Uncertainty Principle Calculator

Calculate Heisenberg uncertainty limits for position-momentum and energy-time conjugate pairs.

Position Uncertainty (Δx)

Particle Mass

Min Momentum Uncertainty (Δp)

0 kg·m/s

Min Velocity Uncertainty (Δv)

578,878.03 m/s

Min Energy Uncertainty (ΔE)

0 J

Min Time Uncertainty (Δt)0 s

Δx·Δp / (ℏ/2)1

De Broglie Wavelength0 m

Min Momentum Uncertainty (Δp)

0 kg·m/s

Min Velocity Uncertainty (Δv)

578,878.03 m/s

Min Energy Uncertainty (ΔE)

0 J

How to Use This Calculator

Start by filling in the input fields below. Results update instantly as you type, so you can experiment with different values to see how they affect the outcome.
Position Uncertainty (Δx) — Uncertainty in position measurement Accepts values from 1e-15 m to 0.00001 m (default: 1e-10 m).
Particle Mass — Mass of the particle (default: electron) Accepts values from 1e-31 kg to 1e-20 kg (default: 9.109e-31 kg).
Once all inputs are set, review your results in the Results panel. Here's what each output means:
Min Momentum Uncertainty (Δp) — shown as a numeric value. This is the primary result of this calculator.
Min Velocity Uncertainty (Δv) — shown as a numeric value. This is the primary result of this calculator.
Min Energy Uncertainty (ΔE) — shown as a numeric value. This is the primary result of this calculator.
Min Time Uncertainty (Δt) — shown as a numeric value.
Δx·Δp / (ℏ/2) — shown as a numeric value.
De Broglie Wavelength — shown as a numeric value.
Explore the related calculators below if you need deeper analysis or want to approach this topic from a different angle.

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Formula

Δx × Δp ≥ ℏ/2

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