# 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.

> Canonical page: https://elysiatools.com/en/tools/hall-effect-calculator

- **Category:** Science & Education

- **Keywords:** hall effect, hall voltage, hall coefficient, carrier density, n-type p-type, magnetometer sensor

## 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.

## Inputs

- **Current I** (number): e.g. 10
- **Current unit** (select)
- **Magnetic field B** (number): e.g. 0.5
- **B field unit** (select)
- **Carrier density n** (number): e.g. 1e21
- **n unit** (select)
- **Thickness t** (number): e.g. 100
- **t unit** (select)
- **Carrier type** (select)

## 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

- Select the majority carrier type as electrons (n-type, q = −e) or holes (p-type, q = +e) to determine the sign of the Hall coefficient.
- Enter the applied current (I) and magnetic field (B) with their respective units (A, mA, T, mT, or µT).
- Specify the material carrier density (n) in m⁻³ or cm⁻³ and the sample thickness (t) in mm, µm, or nm.
- The 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.

## Frequently asked questions

### 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).

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