When current flows through a conductor in a magnetic field, the carriers are pushed sideways, creating a small voltage across the sample – the Hall effect. Its sign reveals whether carriers are electrons or holes, and its size their density.
How to use the Hall Coefficient Calculator
- Hall voltage V_H
- Sample thickness t
- Current I
- Magnetic field B
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the Hall voltage (with sign), the sample thickness, the current and the magnetic field.
Inputs explained
| Field | What to enter |
|---|---|
| Hall voltage V_H | Units: µV, mV, V |
| Sample thickness t | Units: mm, cm, m, in, µm |
| Current I | Units: A, mA, µA, kA |
| Magnetic field B | Units: T, mT, µT, G, nT |
What each result means
- Hall coefficient R_H = [Hall voltage V_H]×[Sample thickness t]÷([Current I]×[Magnetic field B])
- Carrier density = 1÷(abs([Hall coefficient R_H])×1.602176634e-19)
Example values
How the main result changes when Hall voltage V_H changes and everything else stays at the example values above:
| Hall voltage V_H (µV) | Hall coefficient R_H (m³/C) |
|---|---|
| -1.25 | -2.5000e-11 |
| -1.88 | -3.7500e-11 |
| -2.5 | -5.0000e-11 |
| -3.13 | -6.2500e-11 |
| -3.75 | -7.5000e-11 |
| -5 | -1.0000e-10 |
Formula
R_H = V_H·t / (I·B), n = 1 / (|R_H|·e)
Worked example
Inputs — Hall voltage V_H: -2.5 µV; Sample thickness t: 0.1 mm; Current I: 5 A; Magnetic field B: 1 T.
Results — Hall coefficient R_H = -5.0000e-11 m³/C; Carrier density = 1.2483e29 m⁻³; Majority carriers = Electrons (n-type).
Key terms
- Hall effect
- Transverse voltage from carriers deflected by a magnetic field.
Frequently asked questions
What does a negative Hall coefficient mean?
Electrons are the majority carriers.
Why is the Hall voltage small in metals?
Their huge carrier density gives a tiny R_H.
Where are Hall sensors used?
Position sensing, current clamps and smartphone compasses.
What is the quantum Hall effect?
Quantised Hall resistance in 2D systems at low temperature.