3D Shape Calculator - Volume & Surface Area

How to use this tool

1. Choose a solid. Select the sphere, prism, cylinder, cone, torus, pyramid, or frustum.
2. Set a length unit. Choose the unit you want displayed; the calculator does not rescale entered dimensions.
3. Enter dimensions. Provide each positive dimension. Circular solids accept either radius or diameter.
4. Read the results. Review total area, any lateral and base areas, volume, capacity, slant height, and the formula steps.

3D shape formulas and units

Choose a solid and enter its positive dimensions to calculate volume and surface area. The calculator includes a sphere, cube, rectangular prism, cylinder, cone, regular tetrahedron, ring torus, square pyramid, and conical frustum. It shows formula steps and a labeled schematic so you can see which radius, height, or slant length each result uses.

Sphere, cube, rectangular prism, and tetrahedron

• Sphere: total surface area = 4πr²; volume = (4/3)πr³.
• Cube: total surface area = 6a²; volume = a³.
• Rectangular prism: total surface area = 2(lw + lh + wh); volume = l·w·h.
• Regular tetrahedron: total surface area = √3·a²; volume = a³/(6√2).

Cylinder (radius r, height h)

• Lateral area: 2πrh.
• Both bases together: 2πr².
• Total surface area: 2πrh + 2πr²; volume: πr²h.

Cone (base radius r, vertical height h)

• Slant height: ℓ = √(r² + h²).
• Lateral area: πrℓ; base area: πr².
• Total surface area: πrℓ + πr²; volume: (1/3)πr²h.

Ring torus (major radius R, tube radius r)

• Total surface area: 4π²Rr; volume: 2π²Rr².
• A ring torus requires R > r > 0, leaving a hole through its center.

Square pyramid (base side a, vertical height h)

• Face slant height: ℓ = √(h² + (a/2)²).
• Base area: a²; lateral area: 2aℓ.
• Total surface area: a² + 2aℓ; volume: (1/3)a²h.

Conical frustum (larger radius R, smaller radius r, vertical height h)

• Slant height: ℓ = √(h² + (R − r)²).
• Both circular bases: π(R² + r²); lateral area: π(R + r)ℓ.
• Total surface area: π(R² + r²) + π(R + r)ℓ.
• Volume: (πh/3)(R² + Rr + r²), with R > r > 0.

Using the measurements

The radius/diameter control appears for spheres, cylinders, and cones. Diameter is the full distance across a circle, so the calculator divides it by two before applying the radius-based formulas. Switching between radius and diameter doubles or halves the visible input while keeping the represented shape unchanged. The cone, square pyramid, and frustum also report their computed slant height.

Select mm, cm, m, in, or ft to label the results. This selector interprets the numbers you entered; it does not convert or rescale them. For example, a cylinder with r = 3 and h = 4 has volume 36π cubic units. In centimeters this is 36π cm³ and 36π/1000 liters; in inches it is 36π in³ and 36π/231 US gallons. Metric capacity uses 1 L = 1,000 cm³ (or 1,000,000 mm³ and 0.001 m³); US capacity uses 231 in³ per gallon.

Lateral area includes only a cylinder's side, a cone's curved surface, or a pyramid/frustum's sloping faces. Base area is shown separately, and total surface area adds every base. This distinction is useful when estimating paint for the side of a tank, fabric for a tent, or material to cover a closed solid. Enter every dimension in the same selected unit; mixing inches and feet without first converting them produces inconsistent area and volume.

Worked examples

These results assume ideal geometric solids with flat bases and straight sides. The diagrams are schematic rather than engineering drawings, and rounded displays may differ slightly from calculations that use full floating-point precision.