way cable length (m)
Practical Notes
Resistance per meter for common copper wire: 14 AWG = 0.0083 Ω/m, 16 AWG = 0.0132 Ω/m, 18 AWG = 0.021 Ω/m, 22 AWG = 0.053 Ω/m. For long LED strip runs, inject power at both ends or at intervals. For solar panel wiring, voltage drop directly reduces energy harvest. Use thicker wire or higher voltage (with DC-DC conversion at the load) for long runs.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Vdrop | Voltage Drop | V | pV, nV, µV, mV, V, kV |
| I | Current | A | pA, nA, µA, mA, A, kA |
| R | Resistance per meter (Ω/m) | Ω/m | Ω/m |
| L | One-Way Length | m | mm, cm, m, km |
Step by step
- 1. What you know: Current 2 A, Resistance per meter (Ω/m) 0.1 Ω/m, One-Way Length 1 m
- 2. The relation: Vdrop = 2 × I × R × L
- 3. Substitute: I = 2 A, R = 0.1 Ω/m, L = 1 m
- 4. Result: Voltage Drop = 0.4 V
Related quantities from the same inputs
- P = V × I = 0.8 W
Worked examples
Minimum range
Given: Current 2 mA, Resistance per meter (Ω/m) 1 × 10⁻⁴ Ω/m, One-Way Length 1 mm
Result: Voltage Drop = 0.4 nV
Low range
Given: Current 20 mA, Resistance per meter (Ω/m) 0.001 Ω/m, One-Way Length 10 mm
Result: Voltage Drop = 0.4 µV
Typical
Given: Current 2 A, Resistance per meter (Ω/m) 0.1 Ω/m, One-Way Length 1 m
Result: Voltage Drop = 0.4 V
High range
Given: Current 100 A, Resistance per meter (Ω/m) 10 Ω/m, One-Way Length 100 m
Result: Voltage Drop = 200 kV
Maximum range
Given: Current 1 kA, Resistance per meter (Ω/m) 100 Ω/m, One-Way Length 1 km
Result: Voltage Drop = 200000 kV
Solving for each variable
Solve for Voltage Drop
Current 2 mA, Resistance per meter (Ω/m) 1 × 10⁻⁴ Ω/m, One-Way Length 1 mm → 0.4 nV
Solve for Current
Voltage Drop 0.33 V, Resistance per meter (Ω/m) 1 × 10⁻⁴ Ω/m, One-Way Length 1 mm → 1650 kA
Solve for Resistance per meter (Ω/m)
Voltage Drop 0.33 V, Current 2 mA, One-Way Length 1 mm → 82500 Ω/m
Solve for One-Way Length
Voltage Drop 0.33 V, Current 2 mA, Resistance per meter (Ω/m) 1 × 10⁻⁴ Ω/m → 825 km
How Voltage Drop changes with Current
| Current (input) | Voltage Drop (result) |
|---|---|
| 0.2 A | 40 mV |
| 0.5 A | 100 mV |
| 1 A | 0.2 V |
| 1.5 A | 0.3 V |
| 2 A | 0.4 V |
| 3 A | 0.6 V |
| 4 A | 0.8 V |
| 8 A | 1.6 V |
| 14 A | 2.8 V |
| 20 A | 4 V |
The same result in other units
| Unit | Value |
|---|---|
| µV | 400000 |
| mV | 400 |
| V | 0.4 |
| kV | 0.0004 |
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<p><a href="https://vbatpower.com/formulas/cable-voltage-drop/">Cable Voltage Drop</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Cable Voltage Drop?
Use Vdrop = 2 × I × R × L. With Current 2 A, Resistance per meter (Ω/m) 0.1 Ω/m, One-Way Length 1 m, Voltage Drop works out to 0.4 V.
What is the formula for Cable Voltage Drop?
The formula is Vdrop = 2 × I × R × L. The total voltage drop in a cable includes both the outgoing and return conductors, hence the factor of 2.
How do you find Current when you know the other values?
Rearrange for Current: with Voltage Drop 0.33 V, Resistance per meter (Ω/m) 1 × 10⁻⁴ Ω/m, One-Way Length 1 mm, Current is 1650 kA.
How do you find Resistance per meter (Ω/m) when you know the other values?
Rearrange for Resistance per meter (Ω/m): with Voltage Drop 0.33 V, Current 2 mA, One-Way Length 1 mm, Resistance per meter (Ω/m) is 82500 Ω/m.
What units does Cable Voltage Drop use?
Voltage Drop is shown in µV, mV, V, kV. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Wire & Cable formulas →Need more features?
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