How to calculate a circle — radius, circumference and area step by step
A circle is fully described by a single quantity: the radius r. From it you get the diameter (d = 2r), the circumference (C = 2πr) and the area (A = πr²). Worked example: r = 5 → C ≈ 31.42 and A ≈ 78.54. These formulas are standard geometry from Grade 7 / Year 8 onward.
Quick answer
A circle is fully determined by its radius r. Everything else follows: the diameter is d = 2r, the circumference C = 2πr and the area A = πr². Example r = 5: d = 10, C ≈ 31.42, A ≈ 78.54.
At a glance
| Example | r = 5 |
|---|---|
| Method | Via the radius (d=2r, C=2πr, A=πr²) |
| Steps | 4 |
| Result | d=10, C≈31.42, A≈78.54 |
| Constant | π ≈ 3.14159 |
| Grade level | Grade 7 (ages 12–13) |
Worked example: r = 5
We start from the radius and work out the diameter, circumference and area.
How to calculate a circle step by step
Whichever quantity you start with, the path always leads to the radius first, then to the other three quantities.
Step 1 · Start
r = 5The radius is given — the starting quantity for everything else.Step 2 · ·2
d = 2r = 2·5 = 10The diameter is twice the radius.Step 3 · ·2π
C = 2πr = 2π·5 ≈ 31.42The circumference is the length of the circle's edge.Step 4 · ·π, ²
A = πr² = π·5² ≈ 78.54The area grows with the square of the radius — the result.
Why the circle formulas work
The constant π ≈ 3.14159 is the fixed ratio of circumference to diameter — the same for every circle. From that, C = πd = 2πr follows at once. Double the radius and the circumference doubles too, but the area quadruples, because in A = πr² the radius is squared. Since all quantities are linked through r, one value is enough to compute the rest.