Math · Geometry

Area & Circumference of Circles

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.

Part 01

What Is Pi (π)?

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.

1 diameter circumference 1 2 3 ≈ 3.14159… diameters
Wrap a piece of string around any circle, then lay it against the diameter — it always takes about 3.14 diameters to go all the way around.

🥧 Why Call It "Pi"?

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.

Part 02

Parts of a Circle

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).

circumference radius (r) diameter (d) = 2 × r
The radius is half the diameter; the diameter is twice the radius.

📏 Given the Diameter Instead?

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.

Part 03

Circumference of a Circle

Since circumference is always about 3.14159 times the diameter, the formula is simply:

C = π × d
(or C = 2 × π × r, since d = 2r)
1

Identify the diameter

d = 10 units

2

Multiply by pi

Using π ≈ 3.14: 3.14 × 10 = 31.4

3

Add the units

Circumference ≈ 31.4 units

💡 Memory Tip

"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.

Part 04

Area of a Circle

The area formula uses the radius multiplied by itself (written r², meaning r × r), then multiplied by pi:

A = π × r²
r r r r × r = r²
The small "2" in r² means "multiply r by itself" — not "multiply r by 2."
1

Identify the radius

r = 5 units

2

Square the radius

r² = 5 × 5 = 25

3

Multiply by pi

Using π ≈ 3.14: 3.14 × 25 = 78.5

4

Add the units

Area ≈ 78.5 square units

⚠️ Common Mix-Up

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.

Part 05

Meet Pi — All 1,000 Digits

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.


  
Scroll inside the box to see all 1,000 digits.

✨ The Feynman Point

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!"

🎉 Fun Pi Facts

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.

Part 06

Practice: Circumference & Area

First, figure out the exact answer in terms of π — no decimals needed yet. Then use the calculator below to estimate its decimal value.

Circumference

Find the Circumference

Find the exact answer in terms of π (for example, if the answer were 7π, you'd type 7).

r = 5
π units
Score: 0 correct out of 0

🧮 Pi Estimator

Once you know the exact answer, type the number in front of π here and multiply by 3.14 to estimate the decimal value.