Volume Calculator
Visually calculate the volume of common 3D geometric shapes. Enter the dimensions to get the volume instantly.
Volume = Side³ (s³)
How to Calculate Cube Volume
The volume of a cube represents the total three-dimensional space it occupies. Since all sides (or edges) of a cube are equal, you can find its volume by multiplying the side length by itself three times. This is also known as "cubing" the side length.
For example, if you have a box where the length, width, and height are all 5 cm, you are calculating the total space inside that box in cubic centimeters.
Formula: Volume = Side³ or s × s × s
Volume = Length × Width × Height
How to Calculate Cuboid Volume
A cuboid, also known as a rectangular prism or a box, has six rectangular faces. To find its volume, you simply multiply its three primary dimensions: length, width, and height. This calculation gives you the total amount of space contained within the cuboid.
Think of calculating the volume of a shoebox or a room—you measure its length, width, and height and then multiply them together.
Formula: Volume = Length × Width × Height
Volume = (4/3) × π × Radius³
How to Calculate Sphere Volume
A sphere is a perfectly symmetrical, ball-shaped object. Its volume is determined by its radius (r)—the distance from the center to any point on its surface. The formula involves cubing the radius and multiplying it by Pi (π ≈ 3.14159) and the fraction 4/3.
This formula is fundamental in physics and engineering for calculating the volume of spherical objects like planets or ball bearings.
Formula: Volume = (4/3) × π × Radius³
Volume = π × Radius² × Height
How to Calculate Cylinder Volume
To find the volume of a cylinder, you first calculate the area of its circular base (which is πr²) and then multiply that area by the cylinder's height (h). You can think of it as "stacking" the circular base on top of itself until it reaches the total height.
This is useful for finding the capacity of objects like a can of soup, a water pipe, or a storage tank.
Formula: Volume = (Area of Base) × Height or πr²h
Volume = (1/3) × π × Radius² × Height
How to Calculate Cone Volume
A cone has a circular base and tapers to a single point called the apex. Interestingly, its volume is exactly one-third of the volume of a cylinder that has the same base radius and height. This 1/3 relationship is a key principle in geometry.
The formula involves finding the area of the circular base (πr²), multiplying by the height, and then dividing by three.
Formula: Volume = (1/3) × π × Radius² × Height
Volume = (1/3) × Base Area × Height
How to Calculate Pyramid Volume
Similar to a cone, the volume of a pyramid is one-third of the volume of the prism it would fit inside (in this case, a cuboid). This calculator is for a pyramid with a rectangular base.
First, find the area of the rectangular base (length × width). Then, multiply that base area by the pyramid's perpendicular height (h) and divide the result by three.
Formula: Volume = (1/3) × (Base Area) × Height
Volume = (½ × b × h) × Length
How to Calculate Triangular Prism Volume
A triangular prism is a 3D shape with two identical triangular bases and three rectangular sides. To find its volume, you first calculate the area of one of the triangular bases (using the formula ½ × base × height).
Once you have the base area, you multiply it by the total length (L) of the prism. This is like "extending" the triangular face along its length.
Formula: Volume = (Area of Triangle) × Length
Volume = (4/3) × π × a × b × c
How to Calculate Ellipsoid Volume
An ellipsoid is the three-dimensional version of an ellipse, resembling a stretched or squashed sphere. Its volume is determined by its three semi-axes (a, b, and c), which are the radii along its three perpendicular axes.
If all three radii are equal (a=b=c), the ellipsoid becomes a sphere, and the formula simplifies to the volume of a sphere.
Formula: Volume = (4/3) × π × a × b × c
Frequently Asked Questions
What is volume?
Volume is the measure of the three-dimensional space occupied by a substance or enclosed by a surface. It's usually measured in cubic units, like cubic meters (m³) or cubic feet (ft³).
How do you calculate the volume of a box?
To find the volume of a box (a cuboid), you multiply its three dimensions: Volume = Length × Width × Height. Our calculator does this for you in the "Cuboid" tab.
What is the formula for the volume of a sphere?
The formula for the volume of a sphere is V = (4/3)πr³, where 'r' is the radius of the sphere and π (pi) is approximately 3.14159. You only need one measurement (the radius) to find its volume.
How do you find the volume of a cylinder?
The volume of a cylinder is found by multiplying the area of its circular base (πr²) by its height (h). The formula is V = πr²h. Select the "Cylinder" tab and enter the radius and height to solve it instantly.
Why is Pi (π) used in some formulas?
Pi (π ≈ 3.14159) is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is fundamental for calculating the area and volume of circular and spherical shapes.
Can I use this calculator for my homework?
Absolutely! This tool is designed to help you check your answers and understand the process. The step-by-step explanations show you exactly how the formulas are used, making it a great study aid.
What's the difference between a cube and a cuboid?
A cube is a special type of cuboid where all six faces are identical squares, meaning its length, width, and height are all equal. A cuboid has rectangular faces, and its dimensions can be different.