Circle Calculator
Area = pi x radius squared. Circumference = 2 x pi x radius. Diameter = 2 x radius.
Start from whatever you already measured
A circle has four numbers that all lock together: radius, diameter, circumference and area. Know any one of them and the other three are fixed. The selector lets you say which one you have, so you can hand the calculator a circumference off a tape measure and get the radius, or start from the area and read back the diameter.
That flexibility matters in practice. You rarely get to choose which measurement is easy to take. A tree trunk gives you a circumference, a dinner plate gives you a diameter, and a garden bed on a plan might only list its area.
Four numbers, one circle
The result lays out radius, diameter, circumference and area side by side. The three length measurements share whatever unit you typed in, and the area comes back in square units of the same kind.
Seeing all four at once is the point. It saves the second and third calculation you would otherwise do by hand, and it lets you sanity-check the shape: if the area looks wrong for the diameter you entered, the numbers are right there to compare.
The formulas behind the result
Area is pi times the radius squared. Circumference is pi times the diameter, which is the same as 2 times pi times the radius. The diameter is simply twice the radius.
Working backward uses the same relationships in reverse. From a circumference, the radius is the circumference divided by 2 pi. From an area, the radius is the square root of the area divided by pi. The calculator picks the right rearrangement based on what you said you know.
A worked example
Take a radius of 5. The diameter is 10. The circumference is 2 times pi times 5, which is about 31.42. The area is pi times 5 squared, or about 78.54 square units.
Now flip it around. If all you had was that area of 78.54, dividing by pi gives 25, and the square root of 25 is 5, so the radius comes straight back. The chain works in every direction.
Radius and diameter are not the same number
The single biggest slip with circles is feeding the diameter into a formula that wants the radius. Because area depends on the radius squared, that mistake makes the area four times too big, not twice.
The radius reaches from the center to the edge. The diameter crosses the entire circle through the center. Whenever a measurement comes from edge to edge, it is a diameter, and it needs halving before it touches a radius-based formula. The selector here removes the guesswork by asking which one you have.
Where these numbers get used
Circumference answers fencing and edging questions, like how much border to buy for a round patio. Area answers covering questions, like turf for a circular lawn or sealant for a tank base.
Diameter and radius drive the physical fit: whether a round rug suits a room, or whether a pipe slides through a hole. For straight-sided rooms and lots, the area calculator covers rectangles, triangles and trapezoids, while this page handles anything round.
Circle Calculator FAQ
How do I find the area of a circle?
Square the radius and multiply by pi. A radius of 4 gives 16 times pi, which is about 50.27 square units.
If you only have the diameter, halve it first, or just select diameter as the known value and let the calculator do it.
How do I get the radius from the circumference?
Divide the circumference by 2 times pi. A circumference of 31.42 divided by 6.283 gives a radius of about 5.
Choose circumference as the known value and the calculator returns the radius, diameter and area together.
What is the difference between radius and diameter?
The radius runs from the center to the edge. The diameter runs all the way across through the center and is exactly twice the radius.
Mixing them up is the most common circle error, because area depends on the radius squared.
Can I find the diameter from the area?
Yes. Divide the area by pi, take the square root to get the radius, then double it.
Enter the area as the known value and the diameter appears in the result without the manual steps.
Does the calculator round pi?
No. It uses the full-precision value of pi built into the browser, not a rounded 3.14, so the results stay accurate well past the decimals you are likely to need.