Maximum Cable Length
L = Vdrop / (2 × I × R/m)
Quick answer
This calculator solves L = Vdrop_max / (2 × I × R_per_m) for Max One-Way Length. With Max Voltage Drop 12 V, Load Current 2 A, Resistance per meter (Ω/m) 0.1 Ω/m, the result is 30 m. It solves in 4 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
This formula calculates the maximum one-way cable run before the round-trip voltage drop exceeds the specified limit. It is the inverse of the cable voltage drop formula and is essential for planning DC power distribution, LED lighting installations, security camera wiring, and any system where power must be delivered over distance. The result tells you the farthest you can place a load from its power source while maintaining adequate voltage. If the required distance exceeds this limit, options include using thicker wire, raising the source voltage, or placing power supplies closer to loads.
Variables
- L — Maximum one-way cable length (m)
- Vdrop_max — Maximum acceptable voltage drop (V)
- I — Expected load current (A)
- R_per_m — Wire resistance per meter (Ω/m)
Practical Notes
For a 12V system allowing 3% drop (0.36V) at 5A using 16 AWG wire (0.0132 Ω/m): max length = 0.36 / (2 × 5 × 0.0132) = 2.73m. This shows why low-voltage DC systems are limited to short cable runs. PoE (Power over Ethernet) works up to 100m by using 48V and low currents. For longer distances, consider 24V or 48V systems with local DC-DC converters.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| L | Max One-Way Length | m | mm, cm, m, km |
| Vdrop | Max Voltage Drop | V | pV, nV, µV, mV, V, kV |
| I | Load Current | A | pA, nA, µA, mA, A, kA |
| R | Resistance per meter (Ω/m) | Ω/m | Ω/m |
Step by step
- 1. What you know: Max Voltage Drop 12 V, Load Current 2 A, Resistance per meter (Ω/m) 0.1 Ω/m
- 2. The relation: L = Vdrop_max / (2 × I × R_per_m)
- 3. Substitute: Vdrop = 12 V, I = 2 A, R = 0.1 Ω/m
- 4. Result: Max One-Way Length = 30 m
Related quantities from the same inputs
- P = V × I = 24 W
Worked examples
Minimum range
Given: Max Voltage Drop 0.33 V, Load Current 2 mA, Resistance per meter (Ω/m) 1 × 10⁻⁴ Ω/m
Result: Max One-Way Length = 825 km
Low range
Given: Max Voltage Drop 3.3 V, Load Current 20 mA, Resistance per meter (Ω/m) 0.001 Ω/m
Result: Max One-Way Length = 82.5 km
Typical
Given: Max Voltage Drop 12 V, Load Current 2 A, Resistance per meter (Ω/m) 0.1 Ω/m
Result: Max One-Way Length = 30 m
High range
Given: Max Voltage Drop 0.23 kV, Load Current 100 A, Resistance per meter (Ω/m) 10 Ω/m
Result: Max One-Way Length = 11.5 cm
Maximum range
Given: Max Voltage Drop 2.3 kV, Load Current 1 kA, Resistance per meter (Ω/m) 100 Ω/m
Result: Max One-Way Length = 11.5 mm
Solving for each variable
Solve for Max One-Way Length
Max Voltage Drop 0.33 V, Load Current 2 mA, Resistance per meter (Ω/m) 1 × 10⁻⁴ Ω/m → 825 km
Solve for Max Voltage Drop
Max One-Way Length 1 mm, Load Current 2 mA, Resistance per meter (Ω/m) 1 × 10⁻⁴ Ω/m → 0.4 nV
Solve for Load Current
Max One-Way Length 1 mm, Max Voltage Drop 0.33 V, Resistance per meter (Ω/m) 1 × 10⁻⁴ Ω/m → 1650 kA
Solve for Resistance per meter (Ω/m)
Max One-Way Length 1 mm, Max Voltage Drop 0.33 V, Load Current 2 mA → 82500 Ω/m
How Max One-Way Length changes with Max Voltage Drop
| Max Voltage Drop (input) | Max One-Way Length (result) |
|---|---|
| 1.2 V | 3 m |
| 3 V | 7.5 m |
| 6 V | 15 m |
| 9 V | 22.5 m |
| 12 V | 30 m |
| 18 V | 45 m |
| 24 V | 60 m |
| 48 V | 120 m |
| 84 V | 0.21 km |
| 120 V | 0.3 km |
The same result in other units
| Unit | Value |
|---|---|
| mm | 30000 |
| cm | 3000 |
| m | 30 |
| km | 0.03 |
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<p><a href="https://vbatpower.com/formulas/max-cable-length/">Maximum Cable Length</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Maximum Cable Length?
Use L = Vdrop_max / (2 × I × R_per_m). With Max Voltage Drop 12 V, Load Current 2 A, Resistance per meter (Ω/m) 0.1 Ω/m, Max One-Way Length works out to 30 m.
How do you calculate maximum length?
Rearrange for Max One-Way Length: with Max Voltage Drop 3.3 V, Load Current 20 mA, Resistance per meter (Ω/m) 0.001 Ω/m, Max One-Way Length is 82.5 km.
What is the formula for Maximum Cable Length?
The formula is L = Vdrop_max / (2 × I × R_per_m). This formula calculates the maximum one-way cable run before the round-trip voltage drop exceeds the specified limit.
How do you find Max Voltage Drop when you know the other values?
Rearrange for Max Voltage Drop: with Max One-Way Length 1 mm, Load Current 2 mA, Resistance per meter (Ω/m) 1 × 10⁻⁴ Ω/m, Max Voltage Drop is 0.4 nV.
How do you find Load Current when you know the other values?
Rearrange for Load Current: with Max One-Way Length 1 mm, Max Voltage Drop 0.33 V, Resistance per meter (Ω/m) 1 × 10⁻⁴ Ω/m, Load Current is 1650 kA.
What units does Maximum Cable Length use?
Max One-Way Length is shown in mm, cm, m, km. 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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