Uncertainty Principle Calculator

Heisenberg's uncertainty principle sets a hard floor on how precisely position and momentum can both be known at once, and this calculator takes your chosen position uncertainty and derives every quantity that floor implies. It starts from the minimum-uncertainty case, Δx·Δp = ℏ/2, so entering a smaller position uncertainty forces the minimum momentum uncertainty higher — the two trade off directly, and no measurement can beat that product regardless of instrumentation quality. From the momentum result it derives a minimum velocity uncertainty by dividing by particle mass, and a minimum energy uncertainty from the momentum-energy relation for a free particle; the energy figure then feeds an energy-time uncertainty calculation and a de Broglie wavelength at that minimum momentum.

The ratio output simply reports how close the combination Δx·Δp sits to ℏ/2 — the calculator always sets this to exactly 1.0 because it computes the smallest possible Δp for your chosen Δx, so it's really confirming the calculator is evaluating the bound itself rather than a looser real-world measurement scenario. Because the calculator solves for the tightest case, it describes an idealized minimum-uncertainty wave packet, not the actual spread a real detector or experiment would report — real measurements typically have larger uncertainty products than this floor, never smaller. It's most useful for building intuition about scale: at atomic dimensions the position-momentum tradeoff becomes physically significant, while at everyday, human-scale distances the same relation produces uncertainties too small to ever notice.