Volume Calculator

MathLast updated: August 17, 2026

Volume is the measure of the space a three-dimensional body occupies. A cube uses the cube of its edge, a rectangular prism the product of its three dimensions, a cylinder the base area times the height, a sphere (4/3)πr³, and a cone one third of the matching cylinder. This calculator works out the volume of five basic solids on a single screen.

Along with the volume, the total surface area is computed too — that is the figure you need for painting, cladding, and packaging. Whatever unit you enter the lengths in, the volume comes out in the cube of that unit (m³, cm³) and the surface area in its square. Remember that 1 liter equals 1 dm³ (1,000 cm³): handy for water tank and aquarium calculations.

Formula

Cube: V = a³, Surface = 6a²
Rectangular prism: V = a × b × c, Surface = 2(ab + ac + bc)
Cylinder: V = πr²h, Surface = 2πr(r + h)
Sphere: V = (4/3)πr³, Surface = 4πr²
Cone: V = πr²h / 3, Surface = πr(r + ℓ), ℓ = √(r² + h²)

Forgetting to divide by 3 in the cone volume is the most common mistake: a cone is one third of the cylinder with the same base and height. To keep the sphere formulas straight, remember that the volume uses r³ while the surface area uses r².

How to Calculate

  1. Select the solid whose volume you want to calculate.
  2. Enter the lengths of that solid in the same unit.
  3. Read the volume (unit³) and the surface area (unit²) results.
  4. If you need the answer in liters, enter the lengths in dm: 1 dm³ = 1 liter.

Worked Examples

A cube with a 3-unit edge

A cube with an edge of 3 units has a volume of 3³ = 27 unit³ and a surface area of 6 × 3² = 54 unit². If you read the edge in dm, this cube holds 27 liters of water.

Volume: 27 unit³ · Surface area: 54 unit²

Cylindrical water tank: r = 2, h = 5

A cylinder with a base radius of 2 units and a height of 5 units has a volume of π × 2² × 5 ≈ 62.83 unit³ and a total surface area of 2π × 2 × (2 + 5) ≈ 87.96 unit². The base area is also reported, as 12.57 unit².

Volume: 62.83 unit³ · Surface area: 87.96 unit² · Base area: 12.57 unit²

A sphere with a radius of 3

For r = 3 the sphere has a volume of (4/3) × π × 3³ ≈ 113.10 unit³ and a surface area of 4π × 3² ≈ 113.10 unit²; the diameter comes out at 6 units — at r = 3 the volume and the surface area happening to match numerically is a pleasant coincidence.

Volume: 113.10 unit³ · Surface area: 113.10 unit² · Diameter: 6 units

Frequently Asked Questions

How is the unit of volume determined, and how do you convert to liters?
Volume is expressed in the cube of the length unit: enter meters and you get m³, enter centimeters and you get cm³. For liters, use 1 liter = 1 dm³ = 1,000 cm³ and 1 m³ = 1,000 liters.
Why is the volume of a cone one third of the cylinder?
A cone with the same base and height can be emptied into the cylinder exactly three times; it is an exact ratio, provable with integral calculus. That is why the cone formula is πr²h/3, and forgetting to divide by 3 makes the result three times too large.
When do you need the surface area?
The material required to cover the outside of a body is computed from its surface area: painting a tank, the cardboard of a box, the fabric of a balloon. What fits inside (water, sand, air) is found from the volume; keeping the two concepts apart matters.
Where does the surface area formula of a cylinder come from?
The surface of a cylinder consists of two circular bases (2 × πr²) and a lateral face that unrolls into a rectangle (circumference × height = 2πrh). Adding them gives 2πr² + 2πrh = 2πr(r + h).
What is the slant height (ℓ) of a cone?
It is the slanted length running from the apex of the cone down to the base circle, found from the Pythagorean relation as ℓ = √(r² + h²). The lateral surface formula πrℓ uses the slant height, not the vertical height; mixing the two is a frequent error.
If the edge doubles, how much does the volume grow?
Because volume is proportional to the cube of the length, it grows by 2³ = 8 times, while the surface area grows by 2² = 4 times. That is why a small increase in size affects material and capacity calculations far more than expected.