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.