Pi (π) is the ratio of a circle's circumference to its diameter — about 3.14. The distance around any circle, divided by the distance straight across it, always lands on the same number: 3.14159... and counting. The value of pi doesn't depend on the circle. A coin, a dinner plate, and the Earth's equator all share it. In math, pi is written with the Greek letter π, and it's one of the most important constants you'll ever meet.
Why Pi Exists — The One Number All Circles Share
Grab a round object. A coffee mug lid. Wrap a string around the rim, then measure it. Now measure straight across the middle. Divide the first number by the second.
You'll get something close to 3.14. Not exactly 3. Not 3.5. Always a little more than 3.
Most students guess the ratio should be exactly 3. That seems tidy. The distance around a circle should be about three times the distance across — and it is, roughly. But roughly isn't exact. That extra sliver — about 0.14 of a diameter — is what pi measures.
Take a circle with a diameter of 10 cm. Its circumference isn't 30 cm. It's 31.4 cm. That 1.4 cm is where pi lives.
The Value of Pi — 3.14 and 22/7
The value of pi is approximately 3.14159265358979... and the digits keep going forever, never settling into a repeating pattern.
For most calculations, we use one of two approximations:
3.14 (decimal)
22/7 (fraction, equal to about 3.142857)
Which one you pick depends on the problem. Quick rule: if the radius or diameter is a multiple of 7, use 22/7 — the sevens cancel and your answer stays a whole number. Otherwise, 3.14 is faster.
Example. Area of a circle with radius 14 cm, using 22/7:
Area = π × r² = (22/7) × 14 × 14 = 22 × 2 × 14 = 616 cm²
Try it with 3.14 and you get 615.44 — close, but messier. That's why Indian textbooks lean on 22/7 when the numbers cooperate.
The Formulas That Use Pi
Two formulas do most of the work in Grade 6–8:
Circumference of a circle = 2 × π × r (the distance around)
Area of a circle = π × r² (the space inside)
One measures around the edge. The other measures the flat space inside. Students mix these up constantly — more on that below.
Pi also appears in volume formulas: sphere volume is (4/3)πr³, cylinder volume is πr²h. And if you stick with math long enough, you'll meet pi in places that have nothing to do with circles — waves, pendulums, orbits. Seeds for later.
At Bhanzu, trainers teach circles by having students measure five round objects before anyone writes down a formula. The ratio has to feel discovered — not handed over. [Link to Bhanzu Grade 6 program]
Why Pi is Called an "Irrational" Number
Irrational doesn't mean "makes no sense." It means pi can't be written as a clean fraction of two whole numbers. 22/7 looks like a fraction, but it's only close — 22/7 works out to 3.142857..., and pi is 3.14159... They drift apart after the third decimal.
Actually — hold on. Numbers like 1/3 also have infinite decimals (0.333...), but those repeat forever. Pi's digits never repeat. They never settle into a pattern. That's what makes it genuinely irrational.
Pi is also transcendental, which is rarer. It means no ordinary algebra equation with whole-number coefficients can produce pi as its answer.
Mistakes Students Make With Pi
Three patterns show up again and again.
The formula-swapper writes πr² when the problem asks for circumference. They've memorized both formulas but haven't locked in which one measures around and which measures inside. Close to 4 in 10 students in a first circles session do this — I've watched it play out in classrooms of eight kids.
The rounder uses 3 instead of 3.14 to save time. Their answer ends up off by about 5%, which is the difference between a right answer and a wrong one.
The unit-forgetter calculates perfectly, writes "616," and forgets the cm². The math is right. The answer isn't.
Fun Facts About Pi
📌 Three surprising facts about π
Pi has been studied for over 4,000 years. Babylonian clay tablets from around 1900 BCE used a value of about 3.125 — impressively close, given they had no algebra.
The symbol π was adopted in 1706 by Welsh mathematician William Jones. Before that, people wrote things like "the quantity which when multiplied by the diameter gives the circumference." You can see why they wanted a shorter name.
March 14 (3/14) is Pi Day. It's also Albert Einstein's birthday.
What to Try Next
Grab three round things in your house — a plate, a cup, a bottle cap. Measure each one's circumference with a piece of string, then measure straight across. Divide. Write the three answers down next to each other.
You'll find pi hiding in all three.
Want your child to learn circles with a live Bhanzu trainer? [Book a free trial class].
FAQs
Q: What is pi in simple words?
Pi is the number you get when you divide any circle's circumference by its diameter. About 3.14.
Q: Why is pi equal to 22/7?
It isn't, actually. 22/7 is a close approximation — it works out to 3.142857..., and pi is 3.14159... They drift apart after the third decimal. Indian textbooks prefer 22/7 because it keeps calculations clean when the radius is a multiple of 7. Western textbooks usually stick with 3.14.
Q: Is pi the same for every circle?
Yes. That's the whole point. Big circle, small circle, pizza, planet — same ratio.
Q: Who discovered pi?
No single person. Babylonian mathematicians were using a value close to pi around 1900 BCE. The Greek mathematician Archimedes, around 250 BCE, was the first to calculate it with real precision using polygons.
Q: Why does pi go on forever?
We covered this above — pi is irrational, which means its decimal never ends and never repeats.
Was this article helpful?
Your feedback helps us write better content