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).

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.

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.