Calculate radius, diameter, circumference, and area of a circle instantly. Enter any one value and get the other three. Free online circle calculator with formulas and step-by-step guide.
Please provide any value below to calculate the remaining values of a circle.
The point within a circle that is equidistant from all other points on the circle.
The distance between any point on the circle and the center. Equal to half the diameter.
The largest distance between any two points on a circle. Always passes through the center. Equal to twice the radius.
The distance around the circle, or the length of a circuit along the circle.
A line segment from one point of a circle to another. A chord through the center is a diameter.
A line that intersects the circle at only a single point.
The area of a circle created between two radii. Major sector > 180°, Minor sector < 180°.
Part of the circumference. Major arc > half circumference, Minor arc < half circumference.
The radius, diameter, and circumference of a circle are all related through the mathematical constant π (pi), which is the ratio of a circle's circumference to its diameter. The value of π is approximately 3.14159. π is an irrational number — it cannot be expressed exactly as a fraction (though often approximated as 22/7) and its decimal representation never ends.
π is also a transcendental number, meaning it is not the root of any non-zero polynomial with rational coefficients. It was not until 1880 that Ferdinand von Lindemann proved π is transcendental, ending all efforts to "square the circle" (constructing a square with the same area as a circle using only compass and straightedge).
D = 2R
Diameter from Radius
C = 2πR
Circumference from Radius
A = πR²
Area from Radius
So you need to figure out something about a circle. Maybe it's for homework. Maybe you're ordering a pizza and want the biggest bang for your buck. Or maybe you're building something round and need exact measurements.
Whatever the reason, our circle calculator is here to help. You just put in one number - any one - and it'll spit out everything else. Radius, diameter, circumference, area. All of it.
But here's the thing. Just getting the answer is fine. But understanding what's happening under the hood? That's where the real magic is. And honestly, it's not as hard as you think.
A circle calculator is a tool that does all the circle math for you. You give it one measurement (like the radius), and it uses the formulas to find the other three. No memorizing equations. No punching numbers into a regular calculator and hoping you did it right.
Think of it like a smart friend who's really good at geometry. You say "the radius is 5 inches" and they instantly tell you the diameter is 10 inches, the circumference is about 31.4 inches, and the area is about 78.5 square inches.
Using our calculator is super simple. Here's the step-by-step:
You know the radius is 7 cm. Type "7" into the radius box. Hit calculate:
There are really only three formulas you need to know. And they all involve this special number called pi (π ≈ 3.14159).
Pi is the ratio of a circle's circumference to its diameter. For any circle, divide the circumference by the diameter and you always get pi. It doesn't matter if the circle is the size of a coin or the Earth.
D = 2R
Diameter is twice the radius
C = 2πR
Circumference from radius
A = πR²
Area from radius
A 10-inch pizza costs $8. A 14-inch pizza costs $12. Which is better? 10" = 78.5 in² (10¢/in²). 14" = 153.9 in² (7.8¢/in²). The 14-inch is the better deal.
Seats 6, each needs 24" of edge space. Circumference = 144". Calculator says diameter = 45.8 inches.
3 feet across, 6 inches deep. Radius = 1.5 ft, Area = 7.07 ft². Soil needed = 7.07 × 0.5 = 3.54 cubic feet.
Mistake #1: Mixing up radius and diameter.
"10 inches across" is diameter, not radius. Radius is half that. Always double-check which one you have.
Mistake #2: Forgetting units.
Inches in = square inches out. Feet in = square feet out. Mixing units gives wrong answers.
Mistake #3: Rounding too early.
Rounding pi to 3.14 early in calculations makes final answers less accurate. Our calculator uses precise pi.
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The radius is the distance from the center to the edge. The diameter is the distance across the whole circle, passing through the center. The diameter is always twice the radius. If the radius is 4, the diameter is 8.
Use C = 2πr. Multiply the radius by 2, then multiply by π (3.14159). For a radius of 5, C = 2 × π × 5 = 31.42.
Use A = πr². Square the radius (multiply by itself), then multiply by π. For r = 5, A = π × 25 = 78.54 square units.
Yes. Use r = √(A/π). Divide the area by π, then take the square root. Our calculator does this automatically.
Pi is the constant ratio between a circle's circumference and its diameter. It's the same for every circle. Without pi, there's no way to relate a circle's straight measurements (radius, diameter) to its curved ones (circumference, area).
Any unit works as long as you're consistent. Use all inches, all centimeters, all feet, etc. Area will be in square units of whatever you input.