# 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.

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### 9 Responses to How to get Pi on Calculator – Without pressing the Pi Button

1. tomcircle says:

Write down: 113355
Breakup as: 113 and 355
Pi = 355/113

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2. ivasallay says:

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!

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• mathtuition88 says:

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• ivasallay says:

Oops, I typed in the reciprocal instead. The fraction should be 355/113.

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3. jessemckeown says:

3, MS; do { sin ; M+ ; MR } untill (happy); return.

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• mathtuition88 says:

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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