What Is Pi (π)?
π (pi) ≈ 3.14159265...
Pi is the ratio of every circle's circumference (distance around) to its diameter (distance across).
Measure any circle — a coin, a wheel, a plate. Divide the circumference by the diameter. You always get the same number: approximately 3.14159. That number is π.
Where π comes from
Take a circle with diameter 1. Its circumference is π (approximately 3.14159). Take a circle with diameter 10. Its circumference is 10π (approximately 31.4159). The ratio is always π, regardless of the circle's size.
This is a physical fact that can be verified with a string and a ruler. Your child can discover π experimentally.
Key properties
- π is irrational — its decimal expansion goes on forever without repeating (3.14159265358979...)
- π is constant — it is the same for every circle in the universe
- π ≈ 3.14 for most calculations (or 22/7 as a fraction approximation)
Where π appears in formulas
- Circumference: C = πd = 2πr
- Area of a circle: A = πr²
- Volume of a cylinder: V = πr²h
- Volume of a sphere: V = (4/3)πr³
Common confusion
Thinking π = 3.14 exactly: 3.14 is an approximation. The actual value has infinitely many decimal places. For most school problems, 3.14 (or the π button on a calculator) is accurate enough.
Thinking π only matters for circles: π appears throughout mathematics — in probability, trigonometry, waves, and even places that seem unrelated to circles.
Related concepts
- Circles: circumference and area: full teaching guide
- Irrational numbers: π is irrational
- Volume: π in 3D formulas