Skip to content

Volume Calculator

Work out the volume and surface area of a cube, box, cylinder, sphere, hemisphere, cone, pyramid, triangular prism, capsule, ellipsoid or cone frustum from its dimensions, with every step shown.

  • Free, no sign-up
  • Runs in your browser
  • Math
Six equal square faces; every edge has the same length.
Use the same length unit for every field; the volume comes out in that unit cubed and the surface area in that unit squared. Heights are measured at a right angle to the base.

Read the guide How to Calculate Volume: Boxes, Cylinders, Cones and Spheres

How to use the calculator

Pick a solid from the list. The form then shows only the measurements that shape needs, such as radius and height for a cylinder or the three semi-axes for an ellipsoid. Fill them in and press Calculate.

The result card gives the volume and the total surface area, plus useful extras like the slant height of a cone or the space diagonal of a box. The details panel repeats the formula and walks through it with your own numbers. Keep every field in one length unit: measurements in centimeters give a volume in cubic centimeters and an area in square centimeters.

Formulas used

  • Cube: V = a³, SA = 6a²
  • Rectangular prism: V = lwh, SA = 2(lw + lh + wh)
  • Cylinder: V = πr²h, SA = 2πr(r + h)
  • Sphere: V = (4/3)πr³, SA = 4πr²
  • Hemisphere: V = (2/3)πr³, SA = 3πr² including the flat base
  • Cone: V = (1/3)πr²h, SA = πr(r + s) with slant height s = √(r² + h²)
  • Rectangular pyramid: V = (1/3)lwh; the four triangular faces are added to the base for the area
  • Triangular prism: V = A × l, where A is the triangle area from its three sides (Heron's formula)
  • Capsule: a cylinder plus one full sphere, V = πr²h + (4/3)πr³
  • Ellipsoid: V = (4/3)πabc
  • Frustum of a cone: V = (1/3)πh(R² + Rr + r²)

Worked examples

Cylinder. A tank with radius 3 and height 10 holds V = π × 3² × 10 = 90π ≈ 282.7433388 cubic units. Its surface is 2π × 3 × (3 + 10) = 78π ≈ 245.044227 square units.

Cone. Radius 3 and height 4 give a slant height of √(9 + 16) = 5. The volume is (1/3) × π × 9 × 4 = 12π ≈ 37.69911184, and the surface area is π × 3 × (3 + 5) = 24π ≈ 75.39822369.

Good to know

  • A cone or pyramid holds exactly one third of the cylinder or prism with the same base and height.
  • Heights are perpendicular to the base. For a cone, do not enter the slant height as the height.
  • The pyramid is assumed to have its tip directly above the center of the base. The volume formula also works for a tilted tip, but the surface area does not.
  • An ellipsoid has no simple exact surface area formula, so the calculator uses Thomsen's approximation, which stays within about 1.1% and is exact for a sphere.
  • For a capsule, the height is the straight middle part only; the total length adds one diameter.
  • This tool computes a volume from a shape's measurements. To change a volume you already know from liters to gallons or similar, use the volume converter instead.

Frequently asked questions

What is the difference between volume and surface area?

Volume is how much space a solid takes up, or how much it holds, and is measured in cubic units. Surface area is the total area of its outside, the amount of material you would need to wrap or paint it, and is measured in square units.

How do I get the volume in liters or gallons?

Measure in centimeters and the result is in cubic centimeters; 1,000 cubic centimeters make one liter. If you measure in meters, one cubic meter is 1,000 liters. For gallons or other units, put the result into a volume converter.

Does the hemisphere surface area include the flat side?

Yes. The total of 3πr² is the curved dome (2πr²) plus the circular base (πr²). The result card also shows the curved part on its own, which is what you need for a dome without a floor.

Why is the ellipsoid surface area marked as approximate?

Unlike the volume, the surface area of a general ellipsoid cannot be written with ordinary functions. The calculator uses a well-known approximation by Knud Thomsen with a worst-case error of about 1.1%, which is accurate enough for most practical purposes.