Trace Resistance
R = ρ × L / A (copper)
Quick answer
This calculator solves R = ρ × L / A for Resistance. With Length (cm) 10 cm, Area (cm²) 10 cm², the result is 0.001724 mΩ. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Trace resistance follows the standard resistance formula with copper resistivity (1.724 × 10⁻⁶ Ω·cm at 20°C). Even though copper is an excellent conductor, long and thin traces can have non-trivial resistance. For 1 oz copper (35μm thick), a 10 mil wide trace has about 0.5Ω per inch (roughly 0.2Ω per cm). This resistance causes voltage drops and power losses that matter for power delivery, current sensing, and low-voltage circuits. The sheet resistance of 1 oz copper is approximately 0.5 mΩ/square.
Variables
- R — Trace resistance (Ω)
- ρ — Copper resistivity (1.724 × 10⁻⁶ Ω·cm)
- L — Trace length (cm)
- A — Cross-sectional area (cm²)
Practical Notes
Copper resistivity increases with temperature: approximately +0.39% per °C. At 100°C, resistivity is about 30% higher than at 20°C. For precision current sense traces, use copper pour with defined geometry and account for the temperature coefficient. Plated vias also add resistance: a typical via adds 0.5-3 mΩ.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| R | Resistance | Ω | mΩ, Ω, kΩ, MΩ |
| L | Length (cm) | cm | cm |
| A | Area (cm²) | cm² | cm² |
Step by step
- 1. What you know: Length (cm) 10 cm, Area (cm²) 10 cm²
- 2. The relation: R = ρ × L / A
- 3. Substitute: L = 10 cm, A = 10 cm²
- 4. Result: Resistance = 0.001724 mΩ
Nearest standard component values
| Series | Nearest value | Error |
|---|---|---|
| E12 | 0.0018 mΩ | 4.4% |
| E24 | 0.0018 mΩ | 4.4% |
Worked examples
Minimum range
Given: Length (cm) 0.1 cm, Area (cm²) 0.1 cm²
Result: Resistance = 0.001724 mΩ
Low range
Given: Length (cm) 1 cm, Area (cm²) 1 cm²
Result: Resistance = 0.001724 mΩ
Typical
Given: Length (cm) 10 cm, Area (cm²) 10 cm²
Result: Resistance = 0.001724 mΩ
High range
Given: Length (cm) 100 cm, Area (cm²) 100 cm²
Result: Resistance = 0.001724 mΩ
Maximum range
Given: Length (cm) 1000 cm, Area (cm²) 1000 cm²
Result: Resistance = 0.001724 mΩ
Solving for each variable
Solve for Resistance
Length (cm) 0.1 cm, Area (cm²) 0.1 cm² → 0.001724 mΩ
Solve for Length (cm)
Resistance 1 Ω, Area (cm²) 0.1 cm² → 58000 cm
Solve for Area (cm²)
Resistance 1 Ω, Length (cm) 0.1 cm → 1.72 × 10⁻⁷ cm²
How Resistance changes with Length (cm)
| Length (cm) (input) | Resistance (result) |
|---|---|
| 1 cm | 1.72 × 10⁻⁴ mΩ |
| 2.5 cm | 4.31 × 10⁻⁴ mΩ |
| 5 cm | 8.62 × 10⁻⁴ mΩ |
| 7.5 cm | 0.001293 mΩ |
| 10 cm | 0.001724 mΩ |
| 15 cm | 0.002586 mΩ |
| 20 cm | 0.003448 mΩ |
| 40 cm | 0.006896 mΩ |
| 70 cm | 0.01207 mΩ |
| 100 cm | 0.01724 mΩ |
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<p><a href="https://vbatpower.com/formulas/trace-resistance/">Trace Resistance</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Trace Resistance?
Use R = ρ × L / A. With Length (cm) 10 cm, Area (cm²) 10 cm², Resistance works out to 0.001724 mΩ.
What is the formula for Trace Resistance?
The formula is R = ρ × L / A. Trace resistance follows the standard resistance formula with copper resistivity (1.724 × 10⁻⁶ Ω·cm at 20°C).
How do you find Length (cm) when you know the other values?
Rearrange for Length (cm): with Resistance 1 Ω, Area (cm²) 0.1 cm², Length (cm) is 58000 cm.
How do you find Area (cm²) when you know the other values?
Rearrange for Area (cm²): with Resistance 1 Ω, Length (cm) 0.1 cm, Area (cm²) is 1.72 × 10⁻⁷ cm².
Related Concepts
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