Hall Coefficient Calculator

Created by Krishna Nelaturu
Last updated: Nov 21, 2022

Our Hall coefficient calculator will help you determine the Hall coefficient of an electric conductor. You can also use it to calculate the voltage induced by the Hall effect in the conductor. Join us below for a brief discussion on the Hall effect phenomenon to learn some fundamentals, including:

  • What is the Hall effect?
  • Definition of the Hall coefficient and its formula
  • Units of Hall coefficient

Be sure also to check the AC wattage calculator if you're planning to work with electricity.

The Hall effect

The Hall effect is a physical phenomenon in which a voltage difference is generated between the ends of a conductor when a magnetic field is applied perpendicular to the direction of current flow. The magnitude of the voltage difference is proportional to the strength of the magnetic field and the amount of current flowing through the conductor.

Setup to observe the Hall effect.
Setup to observe the Hall effect. Source: Wikimedia.org

The effect was first observed in 1879 by Edwin Hall, who found that electrons flowing through a conducting wire were deflected to one side when he placed it in a magnetic field. The resulting voltage difference could be measured using an electrometer, and Hall found that it was proportional to the magnetic field's strength and the amount of current flowing through the wire.

In addition, he discovered that reversing the direction of either the magnetic field or the current flow would reverse the polarity of the voltage difference.

The Hall effect has various practical applications, including electric motor control, RPM measurement, and level sensing. It is also used in research to study the properties of materials such as semiconductors and superconductors. Our intrinsic carrier concentration calculator has more information on semiconductors if you are interested.

🔎 The deflection of the electrons in the presence of the magnetic field is due to the Lorentz force. Our Lorentz force calculator will help you understand this concept better.

Hall coefficient formula

Mathematically, we can describe the Hall effect through the relation:

VHBItV_H \propto \frac{B \cdot I}{t}

Where:

  • VHV_H - Voltage difference due to Hall effect;
  • BB - Magnetic field strength;
  • II - Current passing through the conductor; and
  • tt - Thickness of the conductor.

By introducing a proportionality constant RHR_H, we get the formula for Hall effect:

VH=RHBItV_H = \frac{R_H \cdot B \cdot I}{t}

This proportionality constant RHR_H is the Hall coefficient, a property of the material the conductor is made of. By rearranging the Hall effect formula above, we will get an equation for the Hall coefficient:

RH=VHtBIR_H = \frac{ V_H \cdot t}{B \cdot I}

The units for the Hall coefficient are m3/C\rm{m^3/C} (cubic meter per Coulomb), mm3/C\rm{mm^3/C} (cubic millimeter per Coulomb), or Ωcm/G\rm{\Omega \cdot cm/G} (Ohm - centimeter per Gauss), etc. Our Hall coefficient calculator returns values in mm3/C\rm{mm^3/C} (cubic millimeter per Coulomb) unit.

How to use this Hall coefficient calculator

Using our Hall coefficient calculator is straightforward:

  • Enter the magnitude of the voltage difference induced by the Hall effect.
  • Provide the thickness of the conductor.
  • Input the value of the current passing through the conductor.
  • Enter the strength of the magnetic field, and the calculator will calculate the Hall coefficient based on this data.

If you know the Hall coefficient value, you can also use this calculator to determine the voltage difference instead.

Krishna Nelaturu
Voltage
mV
Thickness
mm
Current
A
Magnetic field
T
Hall coefficient
mm³/C
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