Calculate area and perimeter for 20+ shapes with visual diagrams. Includes circles, polygons, ellipses, and sectors.
Pick a shape from a gallery of more than 20 entries - circles, triangles, quadrilaterals, regular polygons, ellipses, and sectors - and the page draws a labeled diagram showing exactly which dimensions to enter. Type those lengths in and the tool returns the area and the perimeter computed from the standard formulas. The surprise most users hit is scaling: double a circle's radius and the circumference merely doubles, but the area quadruples, so a shape that looks twice as wide holds four times as much. The diagram also exists to stop a subtler error - entering the slant side of a trapezoid where the perpendicular height belongs.
A concrete input and expected output from the current implementation.
Input
Circle, radius = 5 cm
Expected output
Area = 78.54 square cm; perimeter (circumference) = 31.42 cm
Area is pi times the radius squared: pi x 25 = 78.5398, rounded to 78.54. The circumference is 2 x pi x 5 = 31.4159, rounded to 31.42. Both results carry the units entered, so the area is quoted in square centimeters.
Pick a shape and the page draws a labeled figure with the dimensions that shape needs - radius for a circle, base and perpendicular height for a triangle, side length for a square. Enter values and the tool applies the standard formula for that shape and returns both results. The numbers follow the units you entered: perimeter in linear units, area in those units squared.
Polygon perimeters are the sum of the side lengths; curved shapes involve pi. One result deserves caution: an ellipse has no exact elementary perimeter formula, so the perimeter any calculator shows for an ellipse is an approximation - the area, by contrast, is exact (pi x a x b for semi-axes a and b). Regular polygons in the gallery ask for the information that pins the shape down, such as side length and a count of sides.
Because the two quantities scale differently. The circumference is proportional to the radius, so doubling r doubles 2 x pi x r; the area is proportional to the square, so doubling r quadruples pi x r squared. If you expected both to double, that mismatch is the relationship to remember - it holds for every shape: lengths scale linearly, areas scale quadratically.
No. The tool takes typed dimensions for the shapes in its gallery; it does not accept images or freehand outlines. For an irregular region, decompose it into gallery shapes - rectangles, triangles, semicircles - compute each one, and add the results, accepting that a curved boundary can only be approximated by such a decomposition.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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