Circle Calculator

Circle geometry rests on one constant, π (pi) ≈ 3.14159, and on how a circle’s radius, diameter, circumference and area hang together.
Know any one of those four and the other three follow, which is what this calculator does.

Fundamental relationships:

Diameter (d) = 2 × r

Circumference (C) = 2 × π × r = π × d

Area (A) = π × r²

Reverse formulas, solving from any known value:

From diameter: r = d ÷ 2

From circumference: r = C ÷ (2π) d = C ÷ π

From area: r = √(A ÷ π) d = 2 × √(A ÷ π)

Arc and sector formulas (with central angle θ in degrees):

Arc Length = (θ ÷ 360) × 2πr

Sector Area = (θ ÷ 360) × πr²

Worked example: A circular fountain has a diameter of 4.5 meters.

• Radius: 4.5 ÷ 2 = 2.25 m
• Circumference: π × 4.5 = 14.14 m (amount of edging needed)
• Area: π × 2.25² = 15.90 m² (surface area for a cover)

Now a sector, which is what the Central Angle box above is for. A pizza slice cut at 60° from a 14-inch (diameter) pizza:

• Radius = 7 in
• Arc length: (60 ÷ 360) × 2 × π × 7 = 7.33 inches (the crust on that slice)
• Sector area: (60 ÷ 360) × π × 49 = 25.66 in²

Enter 14, choose Diameter, and set the central angle to 60, and those are the numbers that come back. Leave the angle blank and the calculator sticks to the whole circle.

Real-world uses of circle formulas:

• Landscaping: calculating sod or mulch for a circular bed
• Fencing: determining how much edging surrounds a circular pool
• Engineering: computing cross-sectional area of pipes and shafts
• Cooking: scaling a round cake recipe between pan sizes (area ratio)

Circle vs. sphere: This calculator handles flat 2D circles. For a 3D sphere, surface area = 4πr² and volume = (4/3)πr³.