# Hall Coefficient Calculator

Created by Miłosz Panfil, PhD
Reviewed by Małgorzata Koperska, MD and Adena Benn
Last updated: Jun 05, 2023

With the Hall Coefficient Calculator, you can easily compute the Hall coefficient. The Hall coefficient unveils the nature of the charge carriers in conductors. If you are wondering what the Hall effect is and what is the Hall coefficient formula, you can learn all of it from the text below.

## What is the Hall effect?

If we apply a voltage difference to a wire, the electric current will start to flow. The charge carriers responsible for electric current will move along straight lines accelerated by the electric field until they collide with each other. You can learn more about this in our acceleration in the electric field calculator. After the collision, they will be again accelerated, resulting in an effective velocity, called the drift velocity, directed along the wire.

Instead of a thin wire, we can imagine a flat, sandwich-like piece of a conductor. Now, besides applying the voltage difference, we also place it in the magnetic field. The magnetic field is in the direction perpendicular to the flat conductor. Due to the Lorentz force, the paths of charge carriers curve, resulting in an accumulation of charge carriers on one side of the conductor. This accumulation leads to a voltage difference V across the conductor. The appearance of the voltage difference due to the magnetic field is the Hall effect.

## Hall coefficient formula

The Hall coefficient formula quantifies the strength of the Hall effect. The Hall coefficient is defined as

RH = V × t / (I × B),

where

• RH [m³/C] is the Hall coefficient,
• V [V] is the observed voltage difference,
• t [m] is the thickness of the conductor,
• I [A] is the current running through the conductor,
• B [T] is the magnetic field.

The Hall coefficient reveals the nature of the charge carriers, their concentration in the conductor, and their charge. The formula is

RH = - 1/(n × q),

where

• n [1/m³] is the concentration of the carriers,
• q [C]  is the charge of a single carrier.

The Hall effect is significant because it allows us to find out the sign of the charge carriers. For example, with the Hall effect, we can demonstrate that in some semiconductors, the current is carried by positively charged holes and not by electrons.

## Hall coefficient calculator

With the Hall coefficient calculator, you can quickly compute the Hall coefficient. You can also get other quantities from the Hall coefficient formula if you know the Hall coefficient. For example, the Hall effect is sometimes used to measure the magnetic field. It is simple to measure the voltage difference V with a voltmeter and the current I with an ammeter. If we know the Hall coefficient, we can then easily find the magnetic field.

For example, the Hall coefficient of copper is RH = 0.133 mm³/C. Say we have a copper plate of thickness t = 0.02 mm. If we run through it a current of I = 10 A and observe a voltage difference V = 0.05 mV, we would get that that the magnetic field is B = 0.7519 T.

Miłosz Panfil, PhD
Voltage
mV
Thickness
mm
Current
A
Magnetic field
T
Hall coefficient
mm³/C
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