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Heisenberg Uncertainty Calculator

Find the textbook lower bound Δp ≥ ħ / (2 Δx) on momentum spread.

 

Δp (kg·m/s)

About this calculator

Use this calculator for the Heisenberg inequality in one dimension. Enter a position uncertainty Δx; the result is the smallest momentum uncertainty this relation allows: Δp = ħ / (2 Δx), with ħ = h / (2π). An atom-scale 10⁻¹⁰ m gives a tiny but nonzero Δp of about 5.3×10⁻²⁵ kg·m/s.

This is a theoretical limit, not a measurement recipe and not a statement about instrument noise. Δx must be greater than zero.

Δx (m): Position uncertainty in metres.

Δp (kg·m/s): Minimum momentum uncertainty.