Circle Calculator

Q: How do I find the radius from the circumference?

Divide the circumference by 2π: r = C / 2π . Choose Circumference in I know the and the tool does it for you, with the exact value and the decimal.

Q: Can I enter the angle in radians?

Yes. Set Angle unit to radians and type a number such as 1.2 or a multiple of π such as π/4 or 3π/2. The angle must be greater than 0 and at most 2π 360° .

Circle Calculator

Circle calculator that finds the radius, diameter, circumference and area from any one of them, plus arc length and sector area, exactly in terms of π.

I know the Radius (r) Length unit

Central angle (optional, for an arc or a sector) Angle unit

Decimals such as 2.5 and fractions such as 3/4 are accepted. You can also type a multiple of π, for example 25π or 25pi for an area of 25π cm². In radians, an angle such as π/3 works too.

Radius (r): –
Diameter (d): –
Circumference (C): –
Area (A): –

Step by step

How to use the circle calculator

In I know the, choose what you already have: Radius (r), Diameter (d), Circumference (C) or Area (A).
Type the value in the box below the label. Decimals (2.5), fractions (3/4) and multiples of π (25π or 25pi) are all accepted.
Pick the Length unit: millimetres, centimetres, metres, kilometres, inches, feet, yards or miles. Areas are given in the matching square unit.
Optionally, enter a Central angle and its Angle unit (degrees or radians) to get the Arc length (L), the Sector area, the Chord length and the Segment area. In radians you can type π/3 or 2π/3 directly.
The results update as you type; Calculate does the same. Clear empties the boxes and Copy copies every result.

Under the results, a diagram shows the circle with its radius and, when you entered an angle, the shaded sector with its chord. Step by step lists each formula with your numbers substituted.

Exact answers in terms of π

Most circle results involve π, which has infinitely many decimals. This tool keeps the exact form and adds a rounded decimal after the ≈ sign. A radius of 5 cm gives a circumference of 10π ≈ 31.415927 cm and an area of 25π ≈ 78.539816 cm². Going backwards works too: a circumference of 10 cm means a radius of 5/π ≈ 1.591549 cm, and an area of 10 cm² means a radius of √(10/π). If your area is itself a multiple of π, type it that way: an area of 25π gives a radius of exactly 5.

Circle formulas

Quantity	Formula
Diameter	d = 2r
Circumference	C = 2πr = πd
Area	A = πr² = C² / (4π)
Radius from the circumference	r = C / (2π)
Radius from the area	r = √(A / π)
Arc length (θ in radians)	L = r × θ
Sector area	A = r² × θ / 2
Chord	c = 2r × sin(θ / 2)
Segment area	A = r² / 2 × (θ − sin θ)

The arc and sector formulas use the angle in radians. When you enter degrees, the tool first converts with θ = degrees × π / 180, so 60° becomes π/3 rad, and shows this conversion in the steps. The chord and the segment involve a sine, so they are given as decimals.

A sector is the “pizza slice” between two radii and the arc. A segment is the region between the chord and the arc: the sector minus the triangle formed by the two radii and the chord.

Examples

A round table 1.2 m across: choose Diameter, type 1.2 and pick metres. The area is 0.36π ≈ 1.13 m² and the edge is 1.2π ≈ 3.77 m long.
A tree trunk with a circumference of 150 cm: choose Circumference. The radius is 75/π ≈ 23.87 cm.
A 45° slice of a 30 cm pizza: choose Diameter, type 30 and enter 45 degrees. The slice has an area of 28.125π ≈ 88.36 cm² and a crust of 3.75π ≈ 11.78 cm.

Frequently asked questions

What is the difference between a circle and a disk?

Strictly speaking, the circle is the curved line and the disk is the flat region inside it. The circumference is the length of the circle; the area is the area of the disk. In everyday language, “area of a circle” means the area of the disk.

Why does the answer contain π?

π ≈ 3.14159 is irrational, so any decimal is a rounding. The exact form such as 25π is what math exercises usually expect, while the decimal after ≈ is what you need for measuring or buying material.

How do I find the radius from the circumference?

Divide the circumference by 2π: r = C / (2π). Choose Circumference in I know the and the tool does it for you, with the exact value and the decimal.

Can I enter the angle in radians?

Yes. Set Angle unit to radians and type a number such as 1.2 or a multiple of π such as π/4 or 3π/2. The angle must be greater than 0 and at most 2π (360°).

How accurate are the decimal results?

Exact forms are computed with exact fractions. Decimals are rounded to 8 significant digits, which is far more precise than any physical measurement you would enter.