Area, perimeter, volume and surface area for twenty-four shapes, drawn to scale, with every assumption stated and every approximation named.
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Exact arithmetic on rationals, with both evaluation conventions named and the precedence table the parser runs on printed on the page.
Plot functions with a real expression parser, poles drawn as gaps, and roots, turning points and integrals found by bracketing with the check printed.
Plot 3D surfaces from z = f(x, y), polar z = f(r, theta), or fully parametric equations. Exact evaluation via mathjs, real holes where a function is undefined, and OBJ or STL export for 3D printing.
You have a triangle with a base of 10 cm and a height of 6 cm and want its area and its perimeter.
Triangle from base and height
base 10 cm · height 6 cm
Results
Area 30 cm² Perimeter if right-angled: 27.6619037897 cm Perimeter if isosceles: 25.6204993518 cm (the smallest possible)
A base and a height give the area and nothing else: the apex can slide along a line parallel to the base for ever, changing every side while the area stays 30. So the tool gives both of the cases people usually mean and says in words that the perimeter is not determined, rather than quietly assuming one of them.
Area, perimeter, volume and surface area for twenty-four shapes, with a drawing to scale, every assumption stated in words, and every approximation named as one. Results follow the inputs as you type; nothing waits behind a Calculate button.
The interesting fault in a geometry calculator is not usually the arithmetic, it is that a shape is often NOT determined by the numbers it asks for and the tool picks one anyway. A triangle with a base of 10 and a height of 6 has an area of 30, but its perimeter can be anything above a minimum: the apex slides along a parallel line for ever. A trapezoid with two parallel sides and a height is the same. A parallelogram needs three numbers, not two, and using the height as the slanted side is true only of a rectangle. Every shape here says what it does and does not determine, and where two readings are ordinary it gives both rather than choosing. Beyond that, two quantities are genuinely approximations and are labelled: an ellipsoid's surface area has no closed form at all, and an ellipse's perimeter is an elliptic integral, computed here to the last bit of a double by the arithmetic-geometric mean with Ramanujan's widely quoted approximation shown beside it and the difference given. A triangle's area from three sides uses Kahan's ordering rather than the textbook Heron formula, which on a thin triangle subtracts nearly equal numbers and loses about seven of its sixteen significant figures. And each shape computes a second route to a number it already printed (a sphere's surface is the derivative of its volume, Pappus's theorem for the torus, the parallelogram law for the diagonals) and shows whether it holds.
The formula used is printed under every result, so the working can be copied rather than guessed at.
Volume and surface area for tanks, boxes and pipes, converted between metric and imperial units exactly.
The scale drawing shows immediately when a set of numbers describes something other than the intended shape.
Three sides give every angle, both radii and the area, with the triangle inequality checked first.
A base and a height do not determine a perimeter, and this tool says so instead of quietly assuming a right angle.
Because a base and a height do not determine one. The apex can sit anywhere on a line parallel to the base, so every side changes while the area stays the same. The two shown are the right-angled case and the isosceles case, which is also the smallest possible perimeter.
Because two parallel sides and a height do not settle the shape either: the top edge slides sideways without changing the area. Leave it blank for the isosceles case, which is what most calculators assume without telling you.
They compute the same thing, but the textbook Heron form takes differences of nearly equal numbers when a triangle is thin. On sides 1, 1 and 1.9999999 it gives 0.00031622774599383683 where the answer is 0.0003162277462526027. Kahan's ordering, with the sides sorted and the products grouped differently, does not lose those figures. Both are shown so the difference is visible.
Because Ramanujan's is an approximation. The perimeter of an ellipse is an elliptic integral with no elementary closed form. The value shown first comes from the arithmetic-geometric mean, which converges to machine precision; the approximation is printed underneath with the difference so you can see how far it is.
Because a negative length describes no shape. The shipped version of this tool accepted a radius of -5 and reported an area of 78.5398 with a perimeter of -31.4159, which is two answers about a thing that does not exist.
Every unit is derived from an exact definition (the inch is exactly 0.0254 m by the 1959 agreement), and areas scale as the square of the length ratio while volumes scale as the cube. A square metre is 10,000 square centimetres, not 100.
Every calculation runs locally in your browser. Your numbers and expressions are not transmitted or stored.