PCB Trace Resistance Calculator

The resistance of a printed circuit board trace depends on the geometry of the trace, the resistivity of the conductive material (typically copper), and the operating temperature. The core formula used is:

Resistance = [ (Rho × Length) / (Trace Thickness × Trace Width) ] × [ 1 + Alpha × (Ambient Temperature - 25) ]

Where Rho is the bulk resistivity of copper at 25°C, and Alpha is the temperature coefficient of resistance. Furthermore, the voltage drop across the trace under a specific operating load is determined by Ohm's Law: Voltage Drop = Current × Resistance.

Let us walk through a practical scenario. Imagine you are designing a power distribution line on a standard 1 oz copper PCB. You have the following parameters:

• Trace Length = 100 mm (0.1 meters)
• Trace Width = 1.5 mm
• Trace Thickness = 0.035 mm (standard for 1 oz copper)
• Ambient Temperature = 45°C
• Current = 2.0 Amps
• Copper Resistivity (Rho) = 1.72 × 10^-8 Ω·m
• Temperature Coefficient (Alpha) = 0.00393 /°C

First, calculate the base cross-sectional area: 1.5 mm × 0.035 mm = 0.0525 mm². Next, compute the resistance at 25°C, and scale it for the elevated operating temperature of 45°C using the temperature coefficient. The resulting trace resistance comes out to approximately 0.0354 Ω. Finally, applying Ohm's Law for a 2 Amp current, the expected voltage drop across the trace is 2 A × 0.0354 Ω = 0.0708 Volts, ensuring minimal power loss.

Keep these guidelines in mind when designing high-current traces on your circuit boards:

• Account for Thermal Rise: Higher current causes Joule heating, which increases trace resistance and can lead to thermal runaway if traces are too narrow.
• Use Wider Traces for Power Rails: For high-current lines (such as motor drivers or power supplies), increase trace width or use heavier copper weights (e.g., 2 oz instead of 1 oz) to keep voltage drops negligible.
• Verify Operating Temperatures: Always input realistic operational temperatures rather than room temperature if your device operates in an enclosed, hot environment.