Calculate the fundamental limits of precision for conjugate variables in quantum mechanics.
Known Precision
Uncertainty Limit
Enter uncertainty to calculate limit
About this calculator
Quick Reference
ΔxPosition Uncertainty
ΔpMomentum Uncertainty
ΔEEnergy Uncertainty
ΔtTime Uncertainty
hPlanck's Constant
Overview
Formulated by Werner Heisenberg in 1927, the uncertainty principle states that certain pairs of physical properties cannot be simultaneously known with arbitrary precision.
💡
Pro Tips
The more precisely the position (Δx) is known, the less precisely the momentum (Δp) can be known, and vice versa.
This is not a measurement error but a fundamental property of matter waves.
The product of uncertainties must be at least h / 4π (or ħ / 2).
Constants used: Planck's constant h ≈ 6.626 x 10⁻³⁴ J·s.
!
Fun Facts
"In the macroscopic world, these uncertainties are so small they are completely unnoticeable."
"The principle explains why electrons don't 'fall' into the nucleus of an atom."
"Quantum tunneling, used in flash memory, is a direct consequence of the uncertainty principle."
