How it works
Every point on a circle is the same distance from its centre; that distance is the radius (r). Everything else follows from r and the constant π ≈ 3.14159. Enter whichever measurement you have — a tape-measured circumference, a pipe’s diameter, a known area — and get the rest.
area A = π r² · circumference C = 2 π r = π d · diameter d = 2 r r from area = √(A ÷ π) · r from circumference = C ÷ (2 π)Worked examples. A circle with radius 5 cm has diameter 10 cm, circumference 2 × π × 5 = 31.4159 cm and area π × 25 = 78.5398 cm². A circular patio of 100 m² has radius √(100 ÷ π) = 5.6419 m and a perimeter of 35.449 m. A tree trunk with a 10 ft circumference is 3.1831 ft across.
Which value of π?
π never ends (3.14159265…). Schools often use 3.14 or 22/7; this calculator uses the exact value, so answers can differ from a textbook in the second decimal. Radius 7 with 22/7 gives exactly 154; with exact π it is 153.938.
Units
- Radius, diameter and circumference are lengths in whatever unit you enter.
- Area is in square units: cm², m², in², ft². To convert cm² to m², divide by 10,000; ft² to yd², divide by 9.
Practical uses
- Gardens and patios: area for mulch, sod or pavers; circumference for edging.
- Concrete columns and footings: area × height = volume — continue in the concrete calculator.
- Pizza maths: a 12-inch pizza (113 in²) has more than twice the area of an 8-inch one (50 in²), because area scales with the square of the diameter.
- Wheels: one turn of a 26-inch wheel covers π × 26 ≈ 81.7 inches.
Semicircles and quarter circles
A semicircle’s area is π r² ÷ 2 and a quarter circle’s is π r² ÷ 4. The perimeter of a closed semicircle is π r + 2r (the arc plus the straight edge).
For rectangular rooms and lots use the square footage calculator; for anything else, the scientific calculator.