Rectangular Prism Volume Calculator (Box)

V = l × w × h

Length times width times height. The standard rectangular box (also called a cuboid or rectangular prism). Three perpendicular edges; six rectangular faces; eight corners.

Worked example — aquarium volume: A standard 20-gallon “long” tank is 30" × 12" × 12" outside dimensions. V = 30 × 12 × 12 = 4,320 cubic inches. Convert to gallons: 4,320 / 231 ≈ 18.7 gal. The advertised 20 gallons accounts for the outer wall thickness — the actual swimming volume is closer to 18.

Where rectangular volumes matter in real life:

• Shipping boxes. Carriers (UPS, FedEx, USPS) charge by either weight or dimensional weight — whichever is greater. Dimensional weight uses l × w × h divided by a divisor (e.g. 139 in³/lb for domestic). So a big light box can cost as much to ship as a small heavy one.
• Aquariums. Each US gallon is 231 in³, each UK gallon is 277 in³, each liter is 1,000 cm³. Don’t trust the advertised size — measure.
• Bedrooms and HVAC sizing. Rooms are billed by air volume for ventilation. A 12 × 14 × 9 ft room is 1,512 ft³ = 42.8 m³. HVAC professionals size systems around this.
• Cabinet capacity. A kitchen pantry 18" × 24" × 72" tall is 7.5 ft³ — about right for two weeks of family pantry storage.
• Truck and van cargo bays. A standard 20-foot intermodal container is 1,165 ft³ usable.
• Refrigerator and freezer specs. Most full-size fridges advertise 18-25 ft³ total capacity.

Conversion shortcuts:

Rectangle vs. cuboid — the dimension count:

A 2D rectangle has 2 dimensions (length × width). A 3D rectangular prism has 3 (length × width × height). If your input data only has two numbers, you have a rectangle — not a box. The most common confusion is mixing up “square feet” (floor area) with “cubic feet” (room volume) when sizing rooms.

Sanity check: if l = w = h, the rectangular prism collapses to a cube and V = s³. ✓