Circle Calculator

The circle calculator derives every property of a circle from any single known value — radius, diameter, circumference, or area. Enter what you know, and you get the other three. Every relationship comes from the constant π (pi ≈ 3.14159), the ratio of a circle's circumference to its diameter, which is the same for every circle in the universe.

Use this calculator for engineering, manufacturing, design, geometry, and everyday tasks like sizing pipes, wheels, lids, gardens, and round tabletops. The four properties — radius (r), diameter (d), circumference (C), and area (A) — are tightly linked: knowing any one of them determines the other three.

Suppose you're building a circular patio with a radius of 6 feet. Compute every property:

• Diameter: 2 × 6 = 12 ft
• Circumference: 2 × π × 6 ≈ 37.70 ft (pavers needed for the edge)
• Area: π × 6² = π × 36 ≈ 113.10 ft² (paving material)

Now reverse it: you bought a circular table cover advertised as 28 inches in diameter. Radius = 14 in, circumference = π × 28 ≈ 87.96 in, area = π × 14² ≈ 615.75 in². If you wanted to know how it scales: a 56-inch table (double the diameter) has 4× the area — 2,463 in² — even though the circumference only doubles.

• Pipes and tubing — convert between outer diameter, cross-section area, and circumference for material calculations.
• Round tabletops, lids, and disks — size cuts and edge banding from a single specification.
• Wheels and gears — derive rolling distance per revolution from the wheel's diameter.
• Circular landscaping — compute paver count for a perimeter and material for a fill area.
• Reverse engineering — back into the radius from a measured circumference (e.g., wrapping a string around a tree trunk).

• Using diameter where radius is required. A = πr² uses radius, not diameter; if you know d, divide by 2 first or you'll get 4× the correct area.
• Squaring π instead of r. The area formula squares the radius only — π is a constant multiplier, not a quantity to square.
• Forgetting that area scales as r². A circle with double the radius has 4× the area, not 2× — a common surprise when sizing patios or pizzas.
• Mismatched units. Always use the same unit throughout; circumference will be in that linear unit, area in that unit squared.
• Rounding π too aggressively. Using 3.14 instead of 3.14159 introduces about 0.05% error — fine for a garden, not for precision machining.