Solid Geometry Calculator
Pick a 3D solid, type its dimensions, and instantly get the volume and surface area — with a clear labeled diagram and extras like slant height and diagonal.
Shape
Results
About the Solid Geometry Calculator
This solid geometry calculator works out the volume and surface area of the seven most common 3D solids: the cube, rectangular box (cuboid), sphere, cylinder, cone, square pyramid and triangular prism. Choose a shape, enter its dimensions in metres, centimetres, millimetres, inches or feet, and the results update instantly alongside a labeled diagram that shows exactly which measurement each number refers to. Beyond volume and surface area you also get the quantities students are usually asked for next — lateral (side) area, base area, the slant height of cones and pyramids, and the space diagonal of cubes and boxes — plus the volume converted into litres. Every formula is computed in your browser using exact geometry, so there is no rounding bias and your numbers never leave your device. It is the visual, interactive companion to a textbook's volume and surface-area formulas.
How to use the calculator
- 1 Pick a 3D shape from the selector — cube, box, sphere, cylinder, cone, square pyramid or triangular prism. The diagram updates to show its dimensions.
- 2 Choose the length unit you are working in (m, cm, mm, in or ft).
- 3 Type each dimension into the labeled fields. Volume, surface area and the related quantities update live as you type.
- 4 Read the results: volume is in your unit cubed (and converted to litres), surface area in your unit squared, plus lateral area, base area, slant height or diagonal where they apply.
The formulas it uses
Cube: V = s³, surface area = 6s², space diagonal = s√3. Rectangular box: V = l·w·h, surface area = 2(lw + lh + wh), diagonal = √(l² + w² + h²). Sphere: V = 4⁄3·π·r³, surface area = 4πr². Cylinder: V = πr²h, lateral area = 2πrh, surface area = 2πr² + 2πrh. Cone: slant height = √(r² + h²), V = 1⁄3·πr²h, lateral area = πr·slant, surface area = πr² + πr·slant. Square pyramid: slant height = √((b/2)² + h²), V = 1⁄3·b²·h, surface area = b² + 2b·slant. Triangular prism (isosceles cross-section, base b, triangle height t, prism length L): V = ½·b·t·L, surface area = 2·(½·b·t) + (b + 2·√((b/2)² + t²))·L.
Frequently asked questions
What is the difference between volume and surface area?
Volume measures how much space a solid takes up and is given in cubic units (such as cm³ or m³). Surface area measures the total area of all its outer faces and is given in square units (such as cm² or m²). This calculator reports both for every shape, plus the volume in litres.
How do I find the surface area of a cone?
The total surface area of a cone is πr² + πr·s, where r is the base radius and s is the slant height, s = √(r² + h²). The first term is the circular base and the second is the curved lateral surface. Enter the radius and height and the calculator computes the slant height and both areas for you.
Which units can I use?
You can enter dimensions in metres, centimetres, millimetres, inches or feet. Volume comes out in that unit cubed and surface area in that unit squared, and the volume is also converted into litres for convenience.
How is the triangular prism's surface area calculated?
The triangular faces use ½·base·height, and the three rectangular sides use the triangle's perimeter times the prism length. The calculator assumes an isosceles triangle, so the two slanted edges are equal — a common textbook assumption. For a different triangle, compute the perimeter separately.
Related tools
Explore more geometry and math on UnitConv. For 2D figures try the triangle solver, and browse the formulas library for areas, volumes and other geometry references. You can also convert between volume and area units directly in the unit converter.