Circle Calculator

Circle formulas

Every measure follows from the radius, so the calculator first finds the radius from what you know and then works out the rest. Results are rounded to six significant digits and also given in terms of π, the way many textbooks and tests want them. The diameter is the easiest to measure on a flat object — the widest distance across through the center — and the circumference on a round one, by wrapping a string or a flexible tape around it.

Working backwards

• From the circumference: a tree trunk 30 inches around has a diameter of 30 ÷ π = 9.55 inches.
• From the area: a round rug of 100 square feet is √(100 ÷ π) × 2 = 11.28 feet across.

Choose what you know at the top, enter it, and the other measures appear as you type.

Round areas for projects

Lawns, patios, ponds, tree rings and round tables are measured across in feet, and materials are sold by the square foot or square yard. A patio 12 feet across is π × 6² = 113.1 square feet; a pond 20 feet across is 314.2 square feet, or 34.9 square yards. With the unit set to feet or yards, the result adds square yards and acres; in inches or meters it adds square feet. For the depth of mulch, gravel or concrete over that area, use the square footage calculator, which has a circle shape, or the concrete calculator for a round slab.

Why a 16-inch pizza beats two 12-inch ones

Area grows with the square of the diameter. A 16-inch pizza has 201 square inches, a 12-inch one 113 — so one 16-inch pizza is 1.78 times a 12-inch, and nearly as much as two of them (226 square inches). Compare price per square inch, not per inch of diameter. The same rule explains why a pipe twice as wide carries four times the water.

Circumference in everyday use

A wheel moves forward one circumference per turn. A 26-inch bicycle wheel travels π × 26 = 81.7 inches each revolution, about 776 turns per mile. Fence, edging and trim for a round bed are sold by the length of the circumference: a bed 8 feet across needs 25.1 feet of edging. For three-dimensional round shapes, see the cylinder volume calculator and the sphere calculator.

About π

π is the ratio of any circle’s circumference to its diameter, 3.14159265…, a number whose digits never end or repeat. The common shortcuts are close: 3.14 is 0.05% too small and 22/7 is 0.04% too big — on a 12-foot patio, a difference of less than a tenth of a square foot. The calculator uses π to full precision, so its answers match the ones from a scientific calculator.