Calculate circle circumference, radius, diameter, and area instantly. Enter any value and get all circle properties with formulas: C = 2πr and A = πr²
Circumference: C = 2πr = πd
Area: A = πr²
Tip: Enter any one value to automatically calculate all other circle properties!
Enter any circle measurement to calculate all properties
Radius, Diameter, Circumference, or Area
The circumference of a circle is the distance around the circle's edge, also known as the circle's perimeter. It represents the total length of the boundary that encloses the circular region. Just as a rectangle has a perimeter that can be measured by adding all its sides, a circle has a circumference that can be calculated using a special mathematical formula involving pi (π).
The relationship between a circle's circumference and its diameter is one of the most fundamental constants in mathematics. No matter how large or small a circle is, when you divide its circumference by its diameter, you always get the same number: π (pi), approximately 3.14159.
There are two primary formulas to calculate the circumference of a circle, depending on whether you know the radius or the diameter:
C = 2πr
Where C is circumference, π ≈ 3.14159, and r is the radius
C = πd
Where C is circumference, π ≈ 3.14159, and d is the diameter
Since the diameter (d) is always twice the radius (d = 2r), both formulas give the same result:
C = 2πr = π(2r) = πd
| To Find | Formula | Given |
|---|---|---|
| Circumference | C = 2πr | Radius |
| Circumference | C = πd | Diameter |
| Area | A = πr² | Radius |
| Area | A = πd²/4 | Diameter |
| Radius | r = C/(2π) | Circumference |
| Radius | r = √(A/π) | Area |
| Diameter | d = C/π | Circumference |
| Diameter | d = 2r | Radius |
Identify the radius
Find or measure the radius (distance from center to edge)
Multiply by 2
Double the radius value
Multiply by π
Multiply the result by π (3.14159)
Example: Radius = 5 cm
C = 2 × π × 5 = 2 × 3.14159 × 5 = 31.4159 cm
Identify the diameter
Find or measure the diameter (distance across through center)
Multiply by π
Multiply the diameter by π (3.14159)
Example: Diameter = 10 cm
C = π × 10 = 3.14159 × 10 = 31.4159 cm
Calculate tire circumference to determine how far a vehicle travels per wheel rotation. Essential for speedometer calibration and fuel efficiency calculations.
Determine the amount of material needed for circular structures like pipes, columns, tanks, and domes. Calculate fencing for round areas.
Calculate ribbon, trim, or border length needed for circular designs, wreaths, decorations, and craft projects.
Calculate track lengths, running distances around circular paths, and wheel circumference for cycling computers.
Calculate Earth's circumference (approximately 40,075 km at the equator), planetary measurements, and orbital paths.
Design gears, pulleys, wheels, and circular components. Calculate belt lengths and rotating machinery dimensions.
The mathematical constant π (pi) has fascinated mathematicians for over 4,000 years. The ancient Babylonians approximated π as 3.125, while the Egyptians used 3.1605. The Greek mathematician Archimedes (287-212 BC) calculated π to be between 3.1408 and 3.1429 using polygons.
Eratosthenes, another Greek mathematician, made history around 240 BC by being the first to calculate Earth's circumference. He observed that the Sun cast no shadow at Syene (modern-day Aswan) at noon on the summer solstice, while it cast a shadow at Alexandria. Using geometry and the distance between the cities, he calculated Earth's circumference to be about 40,000 km—remarkably close to the actual value of 40,075 km!
Fun Fact: The symbol π was first used by Welsh mathematician William Jones in 1706 and was later popularized by Leonhard Euler. Today, π has been calculated to over 100 trillion digits!
Remember: Diameter = 2 × Radius. Using the wrong value will double or halve your result.
While π ≈ 3 is useful for quick estimates, use at least 3.14159 for accurate results.
Always ensure your radius/diameter is in consistent units. The circumference will be in the same unit.
Circumference (C = 2πr) measures distance. Area (A = πr²) measures space. They have different units!
Find the circumference of a circle with radius 7 cm.
C = 2πr = 2 × 3.14159 × 7 = 43.98 cm
A circular table has a diameter of 1.2 meters. What is its circumference?
C = πd = 3.14159 × 1.2 = 3.77 meters
A wheel has a circumference of 62.83 cm. What is its radius?
r = C/(2π) = 62.83 ÷ (2 × 3.14159) = 10 cm
A bicycle wheel has a radius of 35 cm. How far does the bicycle travel in one complete wheel rotation?
Distance = Circumference = 2πr = 2 × 3.14159 × 35 = 219.91 cm ≈ 2.2 meters
The circumference of a circle can be calculated using C = 2πr (where r is the radius) or C = πd (where d is the diameter). Both formulas yield the same result since d = 2r.
Simply multiply the diameter by π (approximately 3.14159). For example, if the diameter is 10 cm, the circumference is 10 × π = 31.4159 cm.
The circumference is directly proportional to the radius. The formula C = 2πr shows that circumference equals 2π (approximately 6.283) times the radius. Doubling the radius doubles the circumference.
Divide the circumference by 2π using the formula r = C/(2π). For example, if C = 31.4159 cm, then r = 31.4159 ÷ 6.283 = 5 cm.
Pi (π) is an irrational number that cannot be expressed as a simple fraction. It equals approximately 3.14159265359... and continues infinitely without repeating. For most calculations, using 3.14159 provides sufficient accuracy.
First, find the radius using r = C/(2π), then calculate area using A = πr². Alternatively, use the direct formula A = C²/(4π).
Earth's circumference at the equator is approximately 40,075 km (24,901 miles). The polar circumference is slightly smaller at about 40,008 km due to Earth being an oblate spheroid.
You can physically wrap a string or flexible tape measure around the circular object, then measure the length of the string. This gives you the circumference directly.
Circumference is measured in units of length—the same units as the radius or diameter. Common units include centimeters, meters, inches, feet, and miles.
Circumference is the specific term for the perimeter (boundary length) of a circle. While "perimeter" can refer to any polygon's boundary, "circumference" is exclusively used for circles.
Understanding circumference is fundamental to working with circles in mathematics, science, engineering, and everyday life. Whether you're calculating the distance around a tire, designing circular structures, or solving geometry problems, the circumference formula C = 2πr is an essential tool.
Our free circumference calculator makes these calculations instant and accurate. Simply enter any circle measurement—radius, diameter, circumference, or area—and instantly get all other properties with step-by-step explanations. No more manual calculations or π approximation errors!