Circle Calculator
Area78.5398
Circumference31.4159
Radius5.0000
Diameter10.0000
Give this circle calculator any one of a circle’s four measurements — radius, diameter, circumference, or area — and it derives the other three. It first works back to the radius from whatever you provide, then computes the full set so every property stays mutually consistent. This makes it useful for design, manufacturing, and geometry homework where one known dimension must yield the rest.
Formula
d = 2r; C = 2πr; A = πr²
- r
- Radius — the distance from centre to edge
- d
- Diameter, equal to twice the radius
- C
- Circumference, the distance around the circle
- A
- Area enclosed by the circle
How it works
- Choose which quantity you know: radius, diameter, circumference, or area.
- Enter its value. The calculator converts it to the radius — halving a diameter, dividing a circumference by 2π, or taking the square root of area divided by π.
- From that radius it reports radius, diameter, circumference, and area together, each rounded to four decimal places.
Worked example
A circle has a radius of 5. Find its diameter, circumference, and area.
- Diameter: 2 × 5 = 10.
- Circumference: 2 × π × 5 = 10π ≈ 31.4159.
- Area: π × 5² = 25π ≈ 78.5398.
Diameter 10, circumference ≈ 31.4159, area ≈ 78.5398.
Frequently asked questions
- Can I start from the area instead of the radius?
- Yes. Enter the area and the calculator solves r = √(A ÷ π) to recover the radius first, then computes the diameter and circumference from it.
- What is the relationship between radius and diameter?
- The diameter is exactly twice the radius, and the radius is half the diameter. So a circle with a 10-unit diameter has a 5-unit radius.
- How is circumference different from area?
- Circumference is the one-dimensional distance around the circle’s edge (in linear units), while area is the two-dimensional surface inside it (in square units). They use different formulas, 2πr and πr².
- Why must the value I enter be positive?
- A circle’s radius, diameter, circumference, and area are all real, positive lengths or surfaces. A zero or negative input has no geometric meaning, so the calculator returns no result for it.