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Heisenberg Uncertainty Calculator

Work out heisenberg uncertainty instantly with clear inputs, formula shown and shareable results.

About Heisenberg Uncertainty Calculator

The uncertainty principle sets dx.dp >= hbar/2, so confining a particle sharpens its position at the cost of its momentum. Localising an electron to 0.1 nm - roughly an atom - forces a momentum spread of 5.3e-25 kg m/s, a speed uncertainty near 5.8e5 m/s. That confinement energy is why atoms have a definite size.

Formulas

Heisenberg uncertainty principle

dx x dp >= hbar / 2

Confinement energy scale

E = dp^2 / (2m)

Worked example

With the default values below, Heisenberg Uncertainty Calculator returns Minimum Momentum Uncertainty of 5.27286 × 10⁻²⁵. Change any input above and every figure here is recalculated in your browser.

Inputs used

Uncertainty in positionminimum 0 m
0 m
Particle massminimum 0 kg
0 kg

Results

Minimum Momentum Uncertainty
5.27286 × 10⁻²⁵ kg m/s
Corresponding Speed Uncertainty
5.7884 × 10⁵ m/s
Associated Kinetic Energy Scale
9.5250 × 10⁻¹ eV
Uncertainty Product Floor
5.2729 × 10⁻³⁵ J s

Step by step

  1. 1Values used
  2. 2Heisenberg uncertainty principle
  3. 3Confinement energy scale
  4. 4Minimum Momentum Uncertainty= 0.00000 kg m/s
  5. 5Corresponding Speed Uncertainty= 578,838.0000 m/s
  6. 6Associated Kinetic Energy Scale= 0.9525 eV
  7. 7Uncertainty Product Floor= 0.0000 J s

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Is this a limitation of measurement?

No - it is a property of the states themselves. A particle simply does not possess arbitrarily sharp position and momentum simultaneously.

Why don't we notice it?

Because hbar/2 is about 5e-35 J s. For a 1 kg object located to a micron the speed uncertainty is 5e-29 m/s, utterly negligible.

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