Rectangular Prism Volume Calculator
Multiply three perpendicular dimensions, mix common length units safely, and convert the result into the cubic or liquid-volume unit you need.
Dimensions and units
Enter positive decimal measurements. Commas are accepted only as standard thousands separators.
Required; greater than 0 and no more than 1 trillion units.
Required; use the inside width when estimating container capacity.
Required; measure perpendicular to the rectangular base.
Required; changes only the displayed and exported result unit, not the physical volume.
Live result
All conversions originate from one canonical volume in cubic meters.
Volume
960 in³
12 in × 10 in × 8 in = 960 in³
Cubic meters
0.0157316 m³
Liters
15.7316 L
Cubic feet
0.555556 ft³
US gallons
4.15584 US gal
Equivalent volume
The same physical volume expressed in commonly used cubic and capacity units.
| Measure | Value | Unit |
|---|---|---|
| Selected output | 960 | in³ |
| Cubic meters | 0.0157316 | m³ |
| Liters | 15.7316 | L |
| Cubic inches | 960 | in³ |
| Cubic feet | 0.555556 | ft³ |
| US gallons | 4.15584 | US gal |
Conversion values are mathematical equivalents. Real containers may hold less because of wall thickness, rounded corners, fill lines, displaced objects, or required freeboard.
How to use the rectangular prism volume calculator
What this calculator does
This calculator finds the volume of a rectangular prism, also called a cuboid or box, from three mutually perpendicular dimensions. It converts each dimension to meters, multiplies them using V = length × width × height, and then expresses the same volume in your chosen output unit. It is suitable for ideal box-shaped solids and interior spaces. It does not automatically allow for curved corners, tapered walls, material thickness, unusable headspace, displacement, or a safety margin.
When to use it
Use it to compare storage boxes or suitcases, estimate the internal capacity of a rectangular tank, calculate soil for a raised garden bed, or check the cubic space occupied by a package. Mixed input units are supported, so a drawing in millimeters can be combined with a height measured in inches without doing the conversions by hand.
How to calculate
- The calculator opens with a ready-to-use demonstration: 12 inches long, 10 inches wide, and 8 inches high. Its validated Excel workbook is immediately available.
- Replace the three dimension values and choose the unit beside each one. Results update live; no Calculate button is required.
- Choose the Volume unit you need. This changes the presentation and workbook output, while the underlying physical volume stays unchanged.
- Read the main Volume, then use the secondary conversions and the Equivalent volume table to check other units.
- Select Download Excel to export the current validated inputs, outputs, conversions, formula, and notes as a real .xlsx workbook.
- Select Reset to clear the demonstration and all calculated content. Export is then disabled until all three positive dimensions are entered again.
Input guide
Length, Width, and Height are required positive decimal numbers. Each accepts millimeters, centimeters, meters, inches, feet, or yards. A realistic entry is 12 in for Length. Increasing any one dimension increases the volume in direct proportion: doubling the height doubles the volume when the other dimensions stay fixed. Use the inside dimensions for usable capacity and the outside dimensions for shipping-space or occupied-space estimates. Do not enter unit symbols in the number box, do not use scientific notation, and do not use a decimal comma such as 1,5; choose the adjacent unit selector instead.
Length unit, Width unit, and Height unit identify the unit of their matching dimension. They are required selectors, not conversion targets. Changing one of these selectors converts the current numeric value to preserve the same physical dimension, so changing 12 in to centimeters produces 30.48 cm. Volume unit is the required result selector. It supports cubic metric and imperial units plus liters, milliliters, and US gallons. The NIST explanation of SI volume units clarifies why cubic meters are the SI unit of volume and why one liter equals one cubic decimeter.
Output guide
Volume is the primary exact geometric identity for the entered ideal dimensions, displayed in the chosen Volume unit. A zero result is not shown because every required dimension must be greater than zero. Cubic meters is the canonical SI conversion used internally. Liters, Cubic feet, and US gallons are equivalent conversions driven by the same three inputs. Large values indicate a larger ideal capacity, not necessarily usable fill volume. The four summary pills repeat the current Length, Width, Height, and Volume at a glance. The Equivalent volume table repeats the selected output and key conversions so they can be compared or exported consistently; its Measure column names the conversion, Value gives the finite numeric amount, and Unit identifies the cubic or capacity unit. Every row describes the same physical volume rather than separate components.
Worked example
With the startup values, the calculation is 12 in × 10 in × 8 in = 960 in³. Converting 960 cubic inches gives approximately 0.0157316 m³, 15.7316 L, 0.555556 ft³, and 4.15584 US gal. The displayed main result, summary pills, conversion table, live announcement, and Excel checkpoints all use this same canonical model. For a deeper derivation, see the OpenStax treatment of rectangular-prism volume, which presents the same length-times-width-times-height formula and explains why unit conversion is cubed.
Formula, units, and practical interpretation
A rectangular prism has six rectangular faces, and its volume equals the area of a rectangular base multiplied by the perpendicular height. The labels length, width, and height can be swapped without changing the product, but the three measurements must describe perpendicular edges of the same box. The MathWorld cuboid reference states the equivalent formula as V = abc.
Unit conversion deserves care because volume scales with the cube of a length conversion. One foot is 12 inches, but one cubic foot is 12 × 12 × 12 = 1,728 cubic inches. Likewise, one meter is 100 centimeters, while one cubic meter is 1,000,000 cubic centimeters. The calculator avoids mixed-unit errors by normalizing each length before multiplying.
Common mistakes
- Mixing centimeters and meters without selecting the correct unit beside each value.
- Using external dimensions when the goal is internal capacity.
- Reporting square units instead of cubic units.
- Assuming liters and cubic meters use the same numeric scale; 1 m³ equals 1,000 L.
- Treating the result as a guaranteed fill amount for a non-rectangular or partially filled container.