Geometry · 5 min read
How to Calculate Circle Area and Circumference
π r² and 2 π r — radius is the only input
A circle is fully determined by its radius r. Area is the shaded disk π r²; circumference is the boundary length 2 π r. This tutorial walks through both formulas, a radius-3 worked example, and a playground that substitutes your r into the π expressions.
Written by the My Calculator Stack editorial team. About our methods
Area and circumference here use the same π as the Circle calculator. Radius must be positive.
1.What area and circumference are
Radius r is the distance from the center to any point on the circle. Diameter is twice that: d = 2r. Circumference C is the length of the boundary — one full trip around. Area A is the region enclosed by that boundary. Both A and C are determined by r alone; you do not need a separate measurement of the rim if you already know the radius.
2.The formulas
Area uses π times radius squared: A = π r². Circumference is π times the diameter, or 2 π r. The same π (about 3.14159) appears in both. If you are given the diameter instead of the radius, convert first: r = d / 2, then apply the same formulas.
\[ A = \pi r^{2},\quad C = 2\pi r \]
3.Worked example
Take radius r = 3 — the same default as the Circle calculator. Then A = π × 3² = 9π ≈ 28.274, and C = 2π × 3 = 6π ≈ 18.850. Diameter is 2 × 3 = 6, which is another way to see C = π d.
\[ A=\pi(3)^{2}=9\pi,\quad C=2\pi(3)=6\pi \]
4.Circle playground
Move the radius slider to substitute r into A = π r² and C = 2 π r. The shaded disk is the area; the coral ring is the circumference. This is a teaching widget — no favorites, no full calculator chrome. Open the Circle calculator when you want the standalone tool.
Inline playground
Area A
28.274
Circumference C
18.850
A = π×3² ≈ 28.274 · C = 2π×3 ≈ 18.850
Teaching aid only — radius must be positive. Both formulas use the same π.
Open the full Circle calculator →5.Open the full calculator
The Circle calculator uses the same π formulas and the same radius-3 example, and also reports diameter, with How it works, FAQ, and related geometry tools on one page. Browse other geometry calculators if you need area, volume, or the Pythagorean theorem next.
Try it yourself
Open the related calculator and put these formulas to work.