Finding Volumes

By Roger Marshall

Figure 1

Suppose you have a rectangular water tank onboard and you need to determine its volume (capacity)? You probably practiced solving this problem using a formula you learned in elementary school math class. That formula is length times width times height (L x W x H). The catch for using that formula on boat tanks is that the tank shapes are often dictated by the irregular shaped interior spaces into which the tanks must fit. Here you’ll find some useful equations for calculating the volume of cylindrical and other odd-shaped tanks.

Let’s say you have a water tank shaped as shown in Figure 1. It’s 3' (91cm) long and one end measures 2' (61cm) across the top, with an inside depth of 1' (30cm), while the outside depth is only 6" (15cm). At the front end, where the boat gets narrower, the tank tapers. Here it’s only 1' (30cm) across at the top, 3" (7.6cm) deep on the outside and 9" (23cm) deep on the inside. How do you figure the volume?

Figure 2

It’s easier than it looks. First, find the area of each end. In order to do that, average the height (shown in feet for clarity). This equates to 1' + 0.5' = 1.5' ÷ 2 = 0.75'. Now the end area becomes 2' x 0.75' = 1.5 sq. ft. Now do the same for the other end: 0.75' + 0.25' = 1.0' ÷ 2 = 0.5'. The end area measures 1' x .5' = 0.5 sq. ft.

The two ends of the tank are sized at 1.5 sq. ft and 0.5 sq. ft. If we add them together and divide by two, we get an average end area equal to 1' (1.5 + 0.5 ÷ 2 = 1). If the average end area is 1 sq. ft. and the tank is 3' long, the volume must be 3 x 1 = 3 cu. ft.

You want to know how much water a 3 cu. ft. tank will hold? Since freshwater weighs 62.2 pounds per cubic foot, the tank holds 186.6lb (84.6kg) of water (3 cu. ft. x 62.2lb) and since a gallon (3.78L) of water weighs 8lb (3.6kg), the total amount of water the tank holds is 23.3. gallons (88L), which is what you get when you do the arithmetic (186.6 ÷ 8 = 23.3 gal/88L).

Figure 3

The trick is to average the areas of the tank ends and then multiply by the length to find the volume. If the tank is oddly shaped, break it down into smaller tanks. For example, to find the area of a tank shaped like a big “U” as in Figure 2, the first step is to break off the end marked A. This measures 6" x 3" x 4". Multiplying all dimensions, converted to feet, results in a volume of .5 x .25 x .334 = 0.04 cu. ft. Now you find the volume of the other end (B) by multiplying 8" x 9" x 6" or .667' x .75' x .5' = 0.25 cu. ft. The last step is to find the volume of the third part (C). This measures 12" x 28" x 6" or 1' x 2.334' x 0.5' = 1.167 cubic feet. Add all three volumes known to find the total volume and then multiply the tank volume by 62.2 pounds of freshwater per cubic foot and divide by 8 gallons per pound to get a total capacity of 9.1gal (34.4L).

How does this work if you have a round tank such as a water heater? As in the first example, find the area of each end. In the case of Figure 3, the diameter is 18" and the tank is 30" long. The calculation for the area of the ends is π r2 or π x 0.752 = 3.142 x .752 = 1.767 sq. ft. All we need to do is multiply that by the length to get the volume 2.5’ x 1.77 sq.ft. = 4.42 cu. ft. Finally, multiply by 62.2 to get the poundage the tank can hold and divide that by 8 to get the number of gallons. In this case we get 4.425 x 62.2 ÷ 8 = 34.4 gallons (130L).

That’s it. Use these formulas to determine the volume of existing tanks or when you plan to add a tank and need to find a place for it and calculate the volume of the space available.

About the author: Roger Marshall is a boat designer and author of 12 books on sailing and yacht design. He has a boat design company in Rhode Island and is the president of Boating Writers International.