Created By : awnish

Reviewed By : Phani Ponnapalli

Last Updated : Apr 10, 2023

Free Heisenberg's Uncertainty Principle Calculator gives the uncertainty in position or uncertainty in the momentum of a quantum sized object easily. All you need to do is provide uncertainty velocity, object mass, and uncertainty momentum and click the calculate button to get the result in less time.

Choose a Calculation:
Momentum uncertainty (σₚ)

Steps to Calculate Uncertainty Position

Following are the step by step process on how to find uncertainty position using Heisenberg's Uncertainty Principle. Go through these steps to get the exact and instant result.

  • Get the object mass, uncertainty in momentum and velocity.
  • Multiply the object mass by the velocity.
  • Obtain the change in momentum uncertainty
  • Find the product of 4π and the change in momentum.
  • Divide the constant by the product to heck the uncertainty in the position.

Heisenberg's Uncertainty Principle Formula

This principle was given by the German physicist Werner Heisenberg in the year 1927. So, it was named Heisenberg Uncertainty Principle. It tells that the momentum and position of any particle cannot be measured with arbitrarily high accuracy. The momentum and position is greater than h/4π. It is an important concept in quantum mechanics.

The formula of the Heisenberg Uncertainty Principle is defined as

σΓéôσΓéÜ ≥ h/4π


σΓéô is the standard deviation in the position measurement

σΓéÜ is the standard deviation in the momentum measurement

h is the Planck's constant


Question: The uncertainty in the momentum of a ball travelling at 20 m/s is 1 x 10-6 of its momentum. Calculate the uncertainty in position? Mass of the ball is 0.5 kg.


Given that

Mass of the ball m = 0.5 kg

Velocity v = 20 m/s

Momentum p = mv

= 0.5 x 20

= 10 kg m/s

Change in momentum Δp = p x 1 x 10-6

= 10 x 1 x 10-6

= 10-5

Heisenberg Uncertainty principle formula is σΓéôσΓéÜ ≥ h/4π

σΓéô ≥ h/4πσΓéÜ

≥ (6.626 x 10-34)/(4 x 3.14 x 10-5

≥ 0.527 x 10-29

Therefore, the uncertainty in ball position is 0.527 x 10-29 m.

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FAQ's on Heisenberg's Uncertainty Principle Calculator

1. What is Heisenberg's Uncertainty Principle formula?

Heisenberg's Uncertainty Principle equation is σΓéôσΓéÜ ≥ h/4π. Here σΓéô is the standard deviation in the position measurement, σΓéÜ is the standard deviation in the momentum measurement.

2. How to solve Heisenberg's Uncertainty Principle?

To find the uncertainty in the position of the object follow these steps. Divide the Planck's constant by 4π and multiply it with the inverse of the uncertainty in momentum. Finally, position certainty is greater than the result.

3. Define Heisenberg's Uncertainty Principle?

Quantum mechanics deals with the measurement of macro and micro-physics. It states that both the position and momentum of a particle cannot be determined at the same time accurately. So, the result of position and momentum is always greater than h/4π.

4. How to use Heisenberg Uncertainty Principle Calculator?

You have to provide all the known values in the input fields of the calculator and press the calculate button to get the velocity uncertainty or position uncertainty.