Circumference Calculator
This circumference calculator finds the circumference or perimeter and the area at the same time: for a circle, rectangle, square, ellipse, triangle, trapezoid, parallelogram, circle sector and regular polygon. The formulas and steps are shown with each result.
Example: Shape: Circle · Unit: cm · Known value: Radius r · Value 5 → Perimeter: Perimeter P = 31.416 cm. Source: Wolfram MathWorld – Circle. Updated: .
How it is calculated
The perimeter is the length of a shape’s outline; for a circle it is called the circumference: C = 2 · π · r. For a rectangle it is P = 2 · (a + b). The area is shown alongside, so you do not have to switch between two calculators.
Formulas at a glance
- Circle: C = 2πr = πd, A = πr². You can start from the radius, diameter, circumference or area – the rest is worked out.
- Rectangle and square: P = 2(a + b) or 4a; A = a · b or a².
- Triangle: P = a + b + c; the area follows from Heron’s formula using all three sides.
- Trapezoid and parallelogram: P is the sum of the four sides, A = midsegment times height or base times height.
- Circle sector: arc length = 2πr · α/360°; the perimeter adds the two radii.
- Regular polygon: P = n · a, with inradius and circumradius.
Input notes
Enter every measurement in the same unit; the area then comes out in that unit squared. Choose the unit at the top – the calculation itself uses the numbers only. For the ellipse the tool uses Ramanujan’s approximation, because the exact perimeter would need an elliptic integral.
Related tools: the triangle calculator for angles and heights, the square meter calculator for rooms and the Pythagorean theorem calculator for missing sides.
Frequently asked questions
How do you calculate the circumference of a circle?
C = 2 · π · r, or π · d. With a radius of 5 cm the circumference is 2 · π · 5 ≈ 31.42 cm. If you know the diameter, use C = π · d.
How do you calculate the perimeter of a rectangle?
P = 2 · (length + width). A rectangle of 8 cm by 5 cm has a perimeter of 2 · 13 = 26 cm.
What is the difference between perimeter and area?
The perimeter measures the length of the outline (in cm, m …), the area measures the space inside (in cm², m² …). Two shapes with the same perimeter can have very different areas.
How do I get the perimeter of a triangle?
Add all three sides: P = a + b + c. The sides must satisfy the triangle inequality, otherwise no triangle exists.
Why is the perimeter of an ellipse only an approximation?
There is no closed formula; the exact value needs an elliptic integral. Ramanujan’s approximation is more accurate than any practical measurement.
Sources and legal basis
- Wolfram MathWorld – Circle
- Wolfram MathWorld – Ellipse: perimeter after Ramanujan
- Wolfram MathWorld – Heron’s formula
- Wolfram MathWorld – Regular polygon
As of: · Editorial policy
Related tools
- Triangle CalculatorTriangle calculator from any three values (SSS, SAS, ASA, AAS, SSA): missing sides and angles, area, perimeter, heights, inradius and circumradius.
- Square Footage CalculatorSquare footage calculator for rooms and whole homes: enter feet and inches or metres, add rooms and L-shapes, get sq ft, m², sq yd, acres, waste and cost.
- Square meters to acres converterConvert square meters to acres and back: 1 acre = 4,046.86 m². Also hectares, square feet, square miles, are and tsubo – with the working and a table.
- Pythagorean Theorem CalculatorPythagorean theorem calculator: enter two sides to get the third side, both angles, area and height – with exact square roots, working and a right-angle check.
- Pi digitsPi digits up to 10,000 decimal places: show any number of digits, look up the digit at a position or search a sequence such as your birthday in π.
- Cylinder CalculatorCylinder calculator from any two values: radius, diameter, circumference, height, volume, lateral or surface area – with formulas, litres and working.
- Online CalculatorCalculator online, free and instant: type or tap and see the answer as you go – order of operations, brackets, percent, square root, steps and a history list.
- Circle skirt calculator: waist radius, hem and fabric for full, half and quarterCircle skirt calculator: waist radius, hem radius, hem width and fabric area for a full, 3/4, half or quarter circle skirt from your waist and skirt length.
- Cake Pan Size Conversion CalculatorCake pan size conversion from round to square and back: the factor for another springform pan or sheet, scaled recipe amount and tips on baking time and depth.