Volume Calculator

Volume is the measure of space occupied by a three-dimensional object or how much it can hold. This calculator allows you to calculate volume for twelve common geometric shapes. Select a shape and enter dimensions to see its volume instantly. The total surface area of the object will also be shown at the same time.

Since volume is a three-dimensional measurement, it will always be expressed in cubic units, such as cubic centimeters or cubic feet. For liquids, liters and gallons are commonly used. By changing the unit of measure in either field, the tool will convert so that you can measure a storage tank in feet and read the volume in gallons or liters, for example.

Here's how to use this calculator:

First select the desired geometric shape in the Shape menu. The input fields will change accordingly and only show the dimensions actually required for that shape.

Enter each dimension and set the unit of measure. The volume will update instantly as you type in anything, and it will show up both in a large easy to see main display and also in a field that can be copied. The surface area is shown next to it. To try out another shape just select a new shape from the menu.

Formulas for calculating volume for each geometric shape.

Each geometric shape has its own formula. This calculator uses the following formulas. Pi is approximately 3.14159. The total surface area is also shown, which is the sum of all surfaces, both flat and curved. If a base exists, it is also taken into account.

The volume increases cubically depending on the dimensions.

If all sides of a geometric shape are doubled, the volume is multiplied by eight instead of just doubling. This is because volume is the product of three sides. If you multiply two by two and then again by two, it becomes eight. The surface area however only changes by a factor of four since it depends on two sides.

For this reason, a small change in dimensions can lead to a large change in volume. Also, it is apparent that cubic units cannot be converted directly into linear units. One meter is approximately 3.28 feet, while one cubic meter is more than 35 cubic feet. This is because the ratio must be raised to the third power.

The one-third rule for cones and pyramids

The volume of a cone is one-third the volume of a cylinder that exactly encloses it, i.e., a cylinder with the same base and height. Similarly, the volume of a pyramid is one-third the volume of an enclosing prism with the same base and height.

So the volume of a cone with radius 3 and height 4 is one-third the product of π and the product of 9 and 4, which is about 37.7 units cubed. The volume of a full cylinder surrounding the cone would be three times that number. To calculate surface area, you also need the slant height, which is measured along the inclined face. You can find the slant height using the Pythagorean theorem with the vertical height and the radius of the base.

Spheres and related bodies

A sphere has the largest volume of any shape with the same surface area, which is why bubbles and water droplets naturally form into a spherical shape. The volume of a sphere is determined by its radius alone.

A hemisphere has half the volume of a full sphere. A capsule is a cylinder with hemispheres at either end. Since the two hemispheres together make one sphere, the volume of the capsule is equal to the sum of the volumes of the cylinder and the sphere. A spherical cap is a portion of a sphere that is cut off by a plane. If the plane cuts the sphere such that the height of the cap is exactly half the diameter of the sphere, then it is called a hemisphere.

Volume of tubes and pipes

A pipe (also called a tube) is a hollow cylinder. To calculate the volume of the pipe wall, first find the volume of the outer complete cylinder and then subtract the volume of the inner hollow cylinder that goes through it.

Where R is the outer radius, r is the inner radius and h is the length. If you know the diameter, divide it by two to get the radius. When a value for the inner radius (0) is entered, this equates to a solid bar, or normal cylinder, so both values are identical.

Examples of calculations:

Since these examples use predefined dimensions, all of the examples can be reproduced. The method for calculating volume varies depending on the shape.

Volume, capacity, liters, gallons:

Volume and capacity are nearly the same thing. Volume is the space occupied by an object while capacity is how much a container can hold. For thin-walled containers, both values will be almost equal.

It is useful to remember the relationship between cubic units and everyday liquid measures. One litre is exactly one thousand cubic centimetres, so a cube with sides of ten centimetres will hold exactly one litre. A cubic metre is one thousand litres, and a US gallon is about 3.785 litres. If you select litres or gallons in the Volume field, the tool will automatically convert.

Areas of application for volume calculation:

Volume is used to determine how much a container can hold or the amount of material that will be required to fill a space. It is used to determine the amount of water in aquariums and swimming pools, the amount of soil needed for flower beds, the amount of concrete for foundations, and the amount of fuel or liquid in storage tanks.

In shipping and storage, costs are often calculated by volume rather than weight. So knowing the volume of boxes and their contents is important for efficient packing. In cooking and medicine, quantities and dosages are often given in terms of volume. And in science, determining an object's volume is the first step to calculating its density, which is mass divided by volume.

Determination of volume for irregular objects:

If the object does not fit into one of these regular geometric shapes, there are two options. You can break up the object into several regular parts and then calculate and add the volume of each part. For example, a grain silo is a cylinder with a cone or dome on top.

Alternatively, the volume can be measured directly by the displacement method. The object is placed in a container of water and it is measured how much the water level rises or how much water overflows. The volume of displaced water equals the volume of the object. This method was developed more than two thousand years ago by Archimedes.

Tips for accurate results:

Before reading the results, make sure all dimensions of the same body are in the same unit. When measuring the height of a cone or pyramid, measure along the centerline and not along the slanted surface. This is because vertical height is used for volume.

Since volume changes in proportion to the third power of length, small errors in measurement lead to much larger errors in the result. If accuracy is required, measure twice.

This tool is for general educational purposes and everyday planning. For technical applications, construction or other high risk work these values should be checked against the standards and tolerances required by your project.