Volume of Rectangular Prism Calculator
Length (L)
Width (W)
Height (H)
Decimal Precision
Enter length, width, and height to calculate volume and properties.
About This Tool
What Is the Volume of a Rectangular Prism?
A rectangular prism — also called a cuboid or box — is the most common three-dimensional shape in everyday life. Every shipping carton, room, swimming pool, storage tank, and brick is a rectangular prism. Its volume tells you exactly how much three-dimensional space it occupies, which is crucial for logistics, construction, science, and manufacturing.
The calculator above computes volume in eight units simultaneously, plus surface area, space diagonal, fill capacity, dimensional (shipping) weight, material weight from density, and packing fit — all from just three measurements.
Volume Formula
The formula is beautifully simple:
Where L is the length, W is the width, and H is the height — all converted to the same unit before multiplying. For example, a box measuring 10 cm × 8 cm × 6 cm gives a volume of 480 cm³ (or 0.48 liters).
Unit Conversions Explained
Each dimension can be entered in any combination of mm, cm, m, in, ft, or yd. Internally, all values are converted to centimetres before calculation using these exact factors:
mm → cm
÷ 10m → cm
× 100in → cm
× 2.54ft → cm
× 30.48yd → cm
× 91.441 cm³ = 1 mL
exactVolume output covers cm³, m³, liters, mL, in³, ft³, US gallons, and UK gallons — so you never need a second converter.
Surface Area and Space Diagonal
Two properties frequently matter alongside volume:
Total surface area — the sum of all six faces — tells you how much material is needed to wrap or coat a box:
Lateral surface area covers only the four side faces (useful for labelling, insulation, and wrapping cylinders inside boxes):
The space diagonal is the longest straight line that fits inside the box — useful for checking whether a rod, pipe, or monitor will fit:
Dimensional Weight for Shipping
Parcel carriers such as FedEx, UPS, and DHL charge based on dimensional (DIM) weight when it exceeds the actual weight. The formula is:
Common divisors are 5000 (standard) or 6000 (economy) for metric shipments, and 139 in³/lb for imperial. Enter your carrier's divisor in the "Dimensional Weight" panel for an instant estimate.
Material Weight from Density
Multiply the volume by the material density to find the mass of a solid block. The calculator accepts density in g/cm³, kg/m³, or lb/ft³. Results are shown in grams, kilograms, and pounds. For reference:
Water
1.00 g/cm³Aluminium
2.70 g/cm³Steel
7.80 g/cm³Concrete
2.40 g/cm³Packing Fit Calculator
Working out how many small boxes fit inside a larger container is a classic logistics problem. The calculator uses axis-aligned stacking:
Enable "try all orientations" to test all six possible rotations of the item box and automatically select the arrangement that fits the most units — a quick bruteforce optimisation without the need for advanced bin-packing algorithms.
Practical Applications
Construction & architecture: Calculate concrete volume for footings and slabs, or total fill needed for landscaping raised beds.
Aquariums & tanks: Know the water capacity in liters or gallons before filling. Use fill % to model partial fills.
E-commerce & logistics: Compare DIM weight versus actual product weight to predict true shipping cost and choose optimal packaging sizes.
Manufacturing: Compute raw material weight for steel, aluminium, or plastic blocks, or verify that a finished part fits its enclosure.
Science & education: Demonstrate the relationship between volume, surface-to-volume ratio, and the space diagonal for geometry coursework.
Frequently Asked Questions
Yes, Volume of Rectangular Prism Calculator is totally free :)
Yes, you can install the webapp as PWA.
Yes, any data related to Volume of Rectangular Prism Calculator only stored in your browser (if storage required). You can simply clear browser cache to clear all the stored data. We do not store any data on server.
The volume of a rectangular prism (also called a cuboid or box) is V = L × W × H, where L is the length, W is the width, and H is the height. All three dimensions must use the same unit before multiplying. For example, a box measuring 10 cm × 8 cm × 6 cm has a volume of 480 cm³.
Input supports mm, cm, m (metric) and in, ft, yd (imperial). Each dimension has its own independent unit selector, so you can freely mix units. Output is automatically provided in cm³, m³, liters (L), milliliters (mL), in³, ft³, US gallons, and UK gallons all at once.
Dimensional weight (DIM weight) is a shipping concept where carriers charge based on package volume instead of actual weight. Metric formula: DIM weight (kg) = L × W × H (in cm) ÷ divisor (e.g., 5000 or 6000). Imperial formula: DIM weight (lb) = volume in in³ ÷ divisor (e.g., 139). The exact divisor varies by carrier and service level.
Enter the container (outer box) dimensions and the item (inner box) dimensions. The calculator determines how many items fit using axis-aligned stacking: count = floor(cL ÷ bL) × floor(cW ÷ bW) × floor(cH ÷ bH). Enabling 'try rotations' tests all six possible box orientations and picks the maximum count.
Enter the material density (g/cm³, kg/m³, or lb/ft³) and the tool multiplies it by the volume in the matching unit. For example, water at 1 g/cm³ in a 480 cm³ box gives 480 g (0.48 kg). Steel at 7.8 g/cm³ in the same box gives about 3.74 kg.
Total surface area is 2(LW + LH + WH), covering all six faces. Lateral surface area is 2H(L + W), covering only the four side faces (excluding top and bottom). The space diagonal (longest internal dimension, corner to corner) is √(L² + W² + H²). All three are useful for packaging, coating, and structural design.