Hall Coefficient Calculator

What Is the Hall Coefficient?

The Hall coefficient $R_H$ describes how a conductor or semiconductor responds to a magnetic field perpendicular to an electric current. When charge carriers are deflected by the Lorentz force, a transverse Hall voltage appears. The sign of $R_H$ reveals whether electrons or holes dominate conduction.

Hall Coefficient Formula

$$R_H = \frac{E_H}{I \times B}$$

$E_H$ is the Hall voltage in volts, $I$ is the current through the sample in amperes, and $B$ is the magnetic field strength in teslas. The result is in cubic meters per coulomb (m³/C).

Carrier Density

$$n = \frac{1}{e \times R_H}$$

For a single carrier type, carrier density $n$ (in carriers per cubic meter) follows from the elementary charge $e$. A negative $R_H$ indicates n-type (electron) conduction; a positive value indicates p-type (hole) conduction.

Frequently Asked Questions

What units does the Hall coefficient use?

The Hall coefficient is expressed in m³/C (cubic meters per coulomb). Some references use cm³/C; multiply by 10⁶ to convert from m³/C to cm³/C.

How do I determine carrier type from R_H?

A negative Hall coefficient means majority electrons (n-type). A positive value means majority holes (p-type). The sign follows the charge of the dominant carriers.

What is the Hall voltage?

The Hall voltage is the potential difference measured across the width of the sample, perpendicular to both the current and the magnetic field.

Does sample thickness affect R_H?

In the standard definition used here, R_H = E_H / (I × B) and does not depend on thickness. Thickness matters when converting to Hall mobility or sheet resistance.

What magnetic field strength should I use?

Use the actual field perpendicular to the current path. Typical lab magnets produce 0.1 to 1 T. Stronger fields give larger, easier-to-measure Hall voltages.

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What Is the Hall Coefficient?

Hall Coefficient Formula

Carrier Density

Frequently Asked Questions

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