Heisenberg Uncertainty Calculator Formula
Understand the math behind the heisenberg uncertainty calculator. Each variable explained with a worked example.
Formulas Used
Minimum Position Uncertainty (dx)
delta_x = 1.0546e-34 / (2 * delta_p)Position Uncertainty (nm)
delta_x_nm = 1.0546e-34 / (2 * delta_p) * 1e9Variables
| Variable | Description | Default |
|---|---|---|
delta_p | Momentum Uncertainty (dp)(kg m/s) | 1e-25 |
How It Works
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.
Worked Example
An electron with dp = 1e-25 kg m/s.
delta_p = 1e-25
- 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
Ready to run the numbers?
Open Heisenberg Uncertainty Calculator