Calculate Hall voltage magnitude, current, perpendicular magnetic field, carrier number density, or sample thickness using the single-carrier Hall-effect model.

undefined

Magnitudes for a uniform single-carrier sample with perpendicular current and field. Thickness is measured along the magnetic field.

Number of mobile carriers per cubic meter, not charge in C/m³.

Result unit

Hall Voltage Formula

For a uniform sample with one dominant type of mobile charge carrier, perpendicular current and magnetic field produce a transverse Hall voltage. This calculator uses nonnegative magnitudes:

VH = (I B) / (n e t)
  • I is current in amperes.
  • B is the perpendicular magnetic field in teslas.
  • n is the number of mobile carriers per cubic meter, not electric charge density in C/m³.
  • t is sample thickness in meters, measured along the magnetic field; it is not the separation between Hall-voltage contacts.
  • e = 1.602176634 × 10⁻¹⁹ C is the exact elementary charge magnitude.

Inverse calculations

I = (VH n e t) / (B), B = (VH n e t) / (I)
n = (I B) / (VH e t), t = (I B) / (VH n e)

Select the quantity to solve for and enter the four known values. Input and result units are independent. The calculator converts mA and kA to A, gauss to teslas, mV to volts, and thickness units to meters before calculation.

Example: Hall voltage

With I = 10 mA, B = 1 T, n = 10²² m⁻³ and t = 1 mm, the Hall-voltage magnitude is 0.006241509 V, or approximately 6.241509 mV.

Example: magnetic field

With VH = 10 mV, I = 20 mA, n = 10²² m⁻³ and t = 1 mm, B = VH n e t / I ≈ 0.801088 T. Current belongs in the denominator of this inverse relation.

Hall Voltage Calculator FAQ

Can a known value be zero?

Zero current or magnetic field produces zero Hall voltage for positive carrier density and thickness. Current and field can also be solved as zero when the other quantities determine them uniquely. A zero inverse denominator, or a zero-response case that cannot determine a positive density or thickness, is rejected.

Does the result show carrier polarity?

No. This magnitude model does not infer polarity. The sign of measured Hall voltage depends on carrier sign, current direction, magnetic-field direction and voltage-lead orientation.

When is the model appropriate?

The relation assumes uniform current flow, a perpendicular magnetic field, one dominant carrier population and charge magnitude e. Materials with multiple carrier populations, nonuniform geometry or additional transport effects require a more detailed model.

Sources: Virtual Labs Hall-effect theory and NIST elementary charge.