Free Heisenberg Uncertainty Calculator
Calculate the minimum uncertainty in position given momentum uncertainty (or vice versa): dx >= hbar / (2 * dp).
kg m/s
Minimum Position Uncertainty (dx)
0.000000000527300 m
Position Uncertainty (nm)0.527300 nm
Heisenberg Uncertainty Principle
The uncertainty principle states a fundamental limit on the precision with which position and momentum can be known simultaneously.
Formula
dx * dp >= hbar / 2
where hbar = h / (2 pi) = 1.0546 x 10^-34 J s.
Given dp, the minimum dx is hbar / (2 dp). This is not a measurement limitation but a fundamental property of nature.
Example Calculation
An electron with dp = 1e-25 kg m/s.
- 01dx_min = hbar / (2 dp)
- 02dx_min = 1.0546e-34 / (2 * 1e-25)
- 03dx_min = 1.0546e-34 / 2e-25
- 04dx_min = 5.273e-10 m = 0.527 nm
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