Heisenberg's Uncertainty Principle Calculator

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This calculator illustrates Heisenberg's Uncertainty Principle, which states that the more precisely the position of a particle is determined, the less precisely its momentum can be known, and vice versa.

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How To Use

How to use this calculator

Start with your values, or try a preset.

Step 1

Enter Uncertainty in Position (Δx) (meters) and Mass of the Particle (m) (kilograms) in the units shown.

Step 2

Read Reduced Planck Constant (ħ) (J·s), Uncertainty in Momentum (Δp) (kg·m/s), and Uncertainty in Velocity (Δv) (m/s) in the results panel. Results update as you change the inputs.

Step 3

Choose a preset to load an example, then adjust the values for your situation.

Worked Examples

Example calculations

See the inputs and their calculated results.

Electron

Uncertainty in Position (Δx) (meters): 0.0000000001 m; Mass of the Particle (m) (kilograms): 0.0000000000000000000000000000009109 kg

Reduced Planck Constant (ħ) (J·s): 0.0000000000000000000000000000000001054560653 J·s; Uncertainty in Momentum (Δp) (kg·m/s): 0.000000000000000000000001054560653 kg·m/s; Uncertainty in Velocity (Δv) (m/s): 1,157,712.87 m/s

Proton

Uncertainty in Position (Δx) (meters): 0.0000000001 m; Mass of the Particle (m) (kilograms): 0.0000000000000000000000000016726 kg

Baseball

Uncertainty in Position (Δx) (meters): 0.01 m; Mass of the Particle (m) (kilograms): 0.145 kg

Reduced Planck Constant (ħ) (J·s): 0.0000000000000000000000000000000001054560653 J·s; Uncertainty in Momentum (Δp) (kg·m/s): 0.00000000000000000000000000000001054560653 kg·m/s; Uncertainty in Velocity (Δv) (m/s): 0.00000000000000000000000000000007272832089 m/s

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