A 55-gallon aquarium — the classic American fish tank at 48 × 13 × 21 inches — holds 48 × 13 × 21 = 13,104 cubic inches of water, which is 56.7 gallons of theoretical space before gravel and glass thickness take their cut. The cuboid's volume is length times width times height (V = lwh): three edges, one product. Refrigerators, microwaves, and shipping cartons are all cuboids wearing different costumes, and their capacity is always the same three-number multiply.

Type the Length, Width, and Height into their boxes and read the Volume output — enter 48, 13, and 21 for the aquarium and get 13,104 cubic inches. Divide by 231 for gallons of liquid capacity, or by 1,728 for cubic feet of storage. A renter checking whether a 36 × 24 × 72-inch wardrobe fits a 60-cubic-foot moving allowance enters the three numbers, reads 62,208 cubic inches (36 cubic feet), and breathes easy.

The formula, and why order never matters

Volume measures how much three-dimensional space a box encloses, and for a rectangular box that space is exactly the product of its three edges. Length times width gives the area of the base, and multiplying by height stacks that base area upward through the full height. Because multiplication commutes, swapping the labels changes nothing: 48 × 13 × 21, 21 × 48 × 13, and 13 × 21 × 48 all equal 13,104. The practical rule is to assign the three edges consistently and measure each one in the same unit; the calculator does not care which edge you call length, but it absolutely cares whether one edge was measured in inches and the others in feet.

Worked example: a refrigerator

A refrigerator measures 30 inches wide, 28 inches deep, and 66 inches tall. Its volume is 30 × 28 × 66 = 55,440 cubic inches. Dividing by 1,728 cubic inches per cubic foot gives 55,440 / 1,728 = 32.08 cubic feet, which lands in the standard large-family range and matches the capacity class printed on the spec sheet. Two cautions travel with this example. First, the outside dimensions include the walls and insulation, so the usable food space inside is smaller, typically by 15 to 25 percent. Second, a refrigerator's advertised cubic feet are measured by the manufacturer's own internal method, so a computed 32.08 from outside dimensions and an advertised 30 are not a contradiction, just different measurements.

Worked example: moving boxes and the truck

A standard medium moving box measures 18 × 18 × 24 inches. Its volume is 18 × 18 × 24 = 7,776 cubic inches, and 7,776 / 1,728 = 4.5 cubic feet exactly. Forty such boxes need 40 × 4.5 = 180 cubic feet of truck space before furniture is counted, which is why a 10-foot rental truck rated around 380 cubic feet holds the boxes plus a modest apartment's furniture, while a cargo van rated near 200 cubic feet is already nearly full on boxes alone. Counting boxes this way, rather than guessing, is the difference between one trip and two, and the second trip is the expensive one.

Worked example: dimensional weight shipping

Carriers bill light, bulky boxes by dimensional weight, not by the scale weight, and the cuboid volume is the starting number. A box measuring 20 × 16 × 12 inches has a volume of 20 × 16 × 12 = 3,840 cubic inches. Domestic air dimensional weight divides by 139, so 3,840 / 139 ≈ 27.63 pounds, billed as 28 pounds. If the contents weigh only 9 pounds, the shipment still bills at 28 pounds, because the box's volume, not its contents, fills the plane. Shrinking the box is the only cure: a 16 × 12 × 10-inch box holds 1,920 cubic inches, bills at about 13.81 pounds, and roughly halves the shipping cost for the same contents when they fit.

Worked example: a room's air volume

A bedroom measuring 14 feet long, 11 feet wide, and 9 feet tall encloses 14 × 11 × 9 = 1,386 cubic feet of air. In liters that is 1,386 × 28.3168 ≈ 39,247 liters, and in cubic yards it is 1,386 / 27 ≈ 51.33 cubic yards. Room volume drives real decisions: air purifiers are rated by the room size they can cycle, dehumidifiers by pints per day against a volume, and paint coverage by wall area rather than volume, a distinction worth keeping straight. Volume answers how much air, water, or material the space holds; surface area answers how much wall, paint, or glass covers it. The same room volume also sizes a portable air conditioner: a unit rated for 1,386 cubic feet cools this bedroom comfortably, while a unit rated for half that volume would run constantly and still fall behind on a hot afternoon.

The cube as a special cuboid

When all three edges are equal, the cuboid is a cube, and the formula collapses to side cubed. A 5-foot cube has a volume of 5 × 5 × 5 = 125 cubic feet. A 2 × 3 × 4-foot box holds 24 cubic feet, a 10 × 8 × 6-foot storage area holds 480 cubic feet, and a 14 × 10 × 8-foot container holds 1,120 cubic feet. The ladder shows the scaling law plainly: doubling one edge doubles the volume, but doubling all three edges multiplies the volume by eight, because 2 × 2 × 2 = 8. The aquarium doubled in every dimension, 96 × 26 × 42 inches, would hold 104,832 cubic inches, exactly eight times its 13,104, before the glass thickness is considered.

Surface area, the companion number

Volume's constant companion is surface area, the amount of material covering the box: SA = 2 × (lw + lh + wh). For the aquarium, that is 2 × (48 × 13 + 48 × 21 + 13 × 21) = 2 × (624 + 1,008 + 273) = 2 × 1,905 = 3,810 square inches, or 3,810 / 144 ≈ 26.46 square feet of glass for a fully closed box. An open-top aquarium skips the top face, 48 × 13 = 624 square inches, leaving 3,810 − 624 = 3,186 square inches, about 22.13 square feet of glass. Volume decides how much water the tank holds; surface area decides how much glass it takes to build, and confusing the two is how material orders go wrong.

Weight of what fills the box

A box's volume becomes a weight the moment it is filled, through the density of the contents. Water weighs 8.34 pounds per gallon, so the aquarium's theoretical 56.73 gallons of water weigh 56.73 × 8.34 ≈ 473.1 pounds, before gravel, glass, and stand, which is why aquarium stands are built like furniture for half a ton rather than like tables. A cubic foot of water weighs about 62.4 pounds, so the 36-cubic-foot wardrobe full of water, hypothetically, would weigh about 2,246 pounds, a number that makes the point: volume tells you the space, density tells you the load, and both are needed before anything heavy is lifted or shipped.

Units, conversions, and inside versus outside

Three conversion constants cover nearly every cuboid job. Divide cubic inches by 1,728 for cubic feet, by 231 for US gallons, and multiply cubic feet by 28.3168 for liters or divide by 27 for cubic yards. Measure inside dimensions when capacity is the question and outside dimensions when shipping or fitting through a door is the question: a refrigerator that measures 32 cubic feet outside may offer only 25 inside, and a shipping carton measured inside understates the dimensional weight the carrier will charge. The single most expensive unit error is mixing inches and feet in one product, a 12-inch edge entered as 12 beside 3-foot edges inflates the volume twelvefold before any conversion is applied.

Five mistakes that cost real money

The first mistake is mixing units inside the product, inches with feet. The second is measuring outside dimensions for a capacity question, or inside dimensions for a shipping question. The third is forgetting the unit conversion after the product, reporting 13,104 as gallons instead of cubic inches. The fourth is treating the theoretical aquarium volume as usable volume, ignoring glass, gravel, and the unfilled inches at the top. The fifth is scaling by the wrong power: doubling one edge doubles the volume, but doubling all three multiplies it by eight, and ordering eight times the concrete for a doubled planter surprises everyone exactly once.

Related calculators on this site

If the cuboid is part of a bigger job, companion tools carry the next step. The volume of a cube calculator handles the equal-edge special case with surface area alongside. The volume of a cylinder calculator covers tanks, barrels, and pipes, where the base is a circle instead of a rectangle. The surface area of a cube calculator isolates the wrapping and painting number when a box becomes a gift or a planter. The volume of a pyramid calculator shows the one-third rule when a box tapers to a point. Each one uses the same discipline: measure three edges, keep one unit, and convert only at the end.

With the pre-filled defaults — Length 5, Width 4, Height 3 — the Volume Of Cuboid Calculator returns Volume 60.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.