Cuboid calculator
Volume, surface area and space diagonal from three edges.
Fill in the fields and the result will appear here automatically.
A rectangular cuboid is specified by three mutually perpendicular edges. The calculator gives volume, total surface area, space diagonal and the combined length of its twelve edges. Three equal edges give a cube using the same formulas. The diagonal is the longest straight segment inside a box; a thick object also needs clearance for its cross-section and opening. Use one length unit, whose square measures area and whose cube measures volume.
How it works
Formula and logic
V = abc; S = 2(ab + bc + ca); the space diagonal d = √(a² + b² + c²) follows from applying Pythagoras twice. The total edge length is 4(a + b + c), because there are four edges in each direction.
Example
A 3 × 4 × 5 cm box has a volume of 60 cm³, a surface of 94 cm² and a diagonal of 7.071 cm.
Fields and units
- Length unit — list option
- Edge a — cm
- Edge b — cm
- Edge c — cm
How to use
- — Pick the length unit.
- — Enter the three edges.
- — Read the volume, the surface and the diagonal.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: solid volumes and surface areas
- Limitation
- All three edges are positive and mutually perpendicular. The model is a closed rectangular solid without subtracting walls, holes or voids. Choosing mm/cm/m does not automatically convert the entered dimensions.
FAQ
What does the space diagonal tell me?
It joins opposite vertices and equals √(a²+b²+c²). An object longer than it cannot fit wholly inside; a shorter length alone does not guarantee a fit because thickness and access through the opening also matter.
Does this handle a cube?
Yes. A cube is a cuboid with three equal edges: enter the same value three times and every formula still holds.
Why is the volume in cubic units and the surface in square ones?
Because volume is measured in the cube of the chosen unit and area in its square. Converting either with a linear factor would be wrong.
How do I get the weight from the volume?
Mass is m = ρV when density and volume use compatible units: kg/m³ with m³ gives kg. For example, 60 cm³ = 0.00006 m³. Weight as a force also depends on gravitational acceleration and is measured in newtons.