Math Tool
Circumference Calculator
Calculate the circumference, radius, diameter, and area of any circle. Enter any one measurement and instantly get all the others โ with step-by-step formulas and a live visual circle.
Circumference equals 2 ร ฯ ร radius
ฯ โ 3.14159265
Circle Calculator
Calculate circumference from any measurement
What do you know?
Enter value
Pi precision
ฯ (pi) is the ratio of circumference to diameter for any circle. It is an irrational number โ 3.14159265358979โฆ
Based on radius = 5 cm
Visual Circle
r = 5 cmStep-by-step solution
How it works
What is circumference?
The circumference of a circle is the total distance around its outer edge โ essentially the perimeter of a circle. It is one of the most fundamental measurements in geometry and appears constantly in real-world applications, from engineering to everyday life.
The relationship between circumference and diameter is always the same for any circle: the ratio C/d always equals ฯ (pi). This remarkable constant, approximately 3.14159, is what makes circle calculations consistent and predictable.
Whether you are calculating the distance a wheel travels per rotation, the length of fencing around a circular garden, or the material needed for a circular frame, this circumference calculator gives you fast, accurate results with full formula explanations.
Formulas
Circumference formulas explained
From Radius
C = 2 ร ฯ ร r Multiply the radius by 2ฯ. Most common formula used in textbooks.
From Diameter
C = ฯ ร d Multiply the diameter by ฯ. Simple one-step calculation.
Reverse (from C)
r = C รท (2ฯ) Divide circumference by 2ฯ to get the radius.
From Area
C = 2ฯโ(Aรทฯ) First find radius from area using r = โ(Aรทฯ), then calculate C.
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Examples
Circumference calculation examples
Example 1 โ Bicycle wheel
A bicycle wheel has a radius of 35 cm. The circumference is C = 2 ร ฯ ร 35 โ 219.91 cm. This means the bike travels about 2.2 m per wheel rotation.
Example 2 โ Pizza
A 12-inch pizza has a diameter of 12 inches. The circumference is C = ฯ ร 12 โ 37.70 inches. The crust length around the edge is about 37.7 inches.
Example 3 โ Garden pond
A circular garden pond has an area of 50 mยฒ. The radius is โ(50รทฯ) โ 3.99 m, and the circumference is approximately 25.07 m โ the length of fencing needed.
Example 4 โ Earth's equator
Earth has an equatorial radius of about 6,371 km. Its circumference is 2 ร ฯ ร 6,371 โ 40,030 km โ the distance around the planet.
Guide
How to use this circumference calculator
- Choose your input type. Click the tab for what you already know โ Radius, Diameter, Circumference, or Area.
- Enter your value. Type the measurement into the input field.
- Select your unit. Pick from mm, cm, m, km, inches, feet, yards, or miles.
- Choose pi precision. Select 3.14 for basic work, 3.14159 for standard, or 3.14159265 for high precision.
- View all results. The circumference, radius, diameter, and area are calculated instantly with a live visual circle and step-by-step solution.
- Copy or share. Use the copy buttons for individual results, or share the full result on WhatsApp or Facebook.
FAQ
Circumference Calculator FAQ
What is the formula for circumference?
The circumference of a circle is calculated using C = 2ฯr, where r is the radius, or equivalently C = ฯd, where d is the diameter. ฯ (pi) is approximately 3.14159.
How do I find circumference from diameter?
Multiply the diameter by ฯ (pi โ 3.14159). For example, a circle with a diameter of 10 cm has a circumference of 10 ร ฯ โ 31.416 cm.
How do I find circumference from radius?
Multiply the radius by 2ฯ. For example, a circle with a radius of 5 cm has a circumference of 2 ร ฯ ร 5 โ 31.416 cm.
Can I find the radius from the circumference?
Yes. Divide the circumference by 2ฯ. So if C = 31.416 cm, then r = 31.416 รท (2 ร ฯ) โ 5 cm.
What is the difference between circumference and perimeter?
Circumference specifically refers to the perimeter of a circle or ellipse. Perimeter is the general term for the total boundary length of any shape. For circles, the two terms mean the same thing.
What units can I use for circumference?
You can use any length unit โ millimeters, centimeters, meters, kilometers, inches, feet, yards, or miles. Just make sure your input and output use the same unit, or use the unit converter built into this calculator.