Heisenberg Uncertainty Principle Calculator

Minimum momentum/velocity uncertainty for a given position uncertainty, and minimum energy uncertainty for a given lifetime.

Results

Minimum Δp—
Minimum Δv—
Minimum ΔE—
Minimum Δf—

How to use the Heisenberg Uncertainty Principle Calculator

  1. Enter or select: Position uncertainty Δx, Mass m, Time uncertainty Δt.
  2. The results (Minimum Δp, Minimum Δv, Minimum ΔE, Minimum Δf) are calculated instantly as you type.
  3. Use “Copy link” to share the calculation with the same input values.

Formula

  • Δx·Δp ≥ ħ/2
  • ΔE·Δt ≥ ħ/2
ExpressionApply operationsCalculated result