What is the formula for the length (circumference) of a circle?

The circumference of a circle is found using C = 2πr, where r is the radius. If you know the diameter instead, the formula becomes C = πd, because the diameter is twice the radius (d = 2r). The constant π is approximately 3.14159265. For example, a circle with radius 5 cm has a circumference of 2 × π × 5 = 31.416 cm.

What is the difference between circumference and arc length?

The circumference is the total length around the complete circle (360°). Arc length is the length of any curved portion of the circle corresponding to a specific central angle. The arc length formula is L = (θ ÷ 360) × 2πr, where θ is the central angle in degrees. For a semicircle (θ = 180°), the arc length is exactly half the circumference.

How do I find the circumference if I only know the area?

If you know the area (A) of the circle, first find the radius using r = √(A ÷ π), then calculate the circumference using C = 2πr. For example, if the area is 78.54 cm², then r = √(78.54 ÷ π) = √25 = 5 cm, and the circumference is 2 × π × 5 = 31.42 cm.

Circle Length Calculator

This calculator finds the circumference of a circle, its "length", along with the diameter, area and arc length for a chosen central angle. Choose how you want to enter your circle's size: by radius, diameter or area, and the calculator works out the other two for you. If you only know the area, it first back-calculates the radius using r = √(A ÷ π), then finds the circumference from there. Add a central angle, either a common preset such as 90° for a quarter circle and 180° for a semicircle, or a custom angle in degrees, and the tool also returns the arc length for that portion of the circle. The results bar highlights the circumference alongside the arc length, diameter and area, while a full breakdown and a step-by-step worked example show how each figure was derived from your radius, using C = 2πr, A = πr², and L = (θ ÷ 360) × 2πr. Pick a unit label such as cm, m, mm, inches or feet purely for display; the maths works in any consistent unit, so keep every measurement the same one. It suits fencing a circular garden, sizing a pipe or tank, working out wheel travel per rotation, or measuring a curved section of road or track. Results are rounded to 6 significant figures and are only as accurate as the measurements you enter.

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Standard Formula Uses C = 2πr. Accurate to 6 significant figures. Works in any unit (cm, m, mm, inches, etc.).

1. Circle Dimensions

Input method

Radius (any unit)

units

Diameter (any unit)

units

Area (square units)

sq units

Unit label (for display only)

2. Arc Length (Optional)

Central angle (for arc length)

Formulas used:
Circumference: C = 2πr
Arc length: L = (θ ÷ 360) × 2πr
Area: A = πr²
Diameter: d = 2r

Circle Length Results

Circumference
31.4159 cm
C = 2πr, r = 5 cm

Arc Length

31.4159 cm

For 360° central angle

Diameter

10 cm

Across the circle

Area

78.5398 cm2

Enclosed area

Full Breakdown

Radius (r)5 cm

Diameter (d = 2r)10 cm

Circumference (C = 2πr)31.4159 cm

Area (A = πr²)78.5398 cm2

Central angle360°

Arc length31.4159 cm

Worked Example

Radius entered5 cm

Step 1: diameterd = 2 × 5 = 10 cm

Step 2: C = 2 × π × r2 × π × 5 = 31.4159 cm

Step 3: A = π × r²π × 52 = 78.5398 cm2

Step 4: arc = (θ/360) × C(360/360) × 31.4159 = 31.4159 cm

Circumference31.4159 cm

How to Calculate the Length of a Circle

The "length" of a circle most commonly refers to its circumference: the total distance around the outside edge. The standard formula is:

C = 2πr

where r is the radius (the distance from the centre to the edge) and π (pi) is the mathematical constant approximately equal to 3.14159265. If you know the diameter (d) rather than the radius, you can use the equivalent form C = πd, since d = 2r.

Circumference vs Arc Length

The circumference is the length of the complete circle (360 degrees). An arc is any curved portion of the circle, and its length depends on the central angle it subtends. The arc length formula is:

L = (θ ÷ 360) × 2πr

where θ is the central angle in degrees. For a quarter-circle (90°), the arc length is one quarter of the circumference. For a semicircle (180°), the arc length is exactly half the circumference.

Quick Reference Table

Radius	Diameter	Circumference	Area
1	2	6.2832	3.1416
2	4	12.5664	12.5664
5	10	31.4159	78.5398
10	20	62.8318	314.159
25	50	157.080	1,963.50
100	200	628.318	31,415.9

All values are in the same unit as the radius input (e.g. if radius is in centimetres, circumference is in centimetres and area is in square centimetres).

Finding the Radius from the Circumference

If you know the circumference and need to find the radius, rearrange the formula: r = C ÷ (2π). For example, if the circumference is 31.416 cm, the radius is 31.416 ÷ (2 × 3.14159) = 5 cm.

Finding the Radius from the Area

If you know the area (A), find the radius using: r = √(A ÷ π). For example, if the area is 78.5398 cm², then r = √(78.5398 ÷ 3.14159) = √25 = 5 cm, and the circumference is 2 × π × 5 = 31.416 cm.

Practical Uses

Fencing a circular garden: measure the radius and use C = 2πr to find how much fencing you need.
Wheel travel: one full rotation of a wheel covers a distance equal to its circumference. A wheel with radius 35 cm travels π × 0.70 ≈ 2.199 m per revolution.
Pipe and tank sizing: the circumference determines how much material is needed to wrap around a circular pipe or tank.
Arc calculations: use the arc length formula when working with curved roads, tracks, or shapes that subtend a specific angle.

Related Calculators

Sources and method: Formula C = 2πr per standard Euclidean geometry (Archimedes, circa 250 BCE). Arc length formula L = (θ/360) × 2πr. Value of π used: JavaScript Math.PI = 3.141592653589793.

This calculator works in any consistent unit. Ensure all inputs use the same unit for correct results. Results are rounded to 6 significant figures for display.