Hall Coefficient Calculator

When a current $$I$$ flows through a conductor of thickness $$t$$ and a perpendicular magnetic field $$B$$ is applied, charge carriers experience a Lorentz force that deflects them to one side, creating a measurable transverse voltage $$V_H$$ (the Hall voltage).

The Hall coefficient is defined as:

$$R_H = \frac{V_H \cdot t}{I \cdot B}$$

The sign of $$R_H$$ reveals the carrier type: negative for electron-dominated (n-type) conduction and positive for hole-dominated (p-type) conduction.

The charge carrier density is related to the Hall coefficient by:

$$n = \frac{1}{|R_H| \cdot e}$$

where $$e = 1.602 \times 10^{-19}$$ C is the elementary charge. This assumes a single-carrier model where one type of carrier dominates conduction. In practice, a Hall scattering factor (typically 1.0–1.9) may modify this relationship depending on the scattering mechanism in the material.

The Hall mobility can be obtained from $$\mu_H = |R_H| \cdot \sigma$$ where $$\sigma$$ is the electrical conductivity, providing a complete picture of the material's transport properties.

Hall Coefficient (R_H) in m³/C quantifies the material's Hall response — larger magnitudes indicate fewer charge carriers. Its sign directly identifies whether the majority carriers are electrons (negative) or holes (positive). Carrier Density (n) gives the number of free charge carriers per cubic meter. Metals typically have $$n \sim 10^{28}$$ m⁻³, while semiconductors range from $$10^{15}$$ to $$10^{22}$$ m⁻³ depending on doping. The Carrier Type output classifies the material as n-type or p-type based on the Hall voltage sign.