Hall Coefficient

RH = 1 / (n · q)

Quick answer

This calculator solves RH = 1 / (n × q) (sign gives carrier type) for Hall Coefficient. With Carrier Density 1 × 10¹⁷ 1/cm³, Carrier Charge 100 mC, the result is 1 × 10⁻¹⁶ cm³/C. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

Hall Coefficient (m³/C)
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Formula

RH = 1 / (n × q) (sign gives carrier type)

Description

The Hall coefficient relates the Hall voltage measured across a current-carrying conductor in a magnetic field to the carrier density and charge. Its magnitude reveals how many charge carriers there are per unit volume, and its sign tells whether conduction is by electrons or holes. It is the standard way to characterise semiconductors and Hall-effect sensors.

Variables

  • RH — Hall coefficient (m³/C)
  • n — Charge-carrier density (1/m³)
  • q — Carrier charge (C, ≈1.602×10⁻¹⁹)

Practical Notes

A large Hall coefficient (low carrier density) gives a big, easy-to-measure Hall voltage—which is why Hall sensors use lightly-doped semiconductors rather than metals.

Symbols and units

Symbol Meaning Default unit Accepted units
RH Hall Coefficient m³/C m³/C, cm³/C
n Carrier Density 1/m³ 1/m³, 1/cm³
q Carrier Charge C pC, nC, µC, mC, C

Step by step

  1. 1. What you know: Carrier Density 1 × 10¹⁷ 1/cm³, Carrier Charge 100 mC
  2. 2. The relation: RH = 1 / (n × q) (sign gives carrier type)
  3. 3. Substitute: n = 1 × 10¹⁷ 1/cm³, q = 100 mC
  4. 4. Result: Hall Coefficient = 1 × 10⁻¹⁶ cm³/C

Worked examples

Minimum range

Given: Carrier Density 1 × 10¹³ 1/cm³, Carrier Charge 100 µC

Result: Hall Coefficient = 1 × 10⁻⁹ cm³/C

Low range

Given: Carrier Density 1 × 10¹⁴ 1/cm³, Carrier Charge 1 mC

Result: Hall Coefficient = 1 × 10⁻¹¹ cm³/C

Typical

Given: Carrier Density 1 × 10¹⁷ 1/cm³, Carrier Charge 100 mC

Result: Hall Coefficient = 1 × 10⁻¹⁶ cm³/C

High range

Given: Carrier Density 1 × 10²⁰ 1/cm³, Carrier Charge 1 C

Result: Hall Coefficient = 1 × 10⁻²⁰ cm³/C

Maximum range

Given: Carrier Density 1 × 10²¹ 1/cm³, Carrier Charge 10 C

Result: Hall Coefficient = 1 × 10⁻²² cm³/C

Solving for each variable

Solve for Hall Coefficient

Carrier Density 1 × 10¹³ 1/cm³, Carrier Charge 100 µC → 1 × 10⁻⁹ cm³/C

Solve for Carrier Density

Hall Coefficient 0.001 cm³/C, Carrier Charge 100 µC → 1 × 10⁷ 1/cm³

Solve for Carrier Charge

Hall Coefficient 0.001 cm³/C, Carrier Density 1 × 10¹³ 1/cm³ → 100 pC

How Hall Coefficient changes with Carrier Density

Carrier Density (input) Hall Coefficient (result)
1 × 10¹⁶ 1/cm³ 1 × 10⁻¹⁵ cm³/C
2.5 × 10¹⁶ 1/cm³ 4 × 10⁻¹⁶ cm³/C
5 × 10¹⁶ 1/cm³ 2 × 10⁻¹⁶ cm³/C
7.5 × 10¹⁶ 1/cm³ 1.33 × 10⁻¹⁶ cm³/C
1 × 10¹⁷ 1/cm³ 1 × 10⁻¹⁶ cm³/C
1.5 × 10¹⁷ 1/cm³ 6.67 × 10⁻¹⁷ cm³/C
2 × 10¹⁷ 1/cm³ 5 × 10⁻¹⁷ cm³/C
4 × 10¹⁷ 1/cm³ 2.5 × 10⁻¹⁷ cm³/C
7 × 10¹⁷ 1/cm³ 1.43 × 10⁻¹⁷ cm³/C
1 × 10¹⁸ 1/cm³ 1 × 10⁻¹⁷ cm³/C

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Frequently asked questions

How do you calculate Hall Coefficient?

Use RH = 1 / (n × q) (sign gives carrier type). With Carrier Density 1 × 10¹⁷ 1/cm³, Carrier Charge 100 mC, Hall Coefficient works out to 1 × 10⁻¹⁶ cm³/C.

What is the formula for Hall Coefficient?

The formula is RH = 1 / (n × q) (sign gives carrier type). The Hall coefficient relates the Hall voltage measured across a current-carrying conductor in a magnetic field to the carrier density and charge.

How do you find Carrier Density when you know the other values?

Rearrange for Carrier Density: with Hall Coefficient 0.001 cm³/C, Carrier Charge 100 µC, Carrier Density is 1 × 10⁷ 1/cm³.

How do you find Carrier Charge when you know the other values?

Rearrange for Carrier Charge: with Hall Coefficient 0.001 cm³/C, Carrier Density 1 × 10¹³ 1/cm³, Carrier Charge is 100 pC.

Related Concepts

All Fields & Electromagnetism formulas →
Coulomb’s Law Electric Field of a Point Charge Electric Potential of a Point Charge Gauss’s Law (Electric Flux) Lorentz Magnetic Force Force on a Current-Carrying Wire Force Between Parallel Wires Magnetic Field of a Straight Wire

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