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Hall Voltage Calculator

Find the Hall voltage of a conductor in a magnetic field.

How it is calculated

The tool uses VH = I·B / (n·q·t). Inputs are in SI units: I current in amperes, B magnetic flux density in tesla, n carrier density in carriers per cubic metre, and t thickness in metres (the dimension along the field, not the width). The charge q defaults to the elementary charge, 1.602176634e-19 C, if you leave it empty or enter a value that is not positive. Density and thickness must be greater than zero. The result is printed in scientific notation in volts (four decimals in the mantissa) and also in millivolts, which switch to scientific notation when the value is below 0.01 mV. A negative current or field gives a negative voltage; the tool does not track the carrier type for you.

Worked example

A thin semiconductor strip carries 1 mA (0.001 A) in a 0.1 T field. Carrier density is 1e22 per m³ and thickness 0.5 mm (0.0005 m). Numerator: I·B = 0.001 × 0.1 = 1e-4. Denominator: n·q·t = 1e22 × 1.602e-19 × 0.0005 ≈ 0.8011. Dividing gives a Hall voltage of 1.2483 × 10⁻⁴ V, which the tool also shows as 0.1248 mV.

Try this example →

Common mistakes

  • Entering thickness in millimetres or micrometres. The formula needs metres, so 0.5 mm must be typed as 0.0005.
  • Entering carrier density in cm-3, the unit most data sheets use. Multiply by 1,000,000 to get m-3; otherwise the voltage comes out a million times too large.
  • Using the wrong dimension for t. It is the thickness measured along the magnetic field direction, not the length or width of the strip.
  • Entering the field in gauss. One tesla equals 10,000 gauss.
  • Expecting a metal to give a large signal. With n around 1e28 to 1e29 per m³ the voltage is in the nanovolt range, so a result like 7.3 × 10⁻⁹ V is normal for copper-like densities.

About this calculator

This calculator finds the Hall voltage, V_H = IB / (nqt), produced across a current-carrying conductor placed in a perpendicular magnetic field, where I is the current, B is the magnetic field strength, n is the charge carrier density, q is the elementary charge, and t is the conductor's thickness. The Hall effect arises because the magnetic field deflects moving charge carriers sideways (via the Lorentz force) until an electric field builds up that balances the deflection — in a real measurement the sign of V_H reveals whether the majority carriers are electrons or holes, but this calculator takes the carrier charge as positive and returns the magnitude only.

Solid-state physics students and semiconductor engineers use Hall voltage measurements to determine carrier concentration and mobility in materials, and the same principle underlies Hall effect sensors used for contactless current sensing and position/speed detection in industrial and automotive electronics.

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Comments (1)

  • Editorial team

    The result scales with one over the carrier density, which explains why Hall sensors are made from semiconductors. Try a metal such as copper at about 8.5e28 carriers per cubic metre with 1 A, 1 T and 1 mm thickness: the voltage is only 7.3e-8 V, and the millivolt line also switches to scientific notation, about 7.3e-5 mV. Thickness is the dimension along the field. What material or sensor are you working with?

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