Resistance Calculator

This calculator calculates the resistivity of a component based on its resistance value, length, and cross-sectional area.

Overview

Our resistivity calculator will help you calculate the resistivity of a material which is a function of its resistance value, length, and cross-sectional area. 

 

Equation

$$\rho = \frac{RA}{L}$$

Where: 

$$\rho$$ = resistivity of the material in ohm-m (Ω-m)

$$R$$ = resistance of the material in ohms (Ω).

$$L$$ = length of the material in meters (m).

$$A$$ = cross-sectional area of the material in square meters (m²).

The resistivity of a material is the amount of resistance it can offer to a current based on its dimensions. This is actually inherent to a specific material as each type has its own resistivity values. Normally, we calculate the resistance R of the material given its resistivity and dimensions. 

From the formula above, it can be said that resistivity is directly proportional to the cross-sectional area of the material and inversely proportional to its length. This means that a material with a larger cross-section or a shorter length will have a higher resistivity value. Conversely, a material with a smaller cross-section or a longer length will have a smaller resistivity value. The resistance of the material is also a factor and is directly proportional to its resistivity. 

Conductors tend to have low resistivity while insulators have high resistivity.

Conductivity, usually denoted by

$$\sigma$$ , is the reciprocal of resistivity, $$\sigma = \frac{1}{\rho}$$ . 

Notes

• The resistivity of graphene, a special carbon material, is 1 x 10^-8 Ω-m
• The resistivity of Teflon, the one found in non-stick frying pans, is 1 x 10²⁵ Ω-m
• Semiconductors have resistivities between that between of conductors and insulators
• The resistivity of a material is dependent on temperature. It can be calculated using the formula: 

$$\rho = \rho_{0}[1 + \alpha(T - T_{0})]$$

Further Reading

Textbook - Specific Resistance 

Worksheet - Specific Resistance of Conductors