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About this tool
Explore geometric formulas interactively — calculate area, perimeter, and volume with visual shapes and step-by-step breakdowns.
Geometry Formula Explorer calculates area, perimeter, surface area and volume for ten shapes — circle, rectangle, triangle, trapezoid, parallelogram and ellipse in 2D, plus sphere, cylinder, cone and rectangular prism in 3D — and shows the substitution line by line rather than just the answer. Enter the dimensions and every formula for that shape recalculates at once: a circle returns πr², 2πr and 2r together, a rectangular prism returns volume, surface area and the space diagonal √(l²+w²+h²). Results are rounded to four decimal places and a scaled diagram of the shape updates alongside the numbers.
Open Geometry Formula Explorer on AltFTool — it loads instantly in your browser.
Enter the values you already know.
Fine-tune the options to match your scenario.
Read the result and use it in your planning or reporting.
Each calculation is expanded into Given, Formula and worked-substitution lines so you can copy the method into an answer sheet.
Choosing a shape computes every formula defined for it together, so area, perimeter and diagonal come from one set of inputs.
A visual of the selected shape redraws as you change the dimensions, which catches an input typed into the wrong field straight away.
Twenty-two formulas across ten shapes, including πr² and 2πr for a circle, ½(a + b)h for a trapezoid, (4/3)πr³ for a sphere and (1/3)πr²h for a cone. All results are rounded to four decimal places.
Just the side — the tool computes the lateral surface πr√(r² + h²), which excludes the circular base. Add πr² yourself if you need the total surface area of a closed cone.
It uses Ramanujan's approximation π[3(a + b) − √((3a + b)(a + 3b))], because an ellipse perimeter has no exact closed form. The approximation is accurate to within a tiny fraction of a percent for ordinary eccentricities and only drifts for extremely elongated ellipses.
None — the calculation is unit-agnostic, so whatever unit you enter is the unit of the answer. Enter centimetres and area comes back in square centimetres and volume in cubic centimetres; just keep every field in the same unit, with a minimum value of 0.1.
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