What is the Hall effect?

When current flows through a conductor in a perpendicular magnetic field, a voltage develops across the conductor in the third perpendicular direction. This is the Hall effect, discovered by Edwin Hall in 1879.

What is the Hall voltage formula?

V_H = (I × B) / (n × q × d), where I is current (A), B is magnetic field (T), n is carrier density (m⁻³), q is the elementary charge (1.602 × 10⁻¹⁹ C), and d is the sample thickness (m).

What is the Hall coefficient?

The Hall coefficient R_H = 1 / (n × q). Its sign reveals carrier type: negative for electrons (n-type) and positive for holes (p-type). Units are m³/C.

What units should I use?

Use SI units: current in amperes (A), magnetic field in tesla (T), carrier density in carriers/m³, and thickness in meters (m). The result is in volts (V).

What is a typical carrier density for silicon?

Intrinsic silicon has about 1.5 × 10¹⁶ carriers/m³ at room temperature. Heavily doped silicon can reach 10²⁴ carriers/m³. Metals like copper have ~8.5 × 10²⁸ carriers/m³.

Why is the Hall voltage so small in metals?

Metals have extremely high carrier density (10²⁸–10²⁹ m⁻³), which appears in the denominator of the Hall formula. This makes the Hall voltage in metals very small — typically microvolts. Semiconductors with lower carrier density produce much larger, measurable voltages.

Hall Voltage Calculator

Enter current, magnetic field, carrier density, and thickness to calculate Hall voltage and Hall coefficient for any conductor or semiconductor.

Sample Parameters

Current, I (A)

Current flowing through the sample (amperes)

Magnetic Field, B (T)

Field perpendicular to current direction (tesla)

Carrier Density, n (m^-3)

Charge carriers per cubic meter

Thickness, d (m)

Sample dimension along the magnetic field axis (meters)

Carrier Type

Electrons (n-type) Holes (p-type)

Results

Enter parameters and click Calculate

Formula Reference

V_H = (I × B) / (n × q × d)

R_H = 1 / (n × q)

q = 1.602 × 10^-19 C (elementary charge)

I — Current (A)

B — Magnetic field (T)

n — Carrier density (m⁻³)

d — Thickness (m)

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Summary

The Hall voltage calculator applies the Hall effect formula V_H = IB/(nqd) to find the transverse voltage in a sample carrying current through a magnetic field. It also computes the Hall coefficient, which identifies whether the dominant charge carriers are electrons or holes. Enter the four key parameters — current, field, carrier density, and thickness — to get results instantly.

How it works

Enter the current through the sample in amperes.
Enter the applied magnetic field strength in tesla.
Enter the charge carrier density (carriers per cubic meter).
Enter the sample thickness along the magnetic field direction in meters.
Click Calculate to get the Hall voltage and Hall coefficient.

Use cases

Determine carrier density in a semiconductor from Hall measurements.
Verify experimental Hall voltage results against theoretical values.
Design Hall-effect sensors for current, position, or field detection.
Study charge transport properties of new materials in a lab setting.
Calculate Hall coefficient to distinguish n-type from p-type semiconductors.
Estimate carrier mobility when combined with resistivity measurements.

Frequently Asked Questions

Last updated: 2026-06-19 · Reviewed by Nham Vu