Heisenberg's Uncertainty Principle Calculator

Find the minimum momentum uncertainty from a position uncertainty.

Min momentum uncertainty (kg·m/s) 0

Min velocity uncertainty (electron) 578,838.18

Formula: Δx·Δp ≥ ħ ÷ 2

Step-by-step with your numbers:

1. Values used:

2. Position uncertainty = 0

4. Position uncertainty squared = 0 x 0 = 0

5. Min momentum uncertainty = pi x Position uncertainty squared = 3.142 x 0 = 0kg·m/s

6. Min velocity uncertainty (electron) = 578,838.18

Did we solve your problem today?

You cannot know both a particle's position and momentum with unlimited precision.

The math behind it

Δx·Δp ≥ ħ/2. Pinning down position more tightly forces a larger spread in momentum.

Δx = 0.1 nm → Δp ≥ about 5.3 × 10⁻²⁵ kg·m/s.

Is it a measurement limit?

No — it's a fundamental property of quantum systems, not just our instruments.