Pi Calculator
View pi to any number of digits (up to 100), calculate circle measurements from a radius, and compare how accurate popular pi approximations really are.
Pi is the ratio of a circle's circumference to its diameter. It is the same for every circle and approximately equal to 3.14159265358979.
Key Properties of Pi:
- Pi is irrational: its decimal digits never end and never repeat.
- Pi is transcendental: it is not the root of any polynomial with integer coefficients.
- The symbol was first used by Welsh mathematician William Jones in 1706 and popularized by Euler.
Common Approximations:
- 22/7 = 3.142857... -- accurate to 2 decimal places. Error is about 0.04%. This fraction has been used since antiquity.
- 355/113 = 3.14159292... -- accurate to 6 decimal places. Error is about 0.0000085%. Discovered by Chinese mathematician Zu Chongzhi around 480 AD. Remarkably accurate for such a simple fraction.
- 3.14 -- the basic 2-digit approximation, sufficient for everyday estimates.
Pi in Circle Formulas:
- Circumference: C = 2πr
- Area: A = πr²
- Volume of a sphere: V = (4/3)πr³
Fun Facts:
Pi Day is March 14 (3/14). As of 2024, pi has been computed to over 100 trillion digits. For most engineering applications, 15 digits of pi are more than enough to calculate the circumference of the observable universe to within the width of a hydrogen atom.