Hall Effect Voltage
Vh = Rh × I × B / t
Quick answer
This calculator solves Vh = Rh × I × B / t for Hall Voltage. With Hall Coefficient 0.5 m³/C, Bias Current 20 mA, Magnetic Field 1.1 T, Plate Thickness 10 mm, the result is 1.1 V. It solves in 5 directions, so you can enter the values you have and get the one you need.
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Formula
Description
The Hall effect produces a voltage perpendicular to both current flow and an applied magnetic field. When current-carrying charge carriers are deflected by the Lorentz force, they accumulate on one side of the conductor, creating a measurable voltage. The Hall coefficient Rh depends on the carrier concentration and type (positive for p-type, negative for n-type semiconductors). Hall effect sensors are ubiquitous in current sensing, position detection, speed measurement, and brushless motor commutation.
Variables
- Vh — Hall voltage (V)
- Rh — Hall coefficient (m³/C)
- I — Bias current through the Hall element (A)
- B — Magnetic flux density (T)
- t — Thickness of the Hall element (m)
Practical Notes
Semiconductor Hall elements (InSb, GaAs) have much larger Hall coefficients than metals, producing larger voltages. Integrated Hall sensors like the ACS712 combine a Hall element with signal conditioning for easy current measurement. Linear Hall sensors output voltage proportional to field, while switch/latch types output digital signals. Sensitivity is typically 1-5 mV/mT for raw Hall elements.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Vh | Hall Voltage | mV | pV, nV, µV, mV, V, kV |
| Rh | Hall Coefficient | — | m³/C |
| I | Bias Current | mA | pA, nA, µA, mA, A, kA |
| B | Magnetic Field | — | T |
| t | Plate Thickness | mm | mm |
Step by step
- 1. What you know: Hall Coefficient 0.5 m³/C, Bias Current 20 mA, Magnetic Field 1.1 T, Plate Thickness 10 mm
- 2. The relation: Vh = Rh × I × B / t
- 3. Substitute: Rh = 0.5 m³/C, I = 20 mA, B = 1.1 T, t = 10 mm
- 4. Result: Hall Voltage = 1.1 V
Related quantities from the same inputs
- P = V × I = 22 mW
Worked examples
Minimum range
Given: Hall Coefficient 0.025 m³/C, Bias Current 100 µA, Magnetic Field 0.055 T, Plate Thickness 0.1 mm
Result: Hall Voltage = 1.375 mV
Low range
Given: Hall Coefficient 0.25 m³/C, Bias Current 1 mA, Magnetic Field 0.55 T, Plate Thickness 1 mm
Result: Hall Voltage = 137.5 mV
Typical
Given: Hall Coefficient 0.5 m³/C, Bias Current 20 mA, Magnetic Field 1.1 T, Plate Thickness 10 mm
Result: Hall Voltage = 1.1 V
High range
Given: Hall Coefficient 0.8 m³/C, Bias Current 0.5 A, Magnetic Field 1.76 T, Plate Thickness 100 mm
Result: Hall Voltage = 7.04 V
Maximum range
Given: Hall Coefficient 8 m³/C, Bias Current 5 A, Magnetic Field 17.6 T, Plate Thickness 1000 mm
Result: Hall Voltage = 0.704 kV
Solving for each variable
Solve for Hall Voltage
Hall Coefficient 0.025 m³/C, Bias Current 100 µA, Magnetic Field 0.055 T, Plate Thickness 0.1 mm → 1.375 mV
Solve for Hall Coefficient
Hall Voltage 10 mV, Bias Current 100 µA, Magnetic Field 0.055 T, Plate Thickness 0.1 mm → 0.1818 m³/C
Solve for Bias Current
Hall Voltage 10 mV, Hall Coefficient 0.025 m³/C, Magnetic Field 0.055 T, Plate Thickness 0.1 mm → 0.7273 mA
Solve for Magnetic Field
Hall Voltage 10 mV, Hall Coefficient 0.025 m³/C, Bias Current 100 µA, Plate Thickness 0.1 mm → 0.4 T
Solve for Plate Thickness
Hall Voltage 10 mV, Hall Coefficient 0.025 m³/C, Bias Current 100 µA, Magnetic Field 0.055 T → 0.01375 mm
How Hall Voltage changes with Hall Coefficient
| Hall Coefficient (input) | Hall Voltage (result) |
|---|---|
| 0.05 m³/C | 110 mV |
| 0.125 m³/C | 0.275 V |
| 0.25 m³/C | 0.55 V |
| 0.375 m³/C | 0.825 V |
| 0.5 m³/C | 1.1 V |
| 0.75 m³/C | 1.65 V |
| 1 m³/C | 2.2 V |
| 2 m³/C | 4.4 V |
| 3.5 m³/C | 7.7 V |
| 5 m³/C | 11 V |
The same result in other units
| Unit | Value |
|---|---|
| µV | 1100000 |
| mV | 1100 |
| V | 1.1 |
| kV | 0.0011 |
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<p><a href="https://vbatpower.com/formulas/hall-voltage/">Hall Effect Voltage</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Hall Effect Voltage?
Use Vh = Rh × I × B / t. With Hall Coefficient 0.5 m³/C, Bias Current 20 mA, Magnetic Field 1.1 T, Plate Thickness 10 mm, Hall Voltage works out to 1.1 V.
What is the formula for Hall Effect Voltage?
The formula is Vh = Rh × I × B / t. The Hall effect produces a voltage perpendicular to both current flow and an applied magnetic field.
How do you find Hall Coefficient when you know the other values?
Rearrange for Hall Coefficient: with Hall Voltage 10 mV, Bias Current 100 µA, Magnetic Field 0.055 T, Plate Thickness 0.1 mm, Hall Coefficient is 0.1818 m³/C.
How do you find Bias Current when you know the other values?
Rearrange for Bias Current: with Hall Voltage 10 mV, Hall Coefficient 0.025 m³/C, Magnetic Field 0.055 T, Plate Thickness 0.1 mm, Bias Current is 0.7273 mA.
What units does Hall Effect Voltage use?
Hall Voltage is shown in µV, mV, V, kV. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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