Calculator
Example data table
| Material | Current | Magnetic field | Thickness | Width | Hall voltage | Hall coefficient | Carrier density |
|---|---|---|---|---|---|---|---|
| n-type silicon | 20 mA | 0.80 T | 0.50 mm | 5.00 mm | -4.00 mV | -1.25e-4 m³/C | 4.99e22 m⁻³ |
| p-type germanium | 15 mA | 0.60 T | 0.40 mm | 4.50 mm | 2.70 mV | 1.20e-4 m³/C | 5.20e22 m⁻³ |
| indium antimonide | 10 mA | 0.35 T | 0.20 mm | 3.00 mm | -7.00 mV | -4.00e-4 m³/C | 1.56e22 m⁻³ |
| gallium arsenide | 25 mA | 1.00 T | 0.60 mm | 6.00 mm | -5.20 mV | -1.25e-4 m³/C | 4.99e22 m⁻³ |
Formula used
Here, I is current, B is magnetic flux density, t is sample thickness, w is sample width, q is carrier charge magnitude, ρ is resistivity, and σ is conductivity. The Hall coefficient sign indicates the dominant carrier type.
How to use this calculator
- Select the quantity you want to solve.
- Choose the dominant carrier type.
- Enter measured current, field, thickness, and width as needed.
- Provide either Hall coefficient or carrier density when available.
- Add resistivity if you need mobility or conductivity.
- Press Calculate to show results above the form.
- Review the graph to inspect Hall voltage versus magnetic field.
- Use CSV or PDF export to save the solved values.
Frequently asked questions
1. What does the Hall effect measure?
It measures the transverse voltage produced when current flows through a conductor or semiconductor inside a magnetic field. That voltage reveals carrier type, carrier density, and transport behavior.
2. Why can Hall voltage be negative?
A negative Hall voltage usually indicates electrons dominate conduction. A positive Hall voltage usually indicates holes dominate. The sign depends on carrier charge and probe orientation.
3. Which inputs are required for Hall coefficient?
You need Hall voltage, current, magnetic flux density, and sample thickness. With those values, the calculator directly evaluates the Hall coefficient.
4. Can I use carrier density instead of Hall coefficient?
Yes. If carrier density and charge magnitude are known, the calculator estimates the Hall coefficient and then derives Hall voltage, mobility, and related terms when enough geometry data exists.
5. Why does sample thickness matter so much?
Hall voltage is inversely proportional to thickness. Thinner samples produce larger Hall voltages under the same current, field, and Hall coefficient.
6. What is mobility in this context?
Mobility describes how quickly charge carriers respond to an applied electric field. In Hall analysis, mobility is commonly estimated from Hall coefficient and resistivity.
7. Does this calculator work for metals and semiconductors?
Yes, but semiconductors are the most common Hall-effect application. Materials with multiple carrier types or strong anisotropy may need more advanced modeling than a single-carrier approximation.
8. Why is the graph useful?
The graph shows how Hall voltage changes with magnetic field using the current solved parameters. It helps verify linearity, compare operating ranges, and support experiment planning.