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Signed Hall Coefficient from Measurements

Calculate a signed Hall coefficient from voltage, sample thickness, current and perpendicular magnetic field, retaining inverse measurement calculations.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

For Hall voltage 2 mV, thickness 1 mm, current 0.5 A and perpendicular field 0.2 T, the coefficient is 20,000 mm³/C, equivalent to 2 × 10⁻⁵ m³/C.

RH = VH t/(I B). The displayed coefficient is in mm³/C, so multiply its SI value by 10⁹.

Worked example

Enter these known values and leave the other values blank.

Signed Hall voltage
2 mV
Sample thickness along the field
1 mm
Signed measurement current
0.5 A
Signed perpendicular magnetic field
0.2 T
Signed Hall coefficient
20000 mm³/C

Assumptions and limitations

  • This relation assumes a uniform rectangular sample, transverse Hall voltage and magnetic field perpendicular to the current. Thickness is the sample dimension along the field.
  • The coefficient control uses mm³/C. Divide its displayed value by 10⁹ to obtain m³/C; it is a volume-per-charge coefficient, not resistance.
  • Keep the voltage, current and field sign conventions consistent. Reversing one of these measured signs reverses the inferred coefficient; thickness stays strictly positive.
  • Current and field must be nonzero to infer a coefficient. Zero voltage and zero coefficient are valid algebraic values, but do not uniquely determine every inverse quantity.
  • The result does not identify material composition or establish a single-carrier density. Multiple carrier populations, geometry and measurement offsets can complicate interpretation.
  • All five controls remain editable. A missing quantity is filled only when its inverse has enough information and a finite result.

Common questions

Why can the coefficient be negative?

Its sign depends on the Hall-voltage convention and the signed current and field. Use a consistent orientation when interpreting carrier polarity.

Is the result in m³/C?

The retained control displays mm³/C. Divide by one billion for m³/C.

Can I measure it with zero magnetic field?

No. This coefficient relation divides by field and current; both must be nonzero.

References

Thickness must be strictly positive; signed measurement current and perpendicular field must be nonzero. Preserve signed voltage and coefficient, including zero, and the captured mm³/C coefficient scale.

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