Hall Effect Calculator: Hall Voltage, Hall Coefficient and Carrier Density

Hall voltage, Hall coefficient, carrier density and drift speed in a conductor in a magnetic field.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the current, the magnetic field, the carrier density and the thickness of the plate in the direction of the field. The Hall voltage is V = I B / (n q d). It also gives the Hall coefficient 1/(n q) and the drift speed of the carriers.

To find the carrier density of a material, choose the other mode and enter the measured Hall voltage. The sign of the Hall voltage tells you whether the carriers are electrons or holes.

It is the basis of Hall effect sensors for magnetic field, current, position and speed. Semiconductors with few carriers give a much bigger Hall voltage than metals.

Formulas used

  • V_H = \frac{IB}{nqd}
  • R_H = \frac{1}{nq}
  • v_d = \frac{I}{nqwd}

Worked example

With the default numbers in the calculator above:

  1. Hall voltage: 3.6715 µV
  2. Hall coefficient: 7.343e-11 m³/C (negative for electrons)
  3. Drift speed of the carriers: 0.00036715 m/s
  4. Hall electric field across the width: 0.00036715 V/m

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want? The carrier density from a measured Hall voltage.

  1. Carrier density from the Hall voltage: 8.5034e+28 per m³
  2. Hall coefficient: 7.34e-11 m³/C (negative for electrons)
  3. Drift speed of the carriers: 0.000367 m/s
  4. Hall electric field across the width: 0.000367 V/m

Common questions

Why is the Hall voltage so small in a metal?

Because there are so many carriers per cubic metre. A thin sheet of a semiconductor gives a far bigger voltage.

Which dimension is d?

The thickness along the direction of the magnetic field. The voltage appears across the width.

What is it used for?

Magnetic sensors, current sensors, position and speed sensors, and measuring carrier density and type.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Halliday, Resnick and Walker, Fundamentals of Physics (the Hall effect); Sze, Physics of Semiconductor Devices.

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