Hall Coefficient Calculator

Enter the Hall voltage, current, magnetic field, and sample thickness to calculate the Hall coefficient (R_H = V_H·t / (I·B)), carrier concentration, carrier type, and Hall mobility.

Quick Facts

Hall coefficient
R_H = V_H·t / (I·B)
Equivalent to R_H = 1/(nq); sample width cancels out of the formula.
Carrier concentration
n = 1 / (R_H·e)
e = 1.602 × 10⁻¹⁹ C is the elementary charge.
Sign convention
R_H > 0 → holes, R_H < 0 → electrons
The Hall voltage's polarity flips with the majority carrier type.
Hall mobility
μ_H = |R_H| × σ
Requires the material's electrical conductivity σ.

Your Results

Calculated
Hall Coefficient (R_H)
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R_H = V_H·t / (I·B), in m³/C
Carrier Concentration (n)
-
n = 1 / (R_H·e)
Carrier Type
-
Sign of R_H shows majority carrier
Hall Mobility (μ_H)
-
μ_H = |R_H| × σ, in cm²/(V·s)

Ready

Enter the Hall voltage, current, magnetic field, and thickness, then press Calculate.

About the Hall Coefficient

The Hall effect occurs when a magnetic field is applied perpendicular to the current flowing through a conductor or semiconductor: the moving charge carriers feel a sideways Lorentz force and pile up along one edge of the sample, building a small transverse voltage — the Hall voltage — across it. The Hall coefficient, R_H, is the material property that links this voltage to the current, magnetic field, and sample geometry, and it reveals both the density and the sign (electron or hole) of the dominant charge carrier.

Deriving the Hall coefficient formula

In steady state, the electric force from the built-up Hall field balances the magnetic force on the carriers: qE_y = qv_xB_z. Since the current density is J_x = nqv_x, substituting gives E_y = J_xB_z / (nq), so the Hall coefficient is defined as R_H = E_y / (J_xB_z) = 1 / (nq). Writing the field and current density in terms of measurable quantities — E_y = V_H / w and J_x = I / (w·t), where w is the sample width and t is its thickness along the field direction — the width w cancels out, leaving the practical working formula: R_H = V_H·t / (I·B). From R_H you can also recover the carrier concentration directly: n = 1 / (R_H·e), where e = 1.602 × 10⁻¹⁹ C is the elementary charge.

Working with units and sign convention

  • Keep every quantity in consistent SI units before computing by hand: volts (V), amps (A), tesla (T), and meters (m). This calculator converts your chosen units for you.
  • Common conversions: 1 mT = 0.001 T, 1 gauss (G) = 10⁻⁴ T, and 1 mA = 0.001 A.
  • The Hall voltage's sign matters — enter it as measured (positive or negative). A positive R_H points to holes (p-type); a negative R_H points to electrons (n-type).

Practical limits and assumptions

This single-carrier formula assumes one dominant charge carrier type, a uniform current density, and a thin, geometrically uniform sample with ohmic (non-rectifying) contacts. Real semiconductors can have both electron and hole populations contributing simultaneously, which biases the simple R_H = 1/(nq) result — this is usually handled with a two-carrier model or a Hall scattering factor correction. R_H can also vary with temperature and with the strength of the applied magnetic field, so measurements are typically reported alongside the temperature and field at which they were taken.

Frequently Asked Questions

What is the Hall coefficient?
The Hall coefficient (R_H) is a material property that quantifies the transverse Hall electric field produced per unit current density and per unit applied magnetic field: R_H = E_y / (J_x B_z) = 1 / (nq), where n is the charge carrier concentration and q is the carrier's charge. It reveals both how many charge carriers are present and whether the dominant carriers are electrons or holes.
What is the formula for calculating the Hall coefficient from a measurement?
In a standard Hall-bar measurement, R_H = V_H · t / (I · B), where V_H is the measured Hall voltage, t is the sample thickness in the direction of the magnetic field, I is the current through the sample, and B is the applied magnetic flux density. The sample width cancels out of this formula, so it does not need to be measured.
How do I know if a material is n-type or p-type from its Hall coefficient?
The sign of R_H indicates the dominant carrier: a positive Hall coefficient corresponds to positive majority carriers (holes, p-type), while a negative Hall coefficient corresponds to negative majority carriers (electrons, n-type). This is because the Hall voltage's polarity flips depending on which carrier type accumulates on the sensing edge of the sample.
How is Hall mobility related to the Hall coefficient?
Hall mobility is calculated as μ_H = |R_H| × σ, where σ is the material's electrical conductivity. It measures how quickly the majority charge carriers drift in response to an applied electric field and is commonly reported in cm²/(V·s) for semiconductors.

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