Compute the minimum uncertainty allowed by quantum mechanics with Δx·Δp ≥ ħ/2 — enter the position uncertainty to get the minimum momentum uncertainty, or solve the other way.
Heisenberg's uncertainty principle sets a fundamental limit: the more precisely a particle's position is known, the less precisely its momentum can be, and vice versa. The product of the uncertainties can never fall below ħ/2: Δx·Δp ≥ ħ/2.
This is not a measurement flaw but a property of quantum systems. The calculator returns the minimum uncertainty in one quantity given the other, using the reduced Planck constant ħ = 1.0546×10⁻³⁴ J·s.
For the underlying physics, read our explanation of quantum tunneling and the uncertainty principle.
It states that the position and momentum of a particle cannot both be known exactly: Δx·Δp ≥ ħ/2. Reducing the uncertainty in one increases it in the other.
The reduced Planck constant ħ = h/2π ≈ 1.0546×10⁻³⁴ J·s. It sets the scale of the smallest possible uncertainty product.
No. It is a fundamental property of quantum systems, not a limitation of measurement tools. Even with perfect instruments the product Δx·Δp cannot be less than ħ/2.
Because ħ is extraordinarily small. For macroscopic objects the required uncertainties are far too tiny to detect; the principle only matters at atomic and subatomic scales.