# Explanation of Different factor of $2$ in Formulas for the Uncertainty Principle [duplicate]

I am readind about Heisenberg's Uncertainty Principle and although the main formula most texts use is

$$\Delta x\Delta p_{x}\geq \frac{\hbar}{2}$$

or equivalently

$$\Delta x\Delta p_{x}\geq \frac{h}{4\pi}$$

I have seen it written as

$$\Delta x\Delta p_{x}\geq \hbar$$

or

$$\Delta x\Delta p_{x}\geq h$$

First of all, are all those correct formulas? If so, then how are they equivalent with each other?

• Well if the first statement is true then, logically speaking, all the other statements are true. – Harshit Joshi Jan 12 '19 at 16:55
• In my textbook, it was mentioned that the error is of the order of $h$, however on more rigorous treatment, the $\dfrac{h}{4\pi}$ factor comes into place. – Harshit Joshi Jan 12 '19 at 16:57
• Possible duplicates: physics.stackexchange.com/q/69604/2451 and links therein. – Qmechanic Jan 12 '19 at 17:52