This free online circle calculator solves for radius, diameter, circumference, and area from any single known value. Just choose what you know - radius, diameter, circumference, or area - enter the value, and instantly get all the other circle measurements.
How to Use the Circle Calculator
Choose "What do you know?" - radius, diameter, circumference, or area.
Enter the "Value" you know in the input field.
Click "Calculate" to see the radius, diameter, circumference, and area.
Review the results table for all four circle measurements at once.
How the Four Measurements Are Linked
Every circle is fully described by a single number. Once the radius is known, everything else follows, so the calculator first converts whatever you enter into a radius and then works out the other three values from it.
Diameter is twice the radius: d = 2r.
Circumference, the distance around the edge, is 2πr, which is the same as π × d.
Area, the space enclosed, is π × r × r.
The calculator uses the full-precision value of π built into the browser (3.14159265...) and rounds each answer to three decimal places. School problems that use 22/7 or 3.14 will give slightly different answers in the second or third decimal place. That is a difference in the approximation of π, not an error.
Worked Examples
From a tape measurement: you wrap a tape around a round pillar and read 88 cm. Choose circumference and enter 88. The radius is 88 ÷ 2π = 14.006 cm, the diameter is 28.011 cm and the cross-section area is 616.248 sq cm. This is handy when you cannot measure across the middle of an object.
From an area: a circular garden bed needs to cover 1,000 sq ft. Choose area and enter 1000. The radius comes out as 17.841 ft, the diameter 35.682 ft, and the edging needed around it is 112.1 ft.
Quick Reference Values
Radius
Diameter
Circumference
Area
1
2
6.283
3.142
2
4
12.566
12.566
5
10
31.416
78.54
10
20
62.832
314.159
Notice that doubling the radius doubles the circumference but multiplies the area by four. This is why a 12-inch pizza (area about 113.1 sq in) has more to eat than two 8-inch pizzas together (about 100.5 sq in).
Common Mistakes
Entering a diameter while "radius" is selected. Pipe, wheel and tank sizes are usually quoted as diameters, so pick the matching option or the area will come out four times too large.
Forgetting that area is in square units. If the radius is in metres, the area is in square metres, while the circumference stays in metres.
Using the outer diameter of a pipe or ring when you need the inner opening. For the material in a ring, subtract the inner circle's area from the outer circle's area.
Frequently Asked Questions
Radius is derived first depending on your input: from diameter (r = d/2), from circumference (r = C/2π), or from area (r = √(A/π)). It then computes diameter = 2r, circumference = 2πr, and area = πr².
If you know the area is 78.54, the calculator finds r = √(78.54/π) ≈ 5, then diameter ≈ 10, circumference ≈ 31.416, and area ≈ 78.54.
Textbooks often use π = 22/7 or 3.14, while this calculator uses π to many more decimal places. For a radius of 7, 22/7 gives an area of exactly 154, while the calculator shows 153.938. Both are correct for the value of π used.
For a circle they mean the same thing: the length of the boundary. "Circumference" is simply the name used for circles and ellipses, while "perimeter" is used for polygons.
The rope length is the circumference. Select circumference, enter the length, and the calculator divides it by 2π to give the radius. A 10 m rope forms a circle with a radius of about 1.592 m.