Quantum Hall Resistance Calculator
Enter the Landau level filling factor to compute the quantized Hall resistance R_H = R_K/ν, where R_K = h/e².
Input Data
Results
At a glance:The quantum Hall effect (von Klitzing, 1980, Nobel 1985) shows the Hall resistance of a 2D electron gas in a strong magnetic field is quantized: R_H = R_K/ν, where R_K = h/e² ≈ 25812.807 Ω is the von Klitzing constant (from Planck's constant h and elementary charge e) and ν is the Landau-level filling factor. For integer ν (1,2,3...) the Hall plateaus are exact; certain fractions (1/3, 2/5...) appear in the fractional quantum Hall effect. Because R_K is a fundamental constant, the quantum Hall effect defines the standard of electrical resistance. This tool computes R_H = R_K/ν from ν (and reports R_K, h, e).
Formula
R_H = R_K/ν = (h/e²)/ν
R_K ≈ 25812.807 Ω
$$R_H = \frac{R_K}{\nu}, \quad R_K = \frac{h}{e^2} \approx 25812.807\,\Omega, \quad \nu = \frac{n h}{e B}$$How to Use
- Enter the filling factor ν.
- The calculator returns R_H in Ω and kΩ, plus R_K, h and e.
Case Studies
Integer plateau
ν = 2.
R_H = 25812.807/2 ≈ 12906.4 Ω ≈ 12.9 kΩ.
A standard quantum Hall plateau.
FAQ
Why is the quantum Hall resistance so precise?
The plateaus occur at exactly R_K/ν, set only by fundamental constants h and e, independent of the material — making it the resistance standard.
What is the filling factor ν?
The ratio of electron density to magnetic flux quantum density; integer ν gives the integer quantum Hall effect, certain fractions the fractional effect.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.