How to get Pi on Calculator – Without pressing the Pi Button

5 Ways to get Pi on Calculator without pressing the Pi button:

1) 22/7

22/7 is not an exact value for Pi, but it is a pretty good approximation. 22/7=3.142857143… has just a percentage error of 0.04% compared to the actual value of Pi!

Percentage error is calculated by: \displaystyle\frac{22/7-\pi}{\pi}\times 100\%=0.04\%

2) 355/113

355/113 is an even better approximation for Pi. 355/113=3.14159292… has merely a percentage error of 0.000008%! This is incredibly accurate for a “relatively” simple fraction like 355/113. 355/113 has a cool Chinese name called “Milü密率, given by the ancient Chinese Mathematician astronomer Zǔ Chōngzhī (祖沖之) who discovered it.

3) 3.14

Using the simple and straightforward 3.14 (0.05% error) may be sufficient for everyday purposes. 🙂

4) 2\sin^{-1}(1) or 2 arcsin(1) (Radian Mode)

This relies on the fact that \sin^{-1}(1)=\pi /2.

5) \lim_{n\to\infty}{n\sin(180^\circ/n)}

We can let n=180 for convenience, and get {180\sin(1^\circ)\approx 3.14143}. This is a pretty decent approximation for \pi, with just 0.005% error. The approximation gets better as n gets larger.

Featured Book:

Pi: A Biography of the World’s Most Mysterious Number

We all learned that the ratio of the circumference of a circle to its diameter is called pi and that the value of this algebraic symbol is roughly 3.14. What we weren’t told, though, is that behind this seemingly mundane fact is a world of mystery, which has fascinated mathematicians from ancient times to the present. Simply put, pi is weird.



Author: mathtuition88

9 thoughts on “How to get Pi on Calculator – Without pressing the Pi Button”

  1. Thank you for posting all of these ways in one convenient place. 22/7 is more accurate than 3.14, so good for 22/7! I knew that 113/355 was better still, but I could never remember what the exact fraction was. I really love the 113355 tip. I didn’t know it before, but I will never forget it now!


    1. Thanks for this wonderful tip!
      For those who are curious, this means storing 3 into the calculator’s memory, and pressing Ans+sin(Ans) till you converge to Pi! It is surprisingly quick!


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