Choose a solve mode for voltage, current or resistance, or estimate uniform-wire DC resistance from resistivity, length, temperature and cross-section. Power is a secondary Ohm’s-law result.

Uniform conductor/DC resistance. Material values are approximate examples near 20°C; use supplier data for your alloy and temperature range. This does not determine safe current capacity.

Temperature correction (blank = 20°C)

Linear approximation only. Verify the coefficient and usable range for the actual material.

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 = (ρ 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.