Volume Calculator

Volume of a box: length times width times height

A box, a tank, a shipping carton and a room all share one formula: length times width times height. Measure all three sides in the same unit and the result lands in that unit cubed. Twelve inches by eight inches by ten inches gives 12 x 8 x 10 = 960 cubic inches.

The measurement that matters is the inside one. A cooler listed as 24 inches long has walls, so the space inside is narrower. For a room, measure wall to wall and floor to ceiling; for a tank, measure to the water line rather than the rim. Guessing outside dimensions is the quickest way to buy too little soil, paint or water.

Worked example: a 12 by 8 by 10 inch box

Take the 12 by 8 by 10 inch box. Its volume is 960 cubic inches, and each unit converts from there. In gallons, 960 / 231 = 4.16 US gallons. In liters, 960 x 16.387064 / 1000 = 15.73 liters, since one cubic inch is 16.387064 cubic centimeters and a liter is 1,000 of those. In cubic feet, 960 / 1,728 = 0.556 cubic feet.

Which number you report depends on the job. Paint and aquarium treatments use gallons or liters. Shipping and storage use cubic feet. Concrete and mulch use cubic yards, which is why the calculator lists them all at once instead of asking which one you want.

Aquarium keepers want one extra step. The tank volume inside the glass is not the water you dose for, because substrate, rock and the gap under the rim all take up space. The aquarium volume calculator starts from the same 231 formula and then subtracts those displacements, which is the difference between the shape and the water.

Cylinders, cones and spheres

A cylinder swaps the three sides for a circle and a height: 3.14159 times the radius squared times the height. A 12 inch concrete form tube that stands 48 inches tall has a 6 inch radius, so 3.14159 x 6 x 6 x 48 = 5,428.67 cubic inches, which is 5,428.67 / 231 = 23.5 gallons. That lands within a rounding step of one cubic foot of concrete, and the tube label says as much.

A cone is one third of the cylinder that would wrap it: the same 3.14159 times radius squared times height, divided by 3. A tapered planter 16 inches across and 14 inches tall holds 3.14159 x 8 x 8 x 14 / 3 = 938.29 cubic inches, or 938.29 / 231 = 4.06 gallons of soil.

A sphere is 4 / 3 times 3.14159 times the radius cubed. A 26 inch exercise ball measures 13 inches to the center, so 4 / 3 x 3.14159 x 13 x 13 x 13 = 9,202.77 cubic inches. In gallons that is 9,202.77 / 231 = 39.84 gallons of air, which is a fair way to picture how much space the ball takes up in a room.

Every one of those formulas takes a radius, and every label, tape measure and product listing gives a diameter. Halve the diameter first. A 26 inch ball with a 26 inch radius would come out eight times too large, since 2 cubed is 8.

Cubic inches, gallons and liters: how the units connect

The gallon is not a floating number. NIST Handbook 44, Appendix C defines the US liquid gallon as exactly 231 cubic inches, and one inch as 2.54 centimeters, so 2.54 x 2.54 x 2.54 = 16.387064 cubic centimeters per cubic inch. Multiply 231 by that and the gallon is 3,785.411784 cubic centimeters, or 3.785411784 liters. The liter itself is one cubic decimeter, 1,000 cubic centimeters, per the BIPM SI brochure.

The imperial gallon used in the United Kingdom is a different animal: 4.54609 liters, about 20 percent larger than the US gallon. A recipe or a fuel figure quoted in imperial gallons will not match one quoted in US gallons, and the gap grows with the batch. This calculator always uses the US liquid gallon, the one on a milk jug in Ohio.

Filled volume versus shape volume

The geometric volume of a container is its full shape. The useful volume is smaller whenever something sits inside it or the fill line stops short of the top.

The 12 by 8 by 10 inch box filled one inch below the rim, for instance, holds 12 x 8 x 9 = 864 cubic inches, which is 864 / 231 = 3.74 gallons rather than 4.16. An aquarium with two inches of gravel loses the same kind of space, and a pool loses more to the taper of its walls, which is why pool volume is figured on an average depth rather than the deep end.

For a pool, the round pool volume calculator takes the diameter and the average depth, then runs the same cylinder formula. For a fish tank, the aquarium volume calculator subtracts the substrate and the air gap. This page gives the raw shape, which is the starting point for all of those.

One inch of rain over an acre

The largest volume most people ever compute is rainfall. One inch of rain falling on one acre of ground is about 27,154 gallons, according to the USGS Water Science School. The arithmetic explains the number: an acre is 43,560 square feet, one inch is a twelfth of a foot, and 43,560 / 12 = 3,630 cubic feet. At 7.480519 gallons per cubic foot, 3,630 x 7.480519 = 27,154 gallons.

The same page gives a roof example that is easier to picture: a 40 by 70 foot roof collects about 1,743 gallons from one inch of rain. That is the number behind rain barrel sizing, and it is why a 55 gallon barrel fills in a hurry during a real storm.

Measuring tips that keep the number honest

Volume errors are nearly always measurement errors rather than arithmetic errors. Five habits keep the number honest.

• Measure the inside, not the outside. Wall thickness of half an inch on every side quietly removes about 15 percent from a small box.
• Take the diameter at the widest point. Buckets and planters are rarely round, and the widest reading is the one the manufacturer means.
• Keep one unit for every side. A tank 30 centimeters wide and 2 feet long cannot be multiplied until both are converted.
• Use an average depth for anything tapered. A pool that runs from 3 feet to 8 feet has an average near 5.5 feet, not 8.
• Round once, at the end. Carry the decimals through the multiplication and round the gallons on the last step.

The check worth doing every time: cube a 12 inch box by hand. 12 x 12 x 12 = 1,728 cubic inches, and 1,728 / 231 = 7.48 gallons, which is exactly the gallons per cubic foot figure the calculator reports. If your inputs give a wildly different answer, one side is probably in the wrong unit.