Uncertainty Principle Calculator

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

Position Uncertainty (Δx)

Particle Mass

Tab to move between fields

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

How to Use This Calculator

Enter Position Uncertainty (Δx) in meters — how precisely you know the particle's location. 1e-10 m is atomic scale.
Enter Particle Mass (kg): the default is an electron (9.109e-31 kg); a proton is 1.67e-27 kg.
Read Min Momentum Uncertainty (Δp) — the fundamental limit imposed by Heisenberg's relation Δx·Δp ≥ ℏ/2.
Min Velocity Uncertainty (Δv = Δp/m) shows how precisely speed can be known given the position measurement.
The Ratio (Δx·Δp)/(ℏ/2) shows how close your measurement scenario is to the quantum limit — a value of 1.0 saturates the bound.

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Formula

Δx × Δp ≥ ℏ/2

Calculate quantum wave function properties including probability density, momentum, energy, and phase/group velocities.

Calculate quantum measurement probabilities, expectation values, variance, and wave function collapse.

Calculate atomic energy levels, transition energies, photon wavelengths, and spectral series for hydrogen-like atoms.

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