Sheet Resistance Calculator - Thin Film and Trace

Calculate sheet resistance from resistivity and thickness, trace resistance from squares, or a corrected four-point-probe result with unit conversions.

Sheet Resistance Formula

Rₛ = ρ / t

Variables:

Rₛ is the sheet resistance (Ω/□, ohms per square), not resistance per unit area
ρ is the film resistivity (Ω·m after unit conversion)
t is the uniform film thickness (m after unit conversion)

For a uniform isotropic ohmic film, divide the resistivity by its thickness: Rₛ = ρ/t. Use the resistivity appropriate to that film and its conditions; the inverse forms are ρ = Rₛt and t = ρ/Rₛ. See the NIST electrical metrology discussion of sheet resistance.

How to Calculate Sheet Resistance?

The following steps outline how to calculate the Sheet Resistance.

First, determine the resistivity.
Next, determine the thickness.
Next, use Rₛ = ρ/t after converting resistivity and thickness to compatible units.
Finally, calculate the Sheet Resistance.
After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge.

Hypothetical film resistivity ρ = 6 μΩ·cm = 6 × 10⁻⁸ Ω·m.

Hypothetical film thickness t = 0.45 μm = 4.5 × 10⁻⁷ m. Then Rₛ = (6 × 10⁻⁸)/(4.5 × 10⁻⁷) ≈ 0.13333333 Ω/□. The numbers require these stated units; they do not identify a particular material.

For a uniform rectangular trace with full-width end contacts, R = RₛL/W; optional current gives V = IR and P = I²R, excluding contacts and self-heating. Four-point mode uses Rₛ = [π/ln(2)](V/I)C, with outer current probes and inner voltage probes. C multiplies the ideal result; 1 assumes equal spacing on a sufficiently thin, laterally large uniform sheet. Keithley’s primary measurement guidance describes geometry corrections. Enter offset-corrected magnitudes only after confirming expected passive-sample polarity; an unexpected negative reading must be investigated, not silently converted. A zero voltage reading alone does not prove zero material resistance.

FAQs

What is resistivity and how is it measured?

Resistivity is a measure of a material’s ability to resist electric current. It is measured in ohm-meters (Ω·m) and can be determined by the material’s inherent properties, its temperature, and the presence of impurities.

Why is thickness important in calculating sheet resistance?

Thickness is crucial because sheet resistance is directly proportional to the resistivity of the material and inversely proportional to its thickness. A thinner material will have higher sheet resistance, assuming constant resistivity.

Can sheet resistance be used to measure the quality of conductive materials?

Sheet resistance characterizes lateral conduction at a given film thickness; lower values can reflect lower resistivity, greater thickness or both. It is not a material-quality score by itself. Compare thickness, uniformity, temperature and the intended application; thin-film resistivity can differ from a bulk reference.

How does temperature affect resistivity and sheet resistance?

Ordinary metals often increase in resistivity with temperature, while semiconductors can show the opposite trend depending on doping and temperature range. Sheet resistance also depends on thickness. Use material-specific data rather than a universal temperature rule; the calculator applies no temperature correction. OpenStax’s resistance and resistivity chapter explains the differing temperature coefficients.