Circle Calculator
Calculate a circle’s area, circumference and diameter from its radius.
Enter a circle’s radius to get its area, circumference and diameter instantly. Useful for geometry homework, design and any project involving round shapes.
Formula / method
Examples
Area 78.54, Circ 31.42
Area 314.16
From radius to every measure
Give this tool a circle's radius and it returns the three quantities that follow from it. The diameter is simply twice the radius. The circumference, the distance around the edge, is 2 times pi times the radius. The area, the space inside, is pi times the radius squared. All three use the constant pi, roughly 3.14159, which links a circle's straight-line and curved measurements.
Because these formulas are exact, doubling the radius doubles the circumference but quadruples the area, since area depends on the radius squared, a relationship worth remembering when scaling round objects.
Everyday and design uses
Circle math shows up when sizing a round tabletop or rug, working out how much edging a garden bed needs, calculating pizza value per area, or laying out circular elements in a design. Knowing the area also helps estimate paint or material for a round surface.
Make sure your radius, not the diameter, goes in the radius field; halving the diameter first is the usual fix. If you are working from the circumference instead, divide it by 2 pi to recover the radius. For the pleasing proportions of golden circles and rectangles, see the golden-ratio tool on UtilGears.
Where it's used
- Sizing a round tablecloth, rug or pizza from its diameter
- Calculating the area of a circular garden bed or lawn to buy the right amount of seed or fertilizer
- Finding how much edging or fencing surrounds a circular pool or patio
- Comparing pizza sizes to see which is the better value
- Working out the circumference of a pipe for insulation or wrapping
Real-world examples
- A 12-inch pizza has area π×6² ≈ 113 in², while a 16-inch pizza is π×8² ≈ 201 in² — nearly double the food for a small price jump.
- A circular patio 4 m across (radius 2 m) covers π×2² ≈ 12.57 m².
- Fencing a round pool 3 m in diameter needs π×3 ≈ 9.42 m of edging.
- A round tablecloth for a 120 cm table with a 20 cm drop on each side needs a 160 cm diameter.
Did you know?
Although π has been computed to trillions of digits, NASA's Jet Propulsion Laboratory uses just 15 decimal places (3.141592653589793) for its highest-accuracy interplanetary navigation — enough to keep the error on a 40-billion-mile circle to about half an inch.
FAQ
What value of π is used?
It uses the full-precision π built into your browser (about 3.14159265), so results are accurate to many decimal places.