Confusion regarding factor 2 in uncertainty principle [duplicate]

This question already has an answer here:

I have encountered a problem regarding Heisenberg's uncertainty principle. Somewhere I found the expression

$$\Delta (x) \Delta (p) \geq \hbar$$

Whereas in some other places,

$$\Delta (x) \Delta(p) \geq \frac{h}{4\pi}$$

Here the second expression yields different expression than the first one. Why are the two expressions of uncertainty principle different? Which one is the correct form?

marked as duplicate by ACuriousMind♦, knzhou, Gert, Qmechanic♦Aug 2 '16 at 9:33

• – Sanya Aug 1 '16 at 16:54
• This principle is almost never used for exact calculations but rather to estimate orders of magnitude so you can just as well write $\Delta x \Delta o \geq \pi^{0.3} \hbar$ and it will still be valid. – Blazej Aug 1 '16 at 22:07
• Possible duplicates: physics.stackexchange.com/q/69604/2451 , physics.stackexchange.com/q/103208/2451 and links therein. – Qmechanic Aug 2 '16 at 9:31

See Ballentine: Quantum mechanics p. 224 (chapter 8): the uncertainty principle applied to position and momentum yields, in 1 dimension: $$\Delta_X \Delta_P \geq \frac{\hbar}{2}=\frac{h}{4 \pi}$$ But the other version is often used when it's mainly about an estimation of magnitude and the factor of $0.5$ does not really matter.
Edit: On Wikipedia it says that the first unproofed heuristically motivated version of the principle given by Heisenberg himself was without the factor of $0.5$. Maybe that is a historical explanation.