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Resistivity calculator

A-level Electricity

The resistance of a wire from its resistivity, length and cross-sectional area.

R = ρ L / A

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

RResistance to find 0.170 Ω

ρResistivity Ω m

LLength of the wire

ACross-sectional area

Significant figures

Working

Write the equation
R = ρ L / A
Substitute the values
R = (1.7 × 10⁻⁸) × 10 ÷ (1 × 10⁻⁶)
Calculate
R = 0.17 Ω
Give the answer to 3 significant figures
R = 0.170 Ω

Worked example

Find R, the resistance. Given: resistivity ρ = 1.70 × 10⁻⁸ Ω m; length of the wire L = 10.0 m; cross-sectional area A = 1.00 × 10⁻⁶ m².

Write the equation
R = ρ L / A
Substitute the values
R = (1.7 × 10⁻⁸) × 10 ÷ (1 × 10⁻⁶)
Calculate
R = 0.17 Ω
Give the answer to 3 significant figures
R = 0.170 Ω

Symbols and units

Symbol	Quantity	SI unit
R	Resistance	Ω
ρ	Resistivity	Ω m
L	Length of the wire	m
A	Cross-sectional area	m²

Resistivity: rearranged

To find resistance: R = ρ L / A
To find resistivity: ρ = R A / L
To find length of the wire: L = R A / ρ
To find cross-sectional area: A = ρ L / R

Exam tip

Cross-sectional area is π(d/2)² for a round wire. Convert mm² to m² by multiplying by 10⁻⁶.

Common questions

What is the formula for resistivity?

The equation is R = ρ L / A, where R is the resistance (Ω); ρ is the resistivity (Ω m); L is the length of the wire (m); A is the cross-sectional area (m²).

What units should I use for resistivity?

In SI units: resistance in Ω, resistivity in Ω m, length of the wire in m, cross-sectional area in m². The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange R = ρ L / A?

Rearranging gives these forms: to find resistance: R = ρ L / A. to find resistivity: ρ = R A / L. to find length of the wire: L = R A / ρ. to find cross-sectional area: A = ρ L / R.

Practise resistivity questions

Include unit conversions (km, g, minutes…)

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

Read the full explanation on the Resistivity formula page. More electricity equations: Charge, current and time, Ohm’s law, Electrical power, Electrical power, Energy transferred, Resistors in series, Resistors in parallel, EMF and internal resistance. See the full list on the a-level physics equation calculator page.