Wire Resistance Calculator: R = resistivity x length / area

Find the resistance of a wire or cable, or the length or area that gives a target resistance.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

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

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the resistance: resistance = (resistivity of the material x length) / (cross-section area)
  2. Put the values in (every value in its SI unit): resistance = (1.72e-8 x 100) / (2.5e-6)
  3. The answer: resistance: 0.688 ohm
  4. The same answer in other units: 688 milliohm; 688000 microohm

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Length; Resistance (leave it as it is if this is what you are finding) 0.688 ohm; Resistivity of the material (leave it as it is if this is what you are finding) 1.72E-8 ohm m; Cross-section area (leave it as it is if this is what you are finding) 2.5E-6 m2.

  1. The formula, arranged to find the length: length = (resistance x cross-section area) / (resistivity of the material)
  2. Put the values in (every value in its SI unit): length = (0.688 x 2.5e-6) / (1.72e-8)
  3. The answer: length: 100 m
  4. The same answer in other units: 0.1 km; 328.084 feet

Common questions

What is the formula for the resistance of a wire?

Resistance equals the resistivity times the length divided by the cross-section area. 100 m of 2.5 mm2 copper has a resistance of 0.688 ohm.

Why does a thicker wire have less resistance?

A bigger area gives the current more paths, so the resistance falls in proportion to the area.

What is the resistivity of copper?

About 1.72e-8 ohm metres at 20 C, which is 0.0172 ohm mm2 per metre.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any school physics or electrical text (resistance and resistivity).

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