How to Use the Circumference Calculator
This circumference calculator works in all directions — you can use it as a circumference to diameter calculator, circumference to radius calculator, or even to find the area from the circumference. Simply:
- Select which measurement you know (radius, diameter, circumference, or area)
- Enter the value with the appropriate units
- Click Calculate to see all circle properties instantly
The calculator will compute the radius, diameter, circumference, and area simultaneously, showing you all the formulas used.
Definition of Circumference
The circumference of a circle is the length of the circle's boundary. It is the same as the perimeter of a geometric figure, but the term 'perimeter' is used exclusively for polygons.
Note: Circumference is often misspelled as "circumfrence".
Formula for Circumference
The following equation describes the relation between the circumference and the radius R of a circle:
C = 2πR
where π (pi) is a constant approximately equal to 3.14159265...
Important: It is impossible to find the exact value of π. The number π is irrational, so we typically use approximations such as 3.14 or 22/7.
A similarly simple formula determines the relationship between the area of a circle and its radius:
A = π × R²
How to Find the Circumference of a Circle
Example: Let's calculate the circumference for a circle with radius = 14 cm
- Determine the radius: R = 14 cm
- Calculate circumference: C = 2 × π × R = 2 × π × 14 = 87.9646 cm
- Calculate area: A = π × R² = π × 14² = 615.752 cm²
- Find diameter: D = 2 × R = 2 × 14 = 28 cm
Use our circumference calculator to find the radius when you only have the circumference or area of a circle.
Circumference to Diameter
You have probably noticed that, since diameter is twice the radius, the proportion between the circumference and the diameter is equal to π:
C/D = 2πR / 2R = π
This proportion (circumference to diameter) is the definition of the constant pi. It is used in many areas, such as physics and mathematics.
All Circle Formulas
| Given | Find Radius | Find Diameter | Find Circumference | Find Area |
|---|---|---|---|---|
| Radius (R) | R | D = 2R | C = 2πR | A = πR² |
| Diameter (D) | R = D/2 | D | C = πD | A = π(D/2)² |
| Circumference (C) | R = C/(2π) | D = C/π | C | A = C²/(4π) |
| Area (A) | R = √(A/π) | D = 2√(A/π) | C = 2π√(A/π) | A |
Frequently Asked Questions
How to find the circumference of a circle?
Method 1 - Using radius:
- Multiply the radius by 2 to get the diameter
- Multiply the result by π, or 3.14 for an estimation
- That's it; you found the circumference of the circle
Method 2 - Using diameter:
- Multiply the diameter by π, or 3.14
- The result is the circle's circumference
What is the circumference of a circle?
The circumference of a circle is the length of the circle's boundary. In other words, it is the perimeter of the circle, although the term 'perimeter' is typically used for polygons rather than circles.
How do I find the diameter from the circumference?
- Divide the circumference by π, or 3.14 for an estimation
- The result is the circle's diameter
How to find the area of a circle from the circumference?
- Divide the circumference by 2π to get the circle's radius
- Multiply the radius by itself to get its square
- Multiply the square by π or 3.14 for an estimation
- You found the circle's area from the circumference
How do I find the radius from the circumference?
- Divide the circumference by π, or 3.14 for an estimation (this gives the diameter)
- Divide the diameter by 2
- You found the circle's radius
What is the circumference of a circle with a radius of 1 meter?
- Multiply the radius by 2 to get the diameter: 2 meters
- Multiply the result by π or 3.14
- Result: circumference = 6.28 meters
How do I find the circumference of a cylinder?
To find the circumference of a cylinder, you have to be aware that a cylinder's cross-section is a circle. If you know the cylinder's radius:
- Multiply the radius by 2 to get the diameter
- Multiply the result by π, or 3.14 for an estimation
- That's it; you found the circumference of the cylinder
Who calculated the circumference of the earth first?
The first person to calculate the Earth's circumference was Eratosthenes, a Greek mathematician, in 240 B.C. He discovered that objects in a city on the Northern Tropic do not throw a shadow at noon on the summer solstice, but they do in a more northerly location. Knowing this and the distance between the locations, he succeeded in calculating the Earth's circumference.
What is the unit of the circumference of a circle?
The circumference is the length of the circle's boundary, which is measured in the same units as length. Therefore, the most common units of a circle's circumference are:
- Metric system: millimeter (mm), centimeter (cm), meter (m), kilometer (km)
- Imperial system: inch (in), feet (ft), yard (yd), mile (mi)