Every circle hides the same mysterious number: pi. Learn how to find the distance around a circle (circumference) and the space inside it (area) — then meet pi itself, all 1,000 digits of it.
Take any circle — tiny or huge — and divide its circumference (the distance around it) by its diameter (the distance straight across through the center). You'll always get the exact same number: pi, written π and pronounced "pie." It's approximately 3.14159, but its digits go on forever without ever settling into a repeating pattern.
π is the 16th letter of the Greek alphabet. Mathematicians chose it because it's the first letter of the Greek word for "perimeter." Pi is also called an irrational number — it can never be written as an exact simple fraction, and its decimal digits never end or repeat, no matter how far you calculate.
Before using the formulas, it helps to know three key measurements: the radius (center to edge), the diameter (edge to edge through the center — always twice the radius), and the circumference (the distance all the way around, like a circle's perimeter).
If a problem tells you the diameter but you need the radius, just take half of the diameter. If you have the radius but need the diameter, double it.
Since circumference is always about 3.14159 times the diameter, the formula is simply:
d = 10 units
Using π ≈ 3.14: 3.14 × 10 = 31.4
Circumference ≈ 31.4 units
"Circumference" starts like "circle" — think of it as the circle's version of perimeter. For everyday problems, using π ≈ 3.14 is close enough to get a great estimate.
The area formula uses the radius multiplied by itself (written r², meaning r × r), then multiplied by pi:
r = 5 units
r² = 5 × 5 = 25
Using π ≈ 3.14: 3.14 × 25 = 78.5
Area ≈ 78.5 square units
It's easy to accidentally double the radius instead of squaring it. Remember: r² means r × r, so for r = 5, that's 5 × 5 = 25 — not 5 × 2 = 10.
Because pi is irrational, its decimal digits never end and never repeat in any pattern — mathematicians have used supercomputers to calculate pi to trillions of digits, and it still shows no pattern at all. For virtually every real-world calculation, though, just a handful of digits (3.14159) is more than enough. Below are the first 1,000 digits of pi, just for fun.
Look closely around digit 762 and you'll spot six 9's in a row (highlighted in gold above) — a famous curiosity nicknamed the Feynman Point after physicist Richard Feynman, who joked that he'd like to memorize pi up to that point just so he could recite it and finish with "…nine, nine, nine, nine, nine, nine, and so on!"
Pi Day is celebrated every year on March 14th (3/14) around the world. The record for reciting pi from memory is over 70,000 digits, set by Rajveer Meena in 2015 — it took him nearly 10 hours! And even though pi never ends, NASA only needs about 15 digits of pi to calculate spacecraft trajectories with pinpoint accuracy across the entire solar system.
First, figure out the exact answer in terms of π — no decimals needed yet. Then use the calculator below to estimate its decimal value.
Find the exact answer in terms of π (for example, if the answer were 7π, you'd type 7).
Once you know the exact answer, type the number in front of π here and multiply by 3.14 to estimate the decimal value.