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Heisenberg Uncertainty Calculator.

Find the minimum momentum uncertainty allowed by a position uncertainty.

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Results update as you type.

Minimum momentum uncertainty: 0

Minimum momentum uncertainty

0.000000
Minimum uncertainty product: 0

Minimum uncertainty product

0.000000

Educational SI models with assumptions stated in each description; verify engineering decisions independently.

Use Cases

Quantum Physics Homework

Quickly verify the minimum momentum uncertainty for a given position uncertainty in quantum mechanics problems, ensuring correct application of the uncertainty principle.

Example: If Δx = 1e-10 m, the calculator gives Δp ≈ 5.27e-25 kg·m/s.

Particle Confinement Analysis

Estimate the minimum momentum spread for particles confined to a small region, useful in nanotechnology and quantum well studies.

Example: For an electron confined to 1 nm, find the minimum momentum uncertainty.

Frequently Asked Questions

What does the Heisenberg Uncertainty Calculator do?
This calculator computes the minimum possible momentum uncertainty (Δp) given a position uncertainty (Δx) using the Heisenberg uncertainty principle: Δx * Δp ≥ ħ/2. It uses the reduced Planck constant (ħ ≈ 1.0545718e-34 J·s).
How is the minimum momentum uncertainty calculated?
The calculator uses the formula Δp = ħ / (2 * Δx), where Δx is the position uncertainty in meters. The result is the minimum momentum uncertainty in kg·m/s, representing the lower bound set by quantum mechanics.
What units are used for position and momentum uncertainty?
Position uncertainty is entered in meters (m). The calculated momentum uncertainty is given in kilogram meters per second (kg·m/s), which is the standard SI unit for momentum.

Tips & Common Mistakes

Tips

  • Enter position uncertainty in meters. Use scientific notation for very small values, e.g., 1e-10 for 0.1 nm.
  • Remember that the result is the minimum possible momentum uncertainty; actual uncertainty may be larger.
  • This calculator uses the standard form of the uncertainty principle (Δx·Δp ≥ ħ/2). Some texts use h/(4π) which is equivalent.
  • Double-check your input: a smaller position uncertainty leads to a larger momentum uncertainty.

Common Mistakes to Avoid

  • Forgetting to convert units to meters before entering. For example, entering 1 nm as 1 instead of 1e-9 m.
  • Confusing the reduced Planck constant (ħ) with Planck's constant (h). This calculator uses ħ = h/(2π).
  • Misinterpreting the result as an exact value rather than a minimum bound.

Last updated: August 13, 2026