Hall Voltage Calculator
When a current flows through a conductor in a perpendicular magnetic field, the field pushes the moving charges sideways until a transverse voltage builds up to oppose it. This Hall voltage is the basis of magnetic field sensors, current sensors and semiconductor characterisation. This calculator takes the current, magnetic field, carrier density, carrier charge and sample thickness, then returns the Hall voltage and the geometry-independent Hall coefficient. Carrier density is a material property you supply for your specific sample and doping.
Hall effect formula
Hall voltage: V_H = I * B / (n * q * t)
Hall coefficient: R_H = 1 / (n * q)
I = current (A), B = field (T)
n = carrier density (per m3), t = thickness (m)
The Hall voltage grows with current and field and shrinks with carrier density and thickness. The Hall coefficient isolates the material response from the sample geometry and applied field.
Hall effect context
- The elementary charge is 1.602176634 times ten to the minus nineteenth coulombs.
- Copper has a carrier density of roughly 8.5 times ten to the twenty-eighth per cubic metre.
- Semiconductors have far lower carrier densities, giving much larger Hall voltages.
- The sign of the Hall coefficient tells you whether carriers are electrons or holes.
- The quantum Hall effect provides the standard used to define the ohm.
Hall voltage: frequently asked questions
What is the Hall effect?
The Hall effect is the appearance of a voltage across a current-carrying conductor placed in a perpendicular magnetic field. The field deflects the moving charge carriers to one side, building up a transverse voltage, the Hall voltage, that balances the magnetic force at equilibrium.
What is the Hall voltage formula?
The Hall voltage is V_H = I * B / (n * q * t), where I is the current, B the perpendicular magnetic field, n the charge carrier density, q the carrier charge and t the sample thickness along the field. A thinner sample or lower carrier density gives a larger Hall voltage.
What is the Hall coefficient?
The Hall coefficient is R_H = 1 / (n * q). It captures the material's response independent of geometry and field, and its sign reveals whether the dominant charge carriers are negative (electrons) or positive (holes). Measuring it is a standard way to characterise semiconductors.
What carrier density should I enter?
Carrier density n is the number of mobile charge carriers per cubic metre, a property of the material and its doping. Metals have very high densities (around ten to the twenty-eighth per cubic metre); semiconductors are much lower and tunable. It ships as a user-editable input since it depends on your sample.
Why is the Hall effect useful?
Hall sensors measure magnetic fields, position and current without contact, and appear in cars, phones and industrial equipment. In research, the Hall effect reveals carrier type, density and mobility in semiconductors, and the quantum Hall effect provides a resistance standard used to define the ohm.
Official sources
- U.S. National Institute of Standards and Technology: Hall effect measurements.
- U.S. National Institute of Standards and Technology: Elementary charge.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.