What is the resistivity formula?

The standard formula is R = ρL / A, where R is resistance in ohms (Ω), ρ (rho) is resistivity in ohm-metres (Ω·m), L is the conductor length in metres, and A is its cross-sectional area in square metres. Rearranging gives ρ = RA/L, L = RA/ρ, and A = ρL/R.

How does temperature affect resistivity?

For metals, resistivity rises with temperature because lattice vibrations impede electron flow more strongly. The linear approximation is ρ(T) = ρ₀[1 + α(T − T₀)], where ρ₀ is the reference resistivity at T₀ = 20 °C and α is the temperature coefficient (°C⁻¹). Semiconductors such as silicon have a negative α — their resistivity falls as temperature rises because more charge carriers become available.

What is the difference between resistivity and resistance?

Resistivity (ρ) is an intrinsic material property, measured in Ω·m, that does not depend on the shape of the conductor. Resistance (R) is an extrinsic property of a specific piece of material and depends on both ρ and the geometry (length and area). A longer or thinner conductor has higher resistance, but the same resistivity.

What are typical resistivity values for common conductors?

At 20 °C: silver ≈ 1.59 × 10⁻⁸ Ω·m, copper ≈ 1.72 × 10⁻⁸ Ω·m, aluminium ≈ 2.65 × 10⁻⁸ Ω·m, iron ≈ 1.0 × 10⁻⁷ Ω·m, nichrome ≈ 1.1 × 10⁻⁶ Ω·m. Semiconductors are orders of magnitude higher: germanium ≈ 0.46 Ω·m, silicon ≈ 640 Ω·m. Insulators can exceed 10¹⁰ Ω·m.

What is conductivity and how does it relate to resistivity?

Conductivity σ (sigma) is simply the reciprocal of resistivity: σ = 1/ρ, measured in siemens per metre (S/m). Copper at 20 °C has σ ≈ 5.8 × 10⁷ S/m. High conductivity means low resistivity and vice versa. The calculator displays σ automatically once the other quantities are known.

How do I find the cross-sectional area of a round wire?

For a circular conductor of diameter d, the cross-sectional area is A = π(d/2)² = πd²/4. For example, a 1 mm diameter wire has A = π × (0.5 × 10⁻³)² ≈ 7.85 × 10⁻⁷ m² (0.785 mm²). Enter this value in the area field with the mm² unit selected.

Resistivity Calculator

Electrical resistivity is the fundamental material property that tells you how strongly a substance opposes the flow of electric current. The resistivity calculator implements the complete R = ρL/A relationship — letting you solve for any one of resistance, resistivity, length or cross-sectional area — and adds a full temperature correction so you can work at realistic operating conditions rather than the standard 20 °C reference point.

Whether you are sizing a mains cable, investigating heating in a PCB trace, or studying semiconductor behaviour in a physics course, this tool gives you the exact numbers plus the step-by-step working so you can check every stage.

How it works

The core formula is:

R = ρL / A

where R is resistance (Ω), ρ (rho) is resistivity (Ω·m), L is the conductor length (m) and A is the cross-sectional area (m²). Rearranging the same equation yields the other three forms:

ρ = R × A / L — find resistivity from a measured resistance
L = R × A / ρ — find the maximum wire run before resistance exceeds a limit
A = ρ × L / R — find the minimum conductor area needed to keep R at or below a target

Temperature correction. The resistivity you read on a datasheet is typically quoted at 20 °C. At any other temperature T the corrected value is:

ρ(T) = ρ₀ × [1 + α(T − T₀)]

where T₀ = 20 °C and α is the temperature coefficient of resistivity (°C⁻¹). Copper has α ≈ 3.9 × 10⁻³ °C⁻¹, meaning its resistivity rises roughly 0.39 % per °C above 20 °C. Nichrome, used in heating elements, has α ≈ 4 × 10⁻⁴ °C⁻¹ — much more stable, which is why it is preferred for applications that run hot. Semiconductors have a negative α: silicon’s resistivity falls sharply as temperature rises because thermal energy promotes more electrons into the conduction band.

Conductivity σ = 1/ρ is derived and displayed automatically. Copper at 20 °C has σ ≈ 5.8 × 10⁷ S/m.

Material presets cover 12 standard conductors from silver (lowest resistivity of any element) through graphite and into the semiconductor range, each with accurate α values.

Worked example

A 50-metre copper data cable (ρ = 1.724 × 10⁻⁸ Ω·m) has a circular cross-section of diameter 0.5 mm, so A = π × (0.25 × 10⁻³)² ≈ 1.963 × 10⁻⁷ m².

At 20 °C:

R = (1.724 × 10⁻⁸ × 50) / 1.963 × 10⁻⁷ ≈ 4.39 Ω

At 80 °C (typical for equipment inside a cabinet):

ρ(80) = 1.724 × 10⁻⁸ × [1 + 3.9 × 10⁻³ × (80 − 20)] = 1.724 × 10⁻⁸ × 1.234 ≈ 2.13 × 10⁻⁸ Ω·m

R(80) = (2.13 × 10⁻⁸ × 50) / 1.963 × 10⁻⁷ ≈ 5.42 Ω — 23 % higher than at 20 °C.

Material	ρ at 20 °C (Ω·m)	α (°C⁻¹)
Silver	1.59 × 10⁻⁸	3.8 × 10⁻³
Copper	1.72 × 10⁻⁸	3.9 × 10⁻³
Aluminium	2.65 × 10⁻⁸	4.3 × 10⁻³
Nichrome	1.1 × 10⁻⁶	0.4 × 10⁻³
Silicon	640	−75 × 10⁻³

Every result is computed locally in your browser — no data is uploaded or stored anywhere.