Calculate Hall-effect quantities
Formula used
For a thin rectangular sample carrying current I in a magnetic field B, the Hall voltage is:
VH = (B · I) / (n · q · t)
- n is carrier density (1/m³).
- q is carrier charge (C), including sign.
- t is sample thickness (m) in the field direction.
- Hall coefficient: RH = 1 / (n · q).
- From measurements: RH = (VH · t) / (I · B).
How to use this calculator
- Select what you want to solve for.
- Enter known values and choose the correct units.
- Pick electron, hole, or a custom carrier charge.
- Optionally add width to compute E and J.
- Add resistivity to estimate mobility from RH.
- Press Calculate to see results above the form.
- Use CSV or PDF buttons for reporting and archiving.
Example data table
| Material case | B (T) | I (A) | n (1/m³) | t (mm) | q | Approx. VH |
|---|---|---|---|---|---|---|
| Copper-like metal | 1.0 | 10 | 8.5e28 | 1.0 | −e | ~0.7 µV |
| n-type semiconductor | 0.5 | 2 | 1.0e21 | 1.0 | −e | ~6.2 mV |
| p-type semiconductor | 0.5 | 2 | 1.0e21 | 1.0 | +e | ~−6.2 mV |
Values are illustrative and depend on geometry and contacts.
Hall voltage in practice: professional notes
Why Hall voltage matters in measurements
Hall voltage is the transverse potential that appears when charge carriers move through a conductor or semiconductor in a magnetic field. Engineers use it to infer carrier concentration, mobility trends, and magnetic field strength, and to validate device orientation during testing.
Key variables the calculator combines
This calculator links current, magnetic flux density, thickness, and either Hall coefficient or carrier concentration. With one consistent workflow, you can compute Hall voltage directly or solve backwards for an unknown, which is useful when you have measured Vₕ and want to estimate material properties. For the simplest single‑carrier model, the carrier concentration relates as n ≈ 1/(q·Rₕ). In multi‑carrier materials this becomes an effective value, so treat results as an estimate unless you have a verified model.
Typical magnetic field and current ranges
In teaching and bench experiments, magnetic fields commonly fall between 0.05 and 1.5 T using permanent magnets or small electromagnets. Drive currents are often 1 mA to 2 A depending on sample resistance and heating limits. Thin films may require lower currents to avoid thermal drift.
Material behavior and Hall coefficient data
Metals typically exhibit very small Hall coefficients (on the order of 10⁻¹¹ to 10⁻¹⁰ m³/C), so the resulting Hall voltages can be microvolts and demand careful instrumentation. Doped semiconductors can show Hall coefficients around 10⁻⁶ to 10⁻³ m³/C, producing millivolt-level signals at moderate fields and currents.
Geometry and thickness effects
Thickness enters inversely: halving thickness doubles Vₕ if all other inputs remain fixed. Because thickness uncertainty directly transfers to voltage uncertainty, measure it with calipers or profilometry when possible. For rectangular bars, ensure the thickness chosen matches the dimension perpendicular to both current flow and magnetic field.
Uncertainty, noise, and contact placement
Real data often includes offset voltage from imperfect contacts, thermoelectric effects, and magnetic hysteresis. A standard technique is to reverse the magnetic field (or current) and average: Vₕ ≈ (V(+B) − V(−B))/2. Shielding, twisted-pair wiring, and low-noise amplification improve repeatability. Temperature changes resistance and carrier mobility, so let the sample reach steady state before recording readings, and note the ambient temperature in your lab log.
Interpreting polarity and carrier type
The sign of Vₕ encodes the dominant carrier type when you follow a consistent right‑hand convention for current and field. A polarity flip can indicate p‑type versus n‑type conduction, or simply swapped leads. Use the calculator’s sign note to document your chosen orientation.
Common use cases in labs and industry
Hall-effect sensing supports brushless motor commutation, proximity detection, current sensing, and magnetic field mapping. In materials science, Hall measurements complement resistivity tests by separating geometric effects from carrier physics, especially when comparing samples of different dimensions.
FAQs
What is the Hall voltage?
Hall voltage is the sideways potential difference that develops across a current‑carrying material placed in a magnetic field. It arises from the Lorentz force pushing carriers to one side, creating charge separation.
Which formula does the calculator use?
It uses Vₕ = (Rₕ · I · B) / t. If carrier concentration is provided, it uses Rₕ ≈ 1/(q·n) for a single dominant carrier to estimate the Hall coefficient.
What units should I use for thickness?
Enter thickness in meters for direct SI consistency, or choose a supported unit and let the calculator convert it. Thickness is the dimension perpendicular to both the current direction and the magnetic field.
Why is my measured Hall voltage very small?
Metals have very small Hall coefficients, so Vₕ can be microvolts. Use higher magnetic field, higher current within heating limits, low‑noise amplification, and the field‑reversal method to reduce offsets and improve signal.
How do I determine the carrier type from polarity?
With a fixed sign convention, the sign of Vₕ indicates whether positive or negative carriers dominate. If your sign flips unexpectedly, verify lead orientation, current direction, and magnetic field direction before concluding p‑type or n‑type behavior.
Can I use this for thin films or wafers?
Yes, but be careful with thickness and contact geometry. Thin films can heat quickly and show larger relative errors. Use small currents, stable temperature, and consider van der Pauw setups if you need higher accuracy.
What is a typical magnetic field value to test with?
For basic experiments, 0.1–0.5 T is common with strong permanent magnets, while lab electromagnets may reach 1 T or more. Always confirm B with a gaussmeter if you need quantitative accuracy.