Introduction
This free circle calculator lets you find the radius, diameter, circumference, and area of any circle in seconds. Just enter one value you already know, and the tool solves for the rest. It also shows each answer in terms of π (pi), draws a labeled diagram, and gives you a clear step-by-step solution so you can see exactly how the math works.
A circle is a flat, round shape where every point along its edge is the same distance from the center. That distance is the radius. The diameter is twice the radius and stretches across the full width of the circle. The circumference is the total distance around the outside, and the area is the amount of space inside. These four properties are all connected through simple formulas that use π, a number roughly equal to 3.14159.
Whether you are doing homework, planning a project, or just need a quick answer, this calculator does the work for you. Pick the property you know, type in your number, and hit Calculate.
How to Use Our Circle Calculator
Enter one known circle measurement and this calculator will find the radius, diameter, circumference, and area for you. It also shows a diagram and a step-by-step solution.
Pick your known property: Choose which value you already know — radius, diameter, circumference, or area. Click the matching button at the top of the calculator.
Enter your value: Type the number for the property you picked. It must be greater than zero.
Set significant figures: Choose how many digits you want in your results. The default is 5. Pick "Auto" to let the calculator decide for you. If you need help understanding how significant figures work, try our sig fig calculator.
Choose a display unit: Pick a unit like cm, ft, or m if you want one shown next to your answers. This labels your results but does not convert between units.
Set the value of Pi (π): The calculator uses π = 3.14159265359 by default. You can change this number if your teacher or project needs a different value.
Get your results: Press the Calculate button to see all four circle properties, exact values in terms of π, a labeled diagram, and a full step-by-step solution. Press Clear to reset everything back to the default settings.
What Is a Circle?
A circle is a round shape where every point along its edge is the same distance from the center. Circles are one of the most common shapes in math and in everyday life. Wheels, coins, clocks, and pizza are all circles.
Parts of a Circle
Every circle has four main properties you should know:
- Radius (R) – The distance from the center of the circle to any point on its edge. Think of it as a straight line from the middle to the outside.
- Diameter (D) – The distance across the circle through its center. It is always twice the radius. The formula is D = 2R. You can also use our diameter to circumference calculator to quickly convert between those two values.
- Circumference (C) – The total distance around the outside of the circle. It is the circle's perimeter. The formula is C = 2πR.
- Area (A) – The amount of space inside the circle. The formula is A = πR². For other shapes, see our general area calculator.
What Is Pi (π)?
Pi is a special number in math. It equals roughly 3.14159. Pi tells you the exact relationship between a circle's diameter and its circumference. No matter how big or small a circle is, the circumference divided by the diameter always equals pi.
How the Circle Formulas Work
All four circle properties are connected. If you know just one of them, you can find the other three. For example, if you know the radius, you can double it to get the diameter, multiply it by 2π to get the circumference, and square it then multiply by π to get the area. The same idea works in reverse. If you know the area, you can work backward to find the radius, and then find everything else from there.
Key Circle Formulas
- Diameter from radius: D = 2R
- Radius from diameter: R = D ÷ 2
- Circumference from radius: C = 2πR
- Radius from circumference: R = C ÷ (2π)
- Area from radius: A = πR²
- Radius from area: R = √(A ÷ π)
When Do You Use Circle Calculations?
Circle math shows up in many real situations. You use it to find the area of a round garden, measure how much fencing goes around a circular pool, figure out the size of a pipe, or calculate the surface of a round tabletop. Builders, engineers, students, and teachers all use these formulas regularly. Once you are comfortable with circles, you can move on to related three-dimensional shapes using tools like our sphere volume calculator or cylinder volume calculator. For finding arc measurements along part of a circle, our arc length calculator is another helpful tool.