Compute volume of a box or rectangular prism in m³, L, ft³, or gallons.
Dimensions
Presets
Other properties
Details
Formula derivation
A rectangular prism (also called a cuboid or box) has three perpendicular edges: length (L), width (W), and height (H). Its volume is the product of these three dimensions:
V = L × W × H
All three values must be in the same unit before multiplying. If L is in meters and W in centimeters, convert first. The result carries a cubic unit: meters × meters × meters = cubic meters (m³). 1 m³ = 1 000 liters = 1 000 000 cm³ = 35.3147 ft³ ≈ 264.172 US gallons.
Surface area counts six rectangular faces, paired: two of L×W, two of L×H, two of W×H. Total: A = 2(LW + LH + WH). Useful for paint, wrapping, cladding, or heat-loss estimates.
Space diagonal is the longest straight line that fits inside the box — corner to opposite corner — computed via a 3D Pythagoras: d = √(L² + W² + H²). Used to check whether an object fits through a doorway or inside a container.
Volume-to-mass conversion (water, concrete, sand)
Volume × density = mass. Typical densities:
| Material | Density (kg/m³) | Mass per 1 m³ |
|---|---|---|
| Water (4 °C) | 1 000 | 1 000 kg (1 t) |
| Concrete (reinforced) | 2 400 | 2 400 kg (2.4 t) |
| Dry sand | 1 600 | 1 600 kg (1.6 t) |
| Gravel | 1 680 | 1 680 kg (1.68 t) |
| Air (20 °C) | 1.20 | 1.20 kg |
Example: a pool 10 × 5 × 1.5 m holds 75 m³ of water = 75 000 kg = 75 metric tons. A concrete slab 4 × 3 × 0.2 m (2.4 m³) weighs roughly 5 760 kg.
FAQ
How do I convert between m³ and ft³?
One cubic meter equals 35.3147 cubic feet. To go the other way, 1 ft³ ≈ 0.0283168 m³. So a 60 m³ room is about 2 118.9 ft³, and a 100 ft³ shed is roughly 2.83 m³. The calculator does this automatically — enter dimensions in any unit and read all outputs in the result panel.
How do I calculate box volume for shipping?
Carriers price by whichever is larger: actual weight or dimensional (volumetric) weight. Measure the outer length, width, and height of the box in inches (or cm). Multiply them for cubic inches, then divide by the carrier's DIM factor (commonly 139 in³/lb for domestic US, 5 000 cm³/kg internationally). The calculator gives ft³ and in³ directly, so DIM weight is one division away.
How do I find room volume for HVAC sizing?
HVAC load calculations use the room's air volume in ft³ or m³. Multiply floor length × width × ceiling height. A 5 × 4 × 3 m bedroom = 60 m³ ≈ 2 119 ft³. For sloped ceilings, use the average height. Air-change rates (ACH) tell you how many times this volume must be replaced per hour — typical residential target is 0.35 ACH.
When do I need surface area instead of volume?
Use surface area when the material is applied to the outside: paint, wallpaper, insulation sheets, tile, cladding, sheet metal, thermal-loss estimates. Use volume when the material fills the inside: concrete, water, grain, gravel, air conditioning. For a 5 × 4 × 3 m room the volume is 60 m³ (airflow), and the surface area is 94 m² (painting walls + ceiling + floor).
Does the order of L, W, H matter?
No. Multiplication is commutative: 5 × 4 × 3 = 4 × 3 × 5 = 60. The labels length, width, and height are conventions, not rules — the volume is the same whichever edge you call which. The space diagonal and surface area are also symmetric in the three dimensions. Just make sure all three values are in the same unit before multiplying.
How do I handle irregular shapes that are almost rectangular?
Split the shape into rectangular chunks, compute each volume, and sum. For an L-shaped room, treat it as two rectangles. For a pool with a sloped floor, compute the volume with the average depth: V = L × W × (d_shallow + d_deep) / 2. For round corners or curved walls, approximate the footprint with a rectangle — the error is usually under 2 % for construction-grade estimates.
Enter length, width, and height — in meters, centimeters, millimeters, inches, or feet — and get the volume of a box or cuboid in six units at once: m³, liters, US gallons, ft³, in³, and yd³. The tool also returns the surface area (2(LW + LH + WH)) and the space diagonal (√(L² + W² + H²)), which tells you whether a long object fits inside.
Worked example: a bedroom of 5 m × 4 m × 3 m holds 60 m³ (60 000 L) of air, has 94 m² of wall-plus-ceiling-plus-floor surface, and a 7.07 m space diagonal. A 12″ × 10″ × 8″ shipping box works out to 960 in³ (0.0157 m³, 15.7 L). One-click presets load shipping boxes, rooms, and swimming pools; each unit value can be copied with a tap.