Volume Calculator
Calculate the volume of various 3D shapes.
Understanding Volume Calculator
The Volume Calculator calculates the amount of three-dimensional space occupied by a geometric shape. It supports a range of common solids, from simple cubes and rectangular prisms to cylinders, spheres, cones, capsules, spherical caps, conical frustums, ellipsoids, square pyramids, and hollow tubes.
Select the shape you want to calculate, enter its required dimensions, and the calculator applies the appropriate mathematical formula. The result provides the volume together with the dimensions, formula, intermediate calculation, and additional geometric information when applicable.
Before you read the final number
Volume Calculator is designed to make unit changes easier to verify without doing the conversion by hand. Start with the quantity and source unit, then select the destination unit when the calculator provides that choice. The available units or options include Edge Length (a).
Reading the number correctly
A conversion changes the way a quantity is expressed; it does not change the underlying quantity. Pay attention to squared or cubed units, prefixes such as kilo- or milli-, and regional measurement conventions. Keeping the original value visible while checking the converted value is a simple way to catch a mistaken unit selection.
About the Volume Calculator
The Volume Calculator calculates the amount of three-dimensional space occupied by a geometric shape. It supports a range of common solids, from simple cubes and rectangular prisms to cylinders, spheres, cones, capsules, spherical caps, conical frustums, ellipsoids, square pyramids, and hollow tubes.
Select the shape you want to calculate, enter its required dimensions, and the calculator applies the appropriate mathematical formula. The result provides the volume together with the dimensions, formula, intermediate calculation, and additional geometric information when applicable.
Volume Formulas
V = a³
Rectangular Prism:
V = l × w × h
Cylinder:
V = πr²h
Sphere:
V = 4/3 × r³
Cone:
V = 1/3 × πr²h
Capsule:
V = πr²(L − 2r) + 4/3 × πr³
Spherical Cap:
V = πh²(3R − h) / 3
Conical Frustum:
V = πh(R² + Rr + r²) / 3
Ellipsoid:
V = 4/3 × πabc
Square Pyramid:
V = 1/3 × a²h
Tube:
V = π(R² − r²)h
How to Use the Volume Calculator
First, select the three-dimensional shape from the Shape menu. The calculator will automatically display the dimensions required for that particular shape. Enter each measurement using the same unit, such as centimeters, meters, inches, or feet.
After entering the dimensions, select Calculate. The calculator determines the volume using the standard geometric formula for the selected shape. Because volume measures three dimensions, the final result is expressed in cubic units.
Cube Volume
A cube has six equal square faces and all of its edges have the same length. Therefore, only one dimension is required to calculate its volume.
where a represents the length of one edge of the cube.
Rectangular Prism Volume
A rectangular prism has three independent dimensions: length, width, and height. Its volume is calculated by multiplying these three measurements together.
This formula is commonly used for rectangular boxes, rooms, containers, storage spaces, and other rectangular objects.
Cylinder Volume
A cylinder has a circular base and a perpendicular height. The area of the circular base is πr², and multiplying this area by the height gives the cylinder's volume.
The radius is measured from the center of the circular base to its edge.
Sphere Volume
A sphere is a perfectly round three-dimensional object. Its volume depends on the radius, with the radius raised to the third power.
The radius is the distance from the center of the sphere to any point on its surface.
Cone Volume
A cone has a circular base and a single vertex or apex. Its volume is one-third of the volume of a cylinder with the same base radius and perpendicular height.
Capsule Volume
A capsule consists of a cylindrical section with a hemispherical end on each side. The two hemispherical ends together form one complete sphere.
Here, L represents the total capsule length and r represents its radius. The cylindrical section must have a non-negative length, so the total length must be at least twice the radius.
Spherical Cap Volume
A spherical cap is the portion of a sphere cut off by a plane. Its volume depends on the radius of the original sphere and the height of the cap.
In this formula, R is the radius of the sphere and h is the height of the spherical cap.
Conical Frustum Volume
A conical frustum is the portion of a cone remaining after its top has been removed. It has two circular bases with different radii.
The larger radius is represented by R, the smaller radius by r, and h is the perpendicular height between the two circular bases.
Ellipsoid Volume
An ellipsoid is a three-dimensional shape that can be viewed as a stretched or compressed sphere. It has three principal semi-axis lengths, which may all be different.
The variables a, b, and c represent the three semi-axis lengths.
Square Pyramid Volume
A square pyramid has a square base and an apex above the base. Its volume is one-third of the product of the base area and perpendicular height.
Here, a is the side length of the square base and h is the perpendicular height from the apex to the base.
Tube Volume
A tube is modeled as a hollow cylinder. Its volume represents the material contained between the outer cylindrical surface and the inner cylindrical opening.
The outer radius is represented by R, the inner radius by r, and h is the tube length.
Using Consistent Units
All dimensions used in a single calculation should be expressed in the same unit. If the dimensions are entered in centimeters, the resulting volume will be in cubic centimeters. If they are entered in meters, the result will be in cubic meters.
This is important because volume involves three dimensions. Converting between length units must therefore account for the cubic relationship. For example, one meter equals 100 centimeters, but one cubic meter equals 1,000,000 cubic centimeters.
Understanding Cubic Units
A cubic unit represents a three-dimensional space formed by multiplying the same unit of length three times. For example, one cubic meter is the volume of a cube measuring one meter on each side.
The same principle applies to cubic centimeters, cubic feet, cubic inches, and other units of volume.
Why Volume Calculations Are Useful
Volume calculations are used in geometry, construction, engineering, architecture, manufacturing, packaging, storage, science, and many everyday situations. They can help determine the space occupied by an object or estimate the capacity of a container.
Frequently Asked Questions
What is volume?
Volume is the amount of three-dimensional space occupied by an object or enclosed within a solid. It is expressed using cubic units.
What is the volume formula for a cube?
The volume of a cube is calculated by multiplying its side length three times: V = a³.
What is the volume formula for a cylinder?
The volume of a cylinder is V = πr²h, where r is the radius of the circular base and h is the perpendicular height.
What units are used for volume?
Volume can be expressed in cubic units such as cubic meters, cubic centimeters, cubic feet, and cubic inches. Liquid capacity may also be expressed using units such as liters or gallons.
Can I use decimals?
Yes. The calculator accepts decimal measurements, allowing dimensions such as 2.5, 7.25, or 10.75 to be used in the calculation.
Disclaimer
This calculator is intended for informational purposes only. While we strive for accuracy, we cannot guarantee that every result is correct for every situation.