Volume Calculator
Calculate the volume of common 3D shapes — cube, rectangular box, cylinder, sphere, and cone.
Formulas used
- Cube — Volume = side³
- Rectangular box — Volume = length × width × height
- Cylinder — Volume = π × radius² × height
- Sphere — Volume = (4/3) × π × radius³
- Cone — Volume = (1/3) × π × radius² × height
Worked example
A cylinder with radius 3 and height 10 has a volume of π × 3² × 10 ≈ 282.74 cubic units. A sphere with radius 5 has a volume of (4/3) × π × 5³ ≈ 523.60 cubic units.
What to enter
- Cube: one side. Box: length, width and height. Cylinder and cone: radius and height. Sphere: radius only.
- Use the radius, not the diameter. Halve a diameter before typing it.
- The height for a cone is the straight vertical height from base to tip, not the slanted side length.
- Every value must be greater than zero, and results are shown to two decimals with no unit label.
More worked examples
A cube with side 4 holds 64.00 and a box of 5 × 4 × 3 holds 60.00. A cylinder with radius 5 and height 12 gives 942.48, and a cone with radius 4 and height 9 gives 150.80.
The cone formula is exactly a third of the cylinder's: radius 3 and height 10 gives 94.25 for a cone, against 282.74 for the matching cylinder.
Units and rounding
The answer is in the cube of whatever unit you used. For a cylinder of radius 10 and height 20, entered in centimeters, the result is 6283.19 cm³, or about 6.28 liters since 1,000 cm³ is one liter. Because only two decimals are kept, small objects lose detail: a cube with side 0.1 has a true volume of 0.001 and displays as 0.00. Enter the dimensions in a smaller unit for tiny shapes.
Hollow shapes, pyramids and partial shapes such as a frustum are not covered.
Examples and input rules
A cube with sides of 5 has a volume of 125.00, a box measuring 2 by 3 by 4 has 24.00, and a cone with a radius of 3 and a height of 4 has 37.70. A radius or side of zero or less returns "Please enter a positive value."
For a cone, use the vertical height from the base to the tip, not the slanted side. Volumes are in cubic units of whatever unit you used for the inputs, so measurements in centimeters give cubic centimeters.
Frequently asked questions
Why is a cone's volume a third of a cylinder's?
A cone and a cylinder with the same base radius and height are related by a factor of exactly 1/3 — this is a well-known geometric result, which is why the cone formula reuses the cylinder's base area formula multiplied by 1/3.
What units will the result be in?
Whatever unit you entered your measurements in, cubed. If you enter centimeters, the volume is in cubic centimeters (cm³); if meters, cubic meters (m³), and so on.
Can I enter the diameter of a cylinder or sphere?
Not directly. The tool asks for the radius, so divide the diameter by two first.
Why does a small cube show a volume of 0.00?
Results are rounded to two decimals. A cube of side 0.1 has a volume of 0.001, which rounds to zero. Use millimeters or centimeters in place of meters.
How do I turn the result into liters?
If you measured in centimeters, divide the cubic-centimeter result by 1,000. If you measured in meters, multiply the cubic-meter result by 1,000.