Understanding the PCB trace resistance calculator — concept and principle
This calculator finds the DC resistance of a copper trace on a printed circuit board from its length, width, copper thickness and temperature, and gives the voltage drop, power loss, sheet resistance and cross-section. Electronics designers use it for power traces, sense lines and current paths.
How it is calculated
R = ρ L ÷ (w × t)
ρ(T) = 1.68 × 10⁻⁸ Ω·m × [1 + 0.0039 × (T − 20 °C)]
Voltage drop = R × I; power loss = I² × R; sheet resistance = ρ ÷ t
- L and w in mm, t in µm (35 µm ≈ 1 oz/ft² copper), T in °C.
The principle
A trace is a long, flat rectangular conductor. Its resistance grows with length and falls with cross-sectional area, scaled by copper's resistivity. Resistivity rises with temperature, by about 0.39% per °C for copper. The sheet resistance is handy: any square piece of the copper layer, whatever its size, has the same resistance, so a trace's resistance is simply its number of squares (length ÷ width) times the sheet resistance.
Worked example
Default inputs: L = 100 mm, w = 0.25 mm, t = 35 µm, 25 °C, 1 A.
- ρ = 1.68 × 10⁻⁸ × (1 + 0.0039 × 5) = 17.13 nΩ·m.
- Area = 0.25 mm × 0.035 mm = 0.0088 mm².
- R = 1.713 × 10⁻⁸ × 0.1 ÷ (8.75 × 10⁻⁹) = 195.74 mΩ = 0.1957 Ω.
- At 1 A: drop 195.74 mV, loss 195.74 mW.
- Sheet resistance = 0.489 mΩ per square; the trace is 400 squares long.
| Trace width (mm) | Trace resistance (mΩ) |
|---|---|
| 0.0625 | 782.98 |
| 0.125 | 391.49 |
| 0.188 | 260.99 |
| 0.25 | 195.74 |
| 0.312 | 156.6 |
| 0.375 | 130.5 |
| 0.5 | 97.87 |
How to read the result
A drop of about 0.2 V can matter for low-voltage rails and sensing. Widening the trace or using thicker copper reduces resistance proportionally. Heating from I²R raises the temperature and resistance further, so high-current traces are usually sized with a temperature-rise standard.
Common mistakes
- Entering thickness in mm instead of µm.
- Forgetting the return path, which doubles the loop resistance.
- Ignoring plating, which can add thickness on outer layers.
- Using DC resistance at high frequency, where skin effect increases it.
Frequently asked questions
How thick is 1 oz copper?
About 35 µm.
What is sheet resistance?
The resistance of any square of the copper layer, ρ ÷ t.
How much does temperature matter?
Copper's resistance rises about 0.39% per °C.
Does width or thickness matter more?
Both equally; resistance depends on their product.
Sources: OpenStax, University Physics Volume 2 (2016), section 9.3 "Resistivity and Resistance"