Rectangular Prism Volume Calculator

Volume is V = L × W × H — the simplest of the three. The unit (in, cm, ft, m) determines whether you read the result as in³, cm³, ft³, or m³. As long as all three measurements share the same unit, the math is foolproof.

Total surface area sums all six faces: SA = 2(LW + LH + WH). A 10 × 5 × 3 box has SA = 2 × (50 + 30 + 15) = 190 square units. Knowing surface area matters for paint, wrapping, insulation, and packaging cost — corrugated cardboard, for example, is priced per square foot of sheet, not per cubic foot of finished box.

Space diagonal is d = √(L² + W² + H²), the longest straight line that fits inside the box. This is the dimension airlines and shipping carriers check when you ask whether a long pole fits inside a cube-shaped case.

A retail box for a 50-inch class TV is roughly 48 × 30 × 6 inches. Volume = 48 × 30 × 6 = 8,640 in³, or exactly 5 ft³. Total surface area = 2 × (48 × 30 + 48 × 6 + 30 × 6) = 2 × (1,440 + 288 + 180) = 3,816 in² of cardboard. Space diagonal = √(48² + 30² + 6²) = √(2,304 + 900 + 36) = √3,240 ≈ 56.9 inches.

If your car's trunk has interior dimensions of 42 × 36 × 18 inches, the trunk's space diagonal is √(42² + 36² + 18²) ≈ 57.4 inches — barely longer than the box. The box will technically fit corner-to-corner but only if you fold down a seat to give the long dimension room to clear the bulkhead. This kind of pre-purchase sanity check saves a lot of return trips to the parking lot.

Volume to gallons. 1 US gallon = 231 in³. A 10 × 5 × 3 box holds 150 in³ ≈ 0.65 gallons. For metric, 1 liter = 1,000 cm³ = 61.024 in³.

Volume to weight depends on what fills the box. Water is the easy case: 1 in³ ≈ 0.578 fl oz ≈ 16.4 grams. A 100-gallon aquarium of pure water weighs about 833 lb plus tank, substrate, and stand.

DIM weight. UPS, FedEx, and USPS all charge by the greater of actual weight or dimensional weight, which is L × W × H ÷ 139 for domestic US. A 10 × 5 × 3 = 150 cu in box has DIM weight of about 1.1 lb — meaningless for a heavy shipment but the binding rate for anything light and bulky like pillows or foam.

Volume scaling: doubling every side multiplies volume by 8 (2³). This is why moving from a 'half-size' to a 'full-size' storage tote costs more than double in shipping.