Volume Calculator

What this calculator does

The Volume Calculator finds the three-dimensional space inside a rectangular box, a cylinder, a cone, or a sphere. Volume is expressed in cubic units, such as cubic feet, cubic meters, or cubic inches. Enter all dimensions in the same unit, and the result is reported in that unit cubed.

Volume calculations are common in packing, shipping, storage, concrete and soil estimates, tank capacity, and science experiments. A box volume describes how much a container can hold. A cylinder volume is used for pipes and tanks. Cone and sphere volumes appear in manufacturing, food service, and design.

How to use this calculator

1. Choose the solid: rectangular box, cylinder, cone, or sphere.
2. Enter the dimensions requested for that solid.
3. Click Calculate.
4. Review the volume and the related surface measurements.

The default box is 10 by 5 by 4, giving a volume of 200 cubic units. A cylinder with radius 3 and height 4 has a volume of about 113.0973. A cone with the same radius and height has a volume of about 37.6991, and a sphere with radius 3 has a volume of about 113.0973.

Volume formulas

Box:      V = length × width × height
Cylinder: V = πr²h
Cone:     V = ⅓πr²h
Sphere:   V = (4/3)πr³

For the cylinder and cone, r is the radius of the circular base and h is the perpendicular height. For the sphere, r is the radius. The calculator also reports base area, lateral surface, total surface area, slant height, or diameter where those values are meaningful.

What the results mean

The highlighted result is the volume in cubic units. Supporting values are included so you can compare a solid's capacity with the material needed to build or cover it. For example, the total surface area of a cylinder combines the two circular ends and the curved side, while the lateral surface covers only the side.

The cone's slant height is the distance from the tip to a point on the base edge. It is calculated with the Pythagorean theorem and is different from the perpendicular height.

Assumptions and limitations

• All dimensions must use the same unit. No unit conversion is performed.
• Every dimension must be greater than zero.
• The box is a right rectangular prism, the cylinder is a right circular cylinder, and the cone is a right circular cone.
• The sphere is a perfect sphere, not an ellipsoid or a rounded object.
• Results are approximations when π is involved and are rounded for display.
• This page does not calculate the volume of capsules, frustums, pyramids, or composite solids.

Frequently asked questions

Why is volume measured in cubic units?

Volume combines three lengths, so the unit is multiplied by itself three times. A box measured in feet produces a volume in cubic feet. Converting that value to another unit requires converting each dimension first, not merely multiplying the final number.

Why is a cone's volume one-third of a cylinder's volume?

A cone and a cylinder with the same base radius and height are closely related: the cone fills exactly one-third of the cylinder. That relationship produces the factor ⅓ in the cone formula. The same idea applies to a pyramid and a prism with matching bases and heights.

How is a cylinder different from a prism?

A prism has polygon bases, while a cylinder has circular bases. Both are calculated by multiplying the base area by the perpendicular height. For a cylinder, the base area is πr², so the volume becomes πr²h.

Reference table

Volume unit conversions

Source

Reference: Calculator.net — Volume Calculator.

This page is for general educational and estimation purposes. Confirm container capacities and material quantities before ordering or building.