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Hall Effect Calculator
Hall voltage V_H = I·B/(n·q·t) with signed carrier charge, density in m⁻³ or cm⁻³, the Hall coefficient R_H, and sensitivity in V/T.
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Tool usage guide
Learn when to use this tool, what it supports, and how real users apply it.
Key facts
Category
Science & Education
Input types
number, select
Output type
text
Sample coverage
4
API ready
Yes
Overview
The Hall Effect Calculator computes the Hall voltage, Hall coefficient, and magnetic sensitivity for conducting and semiconducting materials based on the formula V_H = I·B/(n·q·t). By specifying current, magnetic flux density, carrier density, material thickness, and carrier type (electrons or holes), you can instantly determine sensor response and carrier polarity.
When to use
Designing Hall effect sensors or magnetometers to predict output voltage across expected magnetic fields.
Characterizing semiconductor wafers to calculate carrier density and identify n-type or p-type majority carriers.
Evaluating why metals produce negligible Hall voltages compared to semiconductor thin films.
How it works
1Select the majority carrier type as electrons (n-type, q = −e) or holes (p-type, q = +e) to determine the sign of the Hall coefficient.
2Enter the applied current (I) and magnetic field (B) with their respective units (A, mA, T, mT, or µT).
3Specify the material carrier density (n) in m⁻³ or cm⁻³ and the sample thickness (t) in mm, µm, or nm.
4The tool calculates the Hall coefficient R_H = 1/(n·q), device sensitivity (V_H/B), and the resulting Hall voltage V_H.
Use cases
Determining sensor dimensions and bias current required to produce target voltages in solid-state magnetometer design.
Validating physics laboratory Hall effect experimental measurements against theoretical carrier density models.
Analyzing thin-film transport properties to compare n-type versus p-type semiconductor samples.
Examples
1. Silicon Magnetometer Sensor Design
Sensor Design Engineer
Background
An engineer is designing a solid-state Hall effect magnetometer using an n-type silicon layer.
Problem
Calculate the expected voltage output and sensitivity at a current of 10 mA across a 0.5 T magnetic field.
How to use
Input 10 mA for Current, 0.5 T for Magnetic Field, 1e21 m⁻³ for Carrier Density, 100 µm for Thickness, and select Electrons as the carrier type.
Outcome
Calculates a Hall coefficient of −6.24e-3 m³/C, a sensitivity of −0.624 V/T, and a Hall voltage of −0.312 V.
2. Copper Conductor Hall Voltage Evaluation
Physics Student
Background
A student wants to verify why copper strips produce barely measurable Hall voltages in a classroom experiment.
Problem
Evaluate the Hall voltage across a 100 µm copper foil with 10 A current under a 1 T magnetic field.
How to use
Set Current to 10 A, Magnetic Field to 1 T, Carrier Density to 8.5e28 m⁻³, Thickness to 100 µm, and Carrier Type to Electrons.
Outcome
FAQ
What is the physical formula used for the Hall voltage calculation?
The calculator uses V_H = (I · B) / (n · q · t), where I is current, B is magnetic field, n is carrier density, q is carrier elementary charge, and t is thickness.
Why does the Hall voltage have a negative sign?
A negative voltage indicates electron conduction (n-type material), whereas a positive voltage indicates hole conduction (p-type material).
What is the Hall coefficient R_H?
The Hall coefficient is defined as R_H = 1 / (n · q) and represents the material-specific response independent of sample thickness and current.
Why are Hall sensors made of semiconductors instead of metals?
Metals have very high carrier densities (~10²⁸ m⁻³), which makes the resulting Hall voltage minuscule (microvolts), whereas semiconductors produce easily measurable signals (millivolts to volts).
What does the sensitivity output (V/T) represent?
Sensitivity represents the voltage output generated per tesla of magnetic field at the specified operating current (V_H / B).