Circle Calculator
Find a circle’s area, circumference and diameter from any one measurement.
Results update as you type.
About this calculator
A circle calculator works out every property of a circle from a single known value. Tell it whether you know the radius, diameter, circumference or area, enter that value, and it returns all four measurements plus the exact area written as a multiple of π.
Everything is derived from the radius r, using area = π r², circumference = 2 π r, and diameter = 2 r. When you supply a different value it first converts back to the radius: r = diameter ÷ 2, r = circumference ÷ (2π), or r = √(area ÷ π). For a radius of 5, the diameter is 10, the circumference is 2 × π × 5 ≈ 31.42, and the area is π × 25 ≈ 78.54, shown exactly as 25π.
Circle math is needed for pipes and tanks, wheels and gears, circular gardens, pizza and anything round. Because every property follows from the radius, knowing any one of them determines all the others.
Frequently asked questions
What is the formula for the circumference of a circle?
Circumference = 2 × π × radius, or equivalently π × diameter. A radius of 5 gives a circumference of about 31.42.
How do you find the radius from the area?
Rearrange area = π r² to r = √(area ÷ π). This tool does that automatically when you choose to enter the area.
What is the area of a circle with radius 5?
Area = π × 5² = π × 25 ≈ 78.54, shown exactly as 25π.
Can I start from the diameter or circumference?
Yes. Choose which value you know — radius, diameter, circumference or area — and the calculator derives the other three.
What is the exact area shown as ×π?
It is the area written as r²π (for example 25π) so the value stays exact rather than being rounded to a decimal.
What is the relationship between radius and diameter?
The diameter is twice the radius, and the radius is half the diameter. A radius of 5 means a diameter of 10.
API — use this calculator from code
Call this calculator as a free JSON endpoint — no key required. Send the field values below as query parameters or JSON. Read the full API docs →
Endpoint
GET https://calculator.free/api/v1/circle/curl
curl "https://calculator.free/api/v1/circle/?given=radius&value=5"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/circle/?" + new URLSearchParams({
"given": "radius",
"value": "5"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.