Hall Coefficient Calculator

The Hall Effect describes how a magnetic field deflects charge carriers in a conductor, producing a measurable voltage — a key measurement in semiconductor characterization. Enter your Hall Voltage (V_H), sample thickness (t), applied current (I), and magnetic flux density (B) into the Hall Coefficient Calculator to find the Hall Coefficient (R_H) in m³/C. Secondary outputs include carrier concentration and carrier type (n-type or p-type, determined by the sign of V_H). Also try the Coulomb's Law Calculator.

V

The voltage measured perpendicular to both current and magnetic field. Negative values indicate p-type carriers.

m

Thickness of the conductor in the direction of the magnetic field.

A

The current flowing through the conductor along its length.

T

Magnetic field applied perpendicular to both the current and Hall voltage directions.

Charge per carrier used to compute carrier concentration. Usually the elementary charge.

Results

Hall Coefficient (R_H)

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Carrier Concentration (n)

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Carrier Type

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Hall Voltage Used (V_H)

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Frequently Asked Questions

What is the Hall effect?

The Hall effect is a physical phenomenon where a voltage difference — the Hall voltage — develops across a conductor when an electric current flows through it and a magnetic field is applied perpendicular to the current. The magnetic Lorentz force deflects charge carriers to one side, creating a transverse electric field. It was discovered by Edwin Hall in 1879. See also our calculate Lenz's Law Induced EMF (ε).

What does the Hall coefficient tell you?

The Hall coefficient (R_H) reveals the sign and concentration of charge carriers in a material. A negative R_H indicates electrons (n-type) are the majority carriers, while a positive R_H indicates holes (p-type). Its magnitude is inversely proportional to carrier concentration — larger absolute values mean fewer carriers.

What is the Hall coefficient formula?

The Hall coefficient is calculated as R_H = (V_H × t) / (I × B), where V_H is the Hall voltage, t is the sample thickness, I is the applied current, and B is the magnetic flux density. It can also be expressed as R_H = −1 / (n × q), where n is carrier concentration and q is carrier charge.

What are the units of the Hall coefficient?

The SI unit of the Hall coefficient is cubic metres per coulomb (m³/C). It is sometimes also expressed in cm³/C or mm³/C depending on the scale of the measurement. In the formula R_H = V × t / (I × B), combining volts, metres, amperes, and tesla gives m³/C.

How do I determine carrier concentration from the Hall coefficient?

Carrier concentration n = 1 / |R_H × q|, where q is the elementary charge (1.602 × 10⁻¹⁹ C). This gives the number of charge carriers per cubic metre. A smaller Hall coefficient magnitude corresponds to a higher carrier density, which is typical in metals compared to semiconductors.

Why is my Hall coefficient negative?

A negative Hall coefficient means the dominant charge carriers in your material are electrons (n-type). Since electrons carry negative charge, the sign convention in the Hall formula yields a negative value. Positive values indicate hole conduction (p-type), common in many semiconductors like p-doped silicon or germanium.

What is the difference between Hall voltage and Hall coefficient?

Hall voltage (V_H) is the measurable transverse voltage that appears across the sample during the experiment — it depends on current, field strength, and sample geometry. The Hall coefficient (R_H) is a material property derived from V_H; it is independent of sample dimensions and characterises the conductor's carrier type and density.

Can the Hall effect be used to measure magnetic fields?

Yes — Hall effect sensors are widely used to measure magnetic field strength. If R_H and the sample dimensions are known, rearranging the formula gives B = (V_H × t) / (R_H × I). This principle underlies Hall probes used in scientific instruments, electric motors, and proximity sensors.