Pick what you know
Circles have four properties that all derive from each other: radius, diameter, circumference, and area. Knowing any one, you can get the other three. The calculator lets you pick which value you’re starting from and shows everything else.
The math:
- Diameter = 2 × radius
- Circumference = 2π × radius = π × diameter
- Area = π × radius²
π is irrational. The calculator uses JavaScript’s Math.PI which gives ~15 digits of precision, well past anything you’d need for engineering, woodworking, or homework.
Common situations
Three real cases people hit:
Pizza or table: someone says “we need a 60-inch round table.” That’s the diameter. To know how many people fit (one per ~24 inches of circumference), you need the circumference: π × 60 ≈ 188 inches, so about 7-8 people. To know if it fits in your dining room, you need the area: π × 30² ≈ 2,827 sq in ≈ 19.6 sq ft.
Garden bed or pool: “I want a 20-square-meter circular pool.” That’s the area. The radius works out to √(20/π) ≈ 2.52m. Diameter ≈ 5m. So you need a 5-meter clearance to install it.
Wheel or pulley: “the bike wheel is 700mm diameter.” Distance traveled per revolution is the circumference: π × 700 ≈ 2,200mm = 2.2 meters. Multiply by RPM for speed.
Why π matters this much
π ≈ 3.14159 connects every circular measurement. It’s the ratio of any circle’s circumference to its diameter, the same number for every circle, regardless of size. That fixed ratio is why the four formulas above all reduce to one value of π.
For ballpark mental math, π ≈ 22/7 (about 3.143) is close enough. For hand calculations to two decimal places, 3.14 is fine. The calculator uses much more precision, but the additional decimal places matter only for very large circles or precision engineering.
Sectors and arcs
Beyond the four basics, two related calculations come up often:
- Arc length = (θ/360) × C = (θ/360) × 2πr, where θ is the central angle in degrees
- Sector area = (θ/360) × A = (θ/360) × πr²
These aren’t in the calculator yet, for now, multiply the circumference or area by (your angle ÷ 360) to get the arc-length or sector-area portion.
Common circle measurements
For reference:
| Object | Diameter | Circumference | Area |
|---|---|---|---|
| US quarter | 24.26 mm | 76.2 mm | 462 mm² |
| Tennis ball | 67 mm | 210 mm | 3,525 mm² |
| Standard pizza (large) | 14 in | 44 in | 154 sq in |
| US dollar (paper) | , | , | , (not circular) |
| Earth (mean diameter) | 12,742 km | 40,030 km | 510 million km² (surface) |
Frequently asked questions
My textbook says C = πd. The calculator uses 2πr. Are these the same? Yes. Diameter is 2× radius, so π × d = π × 2r = 2πr. Either form works.
What about ellipses? This calculator doesn’t handle ellipses. An ellipse’s area is πab (where a, b are the semi-axes), but its perimeter has no closed-form solution and requires numerical methods.
Does this work for spheres? A sphere is 3D, you’d want surface area (4πr²) and volume (⁴⁄₃πr³). This calculator handles 2D circles only. For sphere math, search the related sphere calculator.
Why is the area not measured in the same units as circumference? Area is always squared units. If your radius is in meters, area comes out in square meters and circumference in meters. Don’t mix linear and area units in the same calculation.