Value of Pi
Pi is the ratio of a circle's circumference to its diameter — the same for every circle, everywhere. Here is its value, in decimals and fractions, and how much of it you'll ever really need.
The decimal value
To thirty places, pi is:
3.141592653589793238462643383279…
And it keeps going forever, with no repeating pattern. Those digits never settle into a loop and never stop, which is what makes pi so endlessly fascinating (and so hard to memorize). For most people the first three digits — 3.14 — are all they'll ever recite, but the full expansion has now been computed to more than 100 trillion places without any sign of order.
Common rounded values
Depending on how much precision you need, pi is usually rounded to one of these:
3.14— the everyday value, fine for school and most quick estimates.3.1416— four decimals, good enough for careful engineering by hand.3.14159— five decimals, the value most scientific calculators show at a glance.
Each is just pi chopped off and rounded at a convenient spot. None is exact, because pi has no exact decimal — but each is close enough for its job.
The value of pi as a fraction
Pi is irrational, so no fraction equals it exactly. But some fractions come remarkably close. The famous one is 22/7 ≈ 3.142857…, which matches pi to two decimal places and has been used as a stand-in for over two thousand years — see our full breakdown of 22/7. Even better is 355/113 ≈ 3.14159292…, which is correct to a jaw-dropping six decimal places and is easy to remember: write 113355, split it down the middle, and put the big half over the small half. These are approximations, not equalities — but wonderfully good ones.
Pi in radians and degrees
Pi isn't only about circles' sizes; it's the natural unit for measuring angles. A full circle is 2π radians, so half a circle is π radians — which means π rad = 180°. That single fact is why pi shows up all through trigonometry: a right angle is π/2, and the angles you sweep on a clock or a wheel are all just fractions of pi.
Why the value never resolves
Pi is irrational — proven by Johann Lambert in 1761 — meaning it cannot be written as a ratio of two whole numbers, and its decimals never repeat. It is also transcendental (Lindemann, 1882), a stronger property meaning it isn't the root of any simple polynomial equation. That's the deep reason you can compute pi forever and never reach a tidy stopping point. The value isn't unknown; it's just infinite. For the full story, see Is Pi Infinite?
How many digits do you actually need?
Fewer than you'd think:
- 2 digits (3.14) — homework, pie charts, and everyday life.
- 15 digits — NASA's Jet Propulsion Laboratory uses this for interplanetary navigation. That's it. Fifteen.
- 39 digits — enough to compute the circumference of the entire observable universe to within the width of a single hydrogen atom.
So the trillions of known digits are a mathematical curiosity and a stress test for supercomputers, not a practical need. The value of pi you'll use in real life fits comfortably on one line — the rest is for the love of the chase.