Use the tabs in the calculator to solve either (1) Ohm’s law (solve for current, voltage, or resistance when the other two are known) or (2) Pouillet’s law (calculate the resistance of a uniform wire from its resistivity, length, cross‑sectional area/diameter/AWG, and temperature).

Ohm’s Law & Pouillet’s Law Calculator

Ohm’s Law Wire Resistance (Pouillet)
Resistance (Ω): —
Resistance per meter (Ω/m): —
Resistance per foot (Ω/ft): —
Area (m²): —
Resistivity at T (Ω·m): —
Conductivity at T (S/m): —

Pouillet's Law Formula

The following formula is used to calculate the electrical resistance of a uniform conductor (such as a wire) from its material resistivity and geometry (Pouillet's law).

R = \frac{\rho L}{A}

Variables:

  • R is the electrical resistance (Ohms, Ω)
  • ρ (rho) is the material resistivity (Ohm-meters, Ω·m)
  • L is the conductor length (meters, m)
  • A is the cross-sectional area (square meters, m²)

To calculate the resistance, multiply the material resistivity by the wire length and divide by the cross-sectional area. If you also know the applied voltage, you can then find the current using Ohm’s law: I = V / R.

What is Pouillet's Law?

Pouillet's law, attributed to French physicist Claude-Servais-Mathias Pouillet, describes how the resistance of a uniform conductor depends on its material and geometry. In its common form, it states that resistance is directly proportional to length and inversely proportional to cross-sectional area: R = ρL/A. This is related to (but not the same as) Ohm’s law; Ohm’s law relates voltage, current, and resistance (V = IR).

How to Calculate Pouillet's Law?

The following steps outline how to calculate wire resistance using Pouillet's law.

  1. Determine the material resistivity ρ (typically tabulated at 20°C) in Ω·m.
  2. If needed, adjust resistivity for temperature using an appropriate temperature coefficient for the material (many metals can be approximated with ρ(T) ≈ ρ20[1 + α(T − 20°C)] over a limited temperature range).
  3. Measure the conductor length L and convert it to meters (m).
  4. Determine the conductor cross-sectional area A and convert it to square meters (m²). (If you have diameter or AWG, first convert to area.)
  5. Compute resistance using R = ρL/A.
  6. If you also know voltage V, you can compute current with Ohm’s law: I = V / R.

Example Problem:

Use the following variables as an example problem to test your knowledge (at 20°C):

resistivity (ρ) = 1.68×10−8 Ω·m (copper)

length (L) = 100 m

area (A) = 1 mm² = 1×10−6 m²

Using Pouillet’s law: R = ρL/A = (1.68×10−8)(100) / (1×10−6) = 1.68 Ω.