Pouillets Law Calculator

Calculate voltage, current, resistance, power, and wire resistance from material, length, temperature, and cross-sectional size inputs.

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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).

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.