Hall Coefficient Calculator — R_H, Carrier Type & Density
Enter the Hall voltage, sample thickness, current and magnetic field from a Hall effect measurement to compute the Hall coefficient R_H, identify whether the material is n-type or p-type, and calculate the free charge carrier density.
V
m
A
T
p-type (holes)
- 1
Numerator (V_H × t)
0.005 × 0.001 = 0.000005 - 2
Denominator (I × B)
0.01 × 0.5 = 0.005 - 3
Hall coefficient R_H = (V_H × t) ÷ (I × B)
0.000005 ÷ 0.005 = 0.001000Positive = p-type (holes); negative = n-type (electrons).
How does this calculator work?
Hall coefficient R_H = (V_H × t) / (I × B) in m³/C, where V_H is the transverse Hall voltage, t is sample thickness, I is longitudinal current and B is applied magnetic field. A positive result indicates p-type (hole) conduction; negative indicates n-type (electron) conduction. Carrier density n = 1 / (|R_H| × 1.602 × 10⁻¹⁹).
Formula
How this is calculated
The Hall effect occurs when a current-carrying conductor is placed in a magnetic field perpendicular to the current flow. The Lorentz force (F = qv × B) deflects charge carriers sideways, causing them to accumulate on one face of the sample until the resulting transverse electric field (the Hall field) balances the magnetic force. The resulting transverse voltage is the Hall voltage V_H.
The Hall coefficient R_H quantifies this response: R_H = (V_H × t) / (I × B), where t is the sample thickness along the magnetic field direction, I is the longitudinal current, and B is the flux density. R_H has SI units of m³/C (or equivalently m³/(A·s)). A positive R_H means the dominant carriers are positive holes (p-type semiconductor); a negative R_H means negative electrons (n-type). This is because holes and electrons deflect in opposite directions under the same Lorentz force.
The carrier density follows from the relation R_H = 1/(n·q) for a single-carrier material in the low-field limit: n = 1/(|R_H| × e). This "simple" formula assumes one dominant carrier type and a Hall scattering factor r_H ≈ 1; real materials with mixed carrier populations or strong magnetic fields may require the full two-band Hall formula. The calculation uses the exact 2019 SI definition e = 1.602176634 × 10⁻¹⁹ C.
Frequently asked questions
A positive R_H indicates that positive charge carriers (holes) dominate — the material is p-type. A negative R_H indicates that negative charge carriers (electrons) dominate — the material is n-type. Metals like copper have a small negative R_H (electron carriers), while p-doped silicon has a positive R_H.
In SI units R_H is m³/C. Many references use cm³/C or cm³/(A·s) instead (1 m³/C = 10⁶ cm³/C). Metals typically have |R_H| in the range 10⁻¹¹–10⁻¹⁰ m³/C, while lightly doped semiconductors can be 10⁻³–10⁻¹ m³/C.
The formula assumes a single dominant carrier species and a Hall scattering factor r_H = 1. It breaks down for metals and intrinsic semiconductors with comparable electron and hole densities (yielding a near-zero or sign-changing R_H), and at high magnetic fields where magnetoresistance is significant. The full two-band Hall model is needed in those cases.
Also known as
TG we-Calculate Editorial Team. (2026). Hall Coefficient Calculator — R_H, Carrier Type & Density [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/hall-coefficient-calculator
TG we-Calculate Editorial Team. "Hall Coefficient Calculator — R_H, Carrier Type & Density." TG we-Calculate. 2026. https://we-calculate.com/calculator/hall-coefficient-calculator.
TG we-Calculate Editorial Team, "Hall Coefficient Calculator — R_H, Carrier Type & Density," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/hall-coefficient-calculator
@misc{wecalculate_hall_coefficient_calculator, title = {Hall Coefficient Calculator — R_H, Carrier Type & Density}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/hall-coefficient-calculator}}, year = {2026}, note = {TG we-Calculate} }
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