Cube, sphere, cylinder, cone, pyramid, prism — calculate volume, surface area, lateral area, and slant height for every standard 3D solid. Free, instant, with step-by-step AI explanations.
3D shape calculators differ from their 2D counterparts in two key ways: they output volume (cubic units) instead of area (square units), and they typically return both surface area and volume from the same set of inputs. Whether you are sizing a fish tank (rectangular prism), wrapping a soup can (cylinder), or computing the silver coating on a bauble (sphere), the calculators below give you every derived measurement.
Pick the solid that matches your problem and click through. Each calculator accepts the dimensions you have, infers the rest from the shape geometry, and returns volume, surface area, lateral area, slant height, diagonals and more — whichever apply. For composite 3D solids (e.g. a cylinder on top of a cube, or a sphere with a cylindrical hole), use the AI Geometry Solver: describe the figure or upload a photo and the AI handles the additive / subtractive composition.
In 2D you compute area (the flat region a shape encloses) and perimeter (the distance around it). In 3D you also need volume (the space a solid occupies) and surface area (the total area of its outer skin). Some 3D solids additionally have a "lateral area" — the curved or side surface only, excluding the top and bottom bases. For a cylinder for example, the lateral area is just the rolled-out rectangle of the side; the surface area adds the two circular caps on top of that.
A useful rule when you double a dimension: a 2D area scales by 4× (k²), but a 3D volume scales by 8× (k³). This is why doubling the size of a cake recipe often requires more than double the baking time — the volume grows much faster than the surface that conducts the heat.
Quick lookup for the formulas applied by the calculators above. Lateral area refers to side surface only (no bases). Slant height (ℓ) is the distance from the apex to the edge of the base along the slanted face.
| Solid | Volume | Surface area | Lateral area |
|---|---|---|---|
| Cube | s³ | 6s² | 4s² |
| Rectangular prism | l × w × h | 2(lw + lh + wh) | 2(lh + wh) |
| Sphere | (4/3) × π × r³ | 4π × r² | — |
| Hemisphere | (2/3) × π × r³ | 3π × r² | 2π × r² |
| Cylinder | π × r² × h | 2π × r² + 2π × r × h | 2π × r × h |
| Cone | (1/3) × π × r² × h | π × r × (r + ℓ) | π × r × ℓ |
| Square pyramid | (1/3) × a² × h | a² + 2 × a × ℓ | 2 × a × ℓ |
| Triangular prism | base × length | 2 × base + perim × length | perim × length |
| Torus (ring) | 2π² × R × r² | 4π² × R × r | — |
Problem: a basketball has a diameter of 24 cm. What is its volume?
Surface area: SA = 4π × 12² = 576π ≈ 1,809.56 cm². Or just open the Sphere & Cylinder Calculator above and enter 24 in the diameter field — both values are returned instantly.
Cube, rectangular prism, sphere, hemisphere, cylinder, cone, square pyramid, triangular prism, and torus — every standard solid covered in middle-school through college geometry. Less common solids (frustums, ellipsoids, irregular polyhedra) are handled by the AI Geometry Solver.
Volume measures the amount of 3D space inside a solid (cubic units, e.g. m³, in³, gallons). Surface area measures the total area of the outer skin (square units). They scale differently with size: doubling every dimension multiplies surface area by 4 but volume by 8.
Yes — most solid calculators on this site work in reverse. Enter volume and the calculator returns the matching radius, edge length or height. For solids with multiple unknowns (a rectangular prism with only volume known has infinite solutions), enter at least one dimension.
For irregular solids — composites, frustums, hollow objects with cavities — use the AI Geometry Solver. Describe the figure (or upload a photo) and the AI splits it into standard solids, computes each, and adds or subtracts as appropriate.
Any consistent unit. The calculator does not interpret units — if you enter "5" for radius, results come back in matching units (5 cm radius gives volume in cm³, 5 in radius gives volume in in³). Mixing units (e.g. radius in cm, height in m) will give wrong results.
Lateral area is the side surface only — for a cylinder it is the rolled-out rectangle, for a cone the unrolled sector, for a prism the rectangles around the perimeter. Surface area adds the top and bottom bases on top. The lateral-only number is useful when you are wrapping a label, painting a wall, or pricing the side material of a container.
The Shape Calculator hub covers triangles, circles, polygons and other flat figures with the same step-by-step solutions.