Circumference Calculator
The circumference of a circle is the distance around it: C = 2πr, or π times the diameter. A circle with a 12 cm radius has a circumference of 75.40 cm, a diameter of 24 cm and an area of 452.39 cm² (A = πr²). Enter any radius to get all three.
C = 2πr = πd and A = πr². When you enter an area, the unit is read as square units.
How to use the Circumference Calculator
- Enter the radius of the circle.
- Choose its unit: cm, m, inches or feet.
- Read the circumference, diameter and area, which update as you type.
- If you only know the diameter, enter half of it as the radius.
Formula
C = 2πr · d = 2r · A = πr²All three values come from the radius r and π at full double precision. Circumference and diameter use the same unit as the radius; area uses that unit squared.
Circle formulas
- Circumference from radius: C = 2πr
- Circumference from diameter: C = πd
- Radius from circumference: r = C ÷ 2π
- Area from radius: A = πr²
- Radius from area: r = √(A ÷ π)
Where it is used
- Wheels and tyres: one turn of a wheel travels one circumference.
- Pipes and ducts: insulation or wrap length is the outer circumference.
- Fencing and edging around circular beds or pools.
- Concrete columns and formwork, where area gives volume per unit height.
Accuracy
The maths is exact; real accuracy depends on how well you measure. For thick materials such as pipe insulation, measure the outside diameter and add the material thickness before calculating the wrap length.
Circumference Calculator questions
How do I calculate circumference from the diameter?
Multiply the diameter by π: C = πd. A pipe with a 10 inch diameter has a circumference of about 31.416 inches. In this calculator, enter half the diameter (5 inches) as the radius and the same result appears.
What is the difference between radius and diameter?
The radius runs from the centre to the edge; the diameter runs edge to edge through the centre, so d = 2r. Pipes, wheels and columns are usually specified by diameter, while most formulas use the radius, so halve the diameter before using them.
How do I find the area of a circle?
Square the radius and multiply by π: A = πr². A circle with a 12 cm radius has an area of about 452.39 cm². Area is always in square units, so a radius in metres gives an area in square metres.
How do I find the radius from the circumference?
Divide the circumference by 2π: r = C ÷ 2π. A tree trunk measuring 157 cm around has a radius of about 25 cm and a diameter of about 50 cm. This is the easiest way to size round objects you cannot measure across.
What are the most common mistakes in circle calculations?
The most common mistakes are using the diameter where the radius belongs, rounding π too early, and mixing units. Use the full value of π (the calculator does), keep every measurement in one unit, and remember that area uses squared units.
How do I convert units for circle calculations?
Choose the unit next to the radius field and the results use the same unit. To convert by hand, put all measurements in one unit first: 1 foot = 12 inches, 1 metre = 100 cm. Convert area with the square of the factor, so 1 m² = 10,000 cm².
How does circumference relate to the volume of a cylinder?
A cylinder's volume is its circular area times its height: V = πr²h. Circumference gives the length of material needed to wrap it. For a column 30 cm in radius and 3 m tall, the volume is about 0.85 m³ and the formwork wraps about 1.88 m around.