# Hall Coefficient Calculator

URL: https://speedycalculator.com/calculators/physics/hall-coefficient/
Last updated: 2026-10-30

> The Hall coefficient calculator finds a material's Hall coefficient from the Hall voltage, sample thickness, current and magnetic field, and the resulting charge carrier density and type.

## Inputs

- Hall voltage V_H (µV, mV, V)
- Sample thickness t (mm, cm, m, in, µm)
- Current I (A, mA, µA, kA)
- Magnetic field B (T, mT, µT, G, nT)

## Results

- Hall coefficient R_H
- Carrier density
- Majority carriers

## Formula

```
R_H = V_H·t / (I·B),  n = 1 / (|R_H|·e)
```

## Explanation

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

FieldWhat to enterHall voltage V_HUnits: µV, mV, VSample thickness tUnits: mm, cm, m, in, µmCurrent IUnits: A, mA, µA, kAMagnetic field BUnits: 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

## 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.

## FAQ

**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.


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)