Heisenberg's Uncertainty Principle Calculator

Estimate Δp and Δv from Δx using the uncertainty relation.

How to Use This Calculator

1

Enter Δx

Provide position uncertainty in nanometers.

2

Choose mass

Use electron by default or enter a custom particle mass.

3

Calculate uncertainties

See Δp and the implied Δv for the chosen mass.

Formula

Δx · Δp ≥ ħ / 2

Using equality gives the minimum Δp = ħ / (2Δx)

Δv = Δp / m

About This Calculator

Estimates the minimum momentum and velocity uncertainties for a particle given a position uncertainty, illustrating the trade-off imposed by quantum mechanics.

Frequently Asked Questions

Is equality always reached?

Equality holds for minimum-uncertainty states (e.g., Gaussians). In general Δx·Δp may be larger.

Does this include relativistic effects?

No. For very small Δx and large Δp, relativistic corrections may be relevant.