How Do I Calculate Capacity?

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The capacity of a container is another word for the volume of material it will hold. It's usually measured in liters or gallons. It isn't the same as the volume the container would displace it you immersed it in water. The difference between these two quantities is the thickness of the container walls. This difference is negligible if the container is made from a thin material, but for wooden or concrete containers with walls that can be several inches thick, it isn't. When measuring capacity, it's always best to measure the inside dimensions. If you don't have access to the inside, you need to know the thickness of the container walls to get an accurate result.

TL;DR (Too Long; Didn't Read)

Calculate the capacity of a container by measuring its dimensions and using the volume formula appropriate for the shape of the container. If you measure from the outside, you have to take the thickness of the walls into account.

Rectangular Containers

You find the volume of a rectangular container by measuring its length (l), width (w) and height (h) and multiplying these quantities. Volume = l • w • h. You express the result in cubic units. For example, if you measure in feet, the result is in cubic feet, and if you measure in centimeters, the result is in cubic centimeters (or milliliters). Because capacity is usually expressed in liters or gallons, you'll probably have to convert your result using an appropriate conversion factor.

If you have access to the inside of the container, you can measure the inside dimensions and calculate capacity directly, using the formula for volume. If you can only measure the outside dimensions, but you know that the walls, base and top are of uniform thicknesses, you must subtract twice the wall thickness and twice the base thickness from each of these measurements first. If the wall and base thickness is t, the capacity is given by:

Capacity of rectangular container with wall thickness t = (l - 2t) • (w - 2t) • (h - 2t).

If you know that the container's walls, base and top have different thicknesses, use those instead of 2t. For example, if you know that a container has a base that's 1 inch thick and a lid that's 2 inches thick, the height would be h - 3.

Cubic Container: A cube is a special type of rectangular container that has three sides of equal length l. The volume of a cube is thus l3. If you measure from the outside, and the thickness of the walls is t, the capacity is given by:

Capacity of cube = (l-2t)3.

Cylindrical Containers

To calculate the volume of a cylinder of length or height h and circular cross-section of radius r, use this formula: Volume of cylinder = π • r2 • h. When measuring a closed container from the outside, you need to subtract the wall thickness (t) from the radius and the lid/base thickness from the height. The capacity formula then becomes (using a uniform thickness for the base and lid):

Capacity of cylinder of radius r and wall thickness t = π • (r - t)2 • (h - 2t).

Note that you don't double the wall thickness before subtracting it from the radius because the radius is a single line from the center to the outside of the circular cross-section.

In practice, it can be easier to measure diameter (d) than radius, since diameter is just the farthest distance between the edges of the cylinder. Diameter is equal to twice the radius (d = 2r, so r = [1/2]d), and the volume formula becomes V = (π • d2 • h) ÷ 4. The capacity is then (again using a uniform thickness):

Capacity of cylinder of diameter d and wall thickness t = [π • (d - 2t)2 • (h - 2t)] ÷ 4.

You double the wall thickness because the diameter line crosses over the walls twice.

Spherical Containers

The volume of a sphere of radius r is (4/3) • π • r3. If you manage to measure the radius from the outside (this might be difficult), and the sphere has walls of thickness t, its capacity is:

Capacity of sphere of radius r and wall thickness t = [π • (r - t)3] 4/3

If you can only measure the sphere's diameter, you can find its volume by using this formula: V = (4/3) • π • (d/2)3 = (π • d3) ÷ 6. If you measure diameter from the outside, and the thickness of the walls is t, the capacity of the sphere is:

Capacity of sphere of diameter d and wall thickness t = [π • (d - 2t)3] ÷ 6.

Pyramids and Cones

The volume of a pyramid with base dimensions l and w and height h is (A • h) ÷ 3 = [(l • w) • h] ÷ 3. If the pyramid has walls of thickness t, and you measure from the outside, its capacity is approximately given by:

Capacity of pyramid with wall thickness t = [(l - 2t) • (w - 2t) • (h - 2t)] ÷ 3.

This is approximate because the walls are angled, and you must consider the angle when calculating t. In most cases, the difference is small enough to ignore.

The volume of a cone of base radius r and height h is (π • r2 • h) ÷ 3. If you measure from the outside, and its walls have a thickness t, the capacity is:

Capacity of cone of radius r and wall thickness t = [π • (r-t)2 • (h - t)] ÷ 3.

If you can only measure the diameter d, the capacity is:

Capacity of cone of diameter d and wall thickness t = [π • (d/2 - 2t)2 • (h - t)] ÷ 3.

References

About the Author

Chris Deziel holds a Bachelor's degree in physics and a Master's degree in Humanities, He has taught science, math and English at the university level, both in his native Canada and in Japan. He began writing online in 2010, offering information in scientific, cultural and practical topics. His writing covers science, math and home improvement and design, as well as religion and the oriental healing arts.

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