Quick answer: the volume of a rectangular prism (a box, or cuboid) is V = length × width × height. Any face can be the base — the product is the same. Measured in feet the answer is cubic feet; divide in³ by 231 for US gallons.
The box formula, step by step
Worked example — a storage tote 2 ft long, 3 ft wide, 4 ft tall (an odd tote, but easy numbers):
- Base area: 2 × 3 = 6 ft²
- Stack it up: 6 × 4 = 24 ft³
- In other units: 24 × 7.4805 ≈ 180 US gal ≈ 680 liters
This is the formula everything else builds on. Every prism is "base area × height" — the rectangular prism just happens to have the easiest base. It's also the formula hiding inside concrete slabs, aquariums, freight CBM and cubic-yard calculations — each of those tools is this math plus trade-specific units and margins.
Common real-world boxes — quick reference
| Container | Dimensions | Volume |
|---|---|---|
| Small moving box | 16 × 12 × 12 in | 1.33 ft³ |
| Medium moving box | 18 × 18 × 16 in | 3.0 ft³ |
| Large moving box | 18 × 18 × 24 in | 4.5 ft³ |
| Standard pallet load (48×40, 60 in tall) | 48 × 40 × 60 in | 66.7 ft³ |
| 20-ft shipping container (interior) | 19.3 × 7.7 × 7.8 ft | ≈ 1,170 ft³ (33.2 m³) |
| Pickup bed (full-size, 6.5 ft) | 78 × 65 × 21 in | ≈ 61.6 ft³ |
| "20-gallon long" aquarium | 30 × 12 × 12 in | 18.7 US gal |
Where box volume shows up in real life
Room air volume
A 12 × 14 ft bedroom with 8-ft ceilings holds 1,344 ft³ of air. An air purifier rated at 200 CFM turns that room over every 6.7 minutes — the "air changes per hour" spec on the box is computed from exactly this number.
Raised garden beds
A 4 × 8 ft bed filled 10 inches deep needs 4 × 8 × 0.833 = 26.7 ft³ ≈ 1 cubic yard of soil. The soil volume calculator converts that to bags and adds compaction allowance.
Freight and dimensional weight
Carriers charge by whichever is greater: actual weight or volume-based "dim weight" (in³ ÷ 139 for most US carriers). A light but bulky 24 × 24 × 24 in box: 13,824 ÷ 139 ≈ 99 lb billable, even if it weighs 20. The volumetric weight calculator covers each carrier's divisor.
Common mistakes & pro tips
- Outside vs. inside dimensions. A container's capacity comes from inside measurements. Corrugated boxes lose ~¼ in per wall; coolers and safes lose far more.
- Mixed units multiplied raw. 48 in × 40 in × 1.5 m is not 2,880 of anything. Convert first, or let the per-field selectors here do it.
- Area vs. volume confusion. Two dimensions give floor area (ft²); volume needs the third. Flooring is bought by area, soil by volume.
- Pro tip — irregular rooms. L-shaped room? Split the floor plan into two rectangles, compute each times the ceiling height, add. Works for any right-angled floor plan.
- Pro tip — usable vs. total volume. Real packing never reaches 100%. Movers plan on 80–85% fill for boxed goods; bulk materials settle 5–10%.
How to use this calculator
- Measure the three dimensions. Length, width and height — inside dimensions if you care about what fits inside a container.
- Multiply them together. V = l × w × h. Order doesn't matter; any face can be the "base".
- Convert the result. Switch the output between in³, ft³, m³, liters and gallons as your task requires.
Frequently asked questions
What is the formula for the volume of a rectangular prism?
V = length × width × height. A box measuring 2 × 3 × 4 ft holds 24 ft³. The three labels are interchangeable — the volume is the same whichever face sits on the ground.
Is a rectangular prism the same as a box or cuboid?
Yes — rectangular prism (US textbooks), cuboid (UK textbooks) and box (everyone else) all name the same solid: six rectangular faces meeting at right angles. A cube is the special case where all three dimensions are equal.
How do I calculate the volume of a room?
Multiply floor length × floor width × ceiling height. A 12 × 14 ft room with an 8-ft ceiling contains 1,344 ft³ — the figure HVAC sizing, air purifiers and paint-fume ventilation calculations start from. For rooms with alcoves, split the floor plan into rectangles and add.
How many gallons does a rectangular tank hold?
Compute the volume in cubic inches and divide by 231. A 30 × 12 × 12 in tank: 4,320 ÷ 231 ≈ 18.7 US gallons — which is why it's sold as a '20-gallon long' aquarium.
What if the dimensions are in different units?
Convert to one unit before multiplying — or use this calculator's per-field unit selectors, which do it automatically. A pallet 48 in × 40 in stacked 1.5 m high is a perfectly normal mixed-unit case.