How to use it
Pick a shape, choose the unit you are measuring in, and fill in the boxes. The main result is shown large, with the other measurements of the same shape below. Areas use square units (cm²) and volumes cubic units (cm³); the unit label changes automatically. The shapes cover rectangles, squares, circles, ellipses, triangles (from a base and height, or from all three sides), parallelograms, trapezoids, regular polygons, cubes, boxes, cylinders, cones and spheres.
Formulas used
Circle area is π × r², and its circumference is 2 × π × r. Triangle area from a base and a height is half of base times height; from three sides it uses Heron’s formula, √(s(s−a)(s−b)(s−c)) with s the half perimeter, and the angles come from the law of cosines. A trapezoid’s area is the average of its two parallel sides times the height. A regular polygon with n sides of length s has area n·s² / (4·tan(π/n)). A cylinder’s volume is π·r²·h, a cone’s is a third of that, and a sphere’s is 4/3·π·r³. The perimeter of an ellipse has no simple exact formula, so Ramanujan’s close approximation is used and marked as such.
Questions
Why does my triangle say it is impossible? The three sides must satisfy the triangle rule: each side has to be shorter than the other two added together. Can I mix units? No; use one unit for every box, or convert first with the Unit Converter. How many decimals does it show? Up to four, trimming trailing zeros. Are my numbers saved? Only the chosen shape and unit are remembered on this device.