Circumference and perimeter calculator
Find the distance around a shape. Pick the shape, type the sizes, and the answer appears with the formula.
How it works
- Pick the shape. For a circle you can start from the radius, the diameter or the area.
- Choose the unit and type the sizes shown in the diagram.
- Read the perimeter and the same length in other units. Copy it with one click.
How perimeter is worked out
The perimeter is the length of the outline of a shape. For shapes with straight sides you simply add up the sides. A rectangle has two lengths and two widths, so its perimeter is 2 × (l + w).
For a circle the outline is called the circumference: π times the diameter, or 2π times the radius. If you only know the area, the radius is the square root of the area divided by π.
An ellipse is harder. There is no simple exact formula for its perimeter, so this tool uses an approximation by the mathematician Ramanujan. It is extremely close for every ellipse you are likely to measure, and exact for a circle.
When you need the perimeter in real life
Perimeter is the length you need for anything that goes around the edge: fencing for a garden, skirting boards for a room, edging for a flower bed, trim for a tablecloth or LED strip around a mirror. Measure each side, pick the shape and the calculator adds it up in the unit you chose.
For skirting boards, subtract the width of each door opening. For fencing, add a little extra for posts and corners. For round objects like a wheel, pot or tree trunk, measure the diameter across the middle, or wrap a string around it and measure the string to check.
If you know the circumference of a circle and need the diameter, divide by π, about 3.14. The Circle option lets you start from radius, diameter or area, so you rarely need to do that sum yourself. For an oval table or a race track shape, use Ellipse with the two half axes.
Questions
How do I calculate the circumference of a circle?
Multiply the diameter by π, about 3.14159. A circle with a diameter of 10 cm has a circumference of about 31,42 cm.
What is the difference between perimeter and circumference?
They mean the same thing: the distance around a shape. Circumference is the word used for circles and ellipses.
How exact is the ellipse result?
It uses Ramanujan's approximation. For ordinary ellipses the error is far below one part in ten thousand, which is much less than any tape measure can show.
What is arc length?
The length of the curved part of a circle slice. It is the angle divided by 360, times the circumference of the full circle. The outline of the whole slice adds two radii.
How do I find the diameter from the circumference?
Divide the circumference by π, about 3,14159. A circumference of 100 cm means a diameter of about 31,83 cm.
How do I calculate how much fence I need?
Choose the shape of your garden, type the sides, and read the perimeter. Subtract the width of any gate.
Can it calculate the perimeter of a hexagon?
Yes. Choose Regular polygon, type the number of sides and the side length.
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