How to use the cuboid calculator
- Choose the unit shared by the length, width and height. Do not mix centimetres and metres in one calculation; convert them first.
- Measure the three edges that meet at one corner and enter positive numbers. Length, width and height may be different, and decimals are accepted.
- Select Calculate cuboid. Read volume for the space inside, total surface area for all six outside faces, and the space diagonal for the straight corner-to-opposite-corner distance.
- If any measurement changes, the old result disappears. Calculate again so a previous answer is never mistaken for the edited box. Clear removes entered values and results but keeps the selected unit.
Formulas and what the results mean
A cuboid has three pairs of matching rectangular faces. Multiplying length × width, length × height and width × height gives the three different face areas. Each occurs twice, so total surface area is twice their sum.
Volume multiplies all three perpendicular dimensions. The unit is therefore cubed: centimetre inputs produce cubic centimetres. Surface area uses squared units, while the space diagonal remains a length.
The space diagonal applies the Pythagorean theorem in three dimensions. It is the straight line through the interior from one corner to the opposite corner, not a route along the edges. The calculator keeps full precision internally and displays ordinary results with at most two decimal places.
V = l × w × h · SA = 2(lw + lh + wh) · d = √(l² + w² + h²)
Worked examples
Shipping box: 30 cm × 20 cm × 15 cm
Volume is 30 × 20 × 15 = 9,000 cm³. Total surface area is 2 × (600 + 450 + 300) = 2,700 cm². The space diagonal is √(900 + 400 + 225) ≈ 39.05 cm.
Cube with 2.5 m edges
Entering 2.5 for all three dimensions gives 15.625 m³, displayed as 15.63 m³. Its total surface area is 37.5 m² and its space diagonal is √18.75 ≈ 4.33 m. No separate cube mode is needed.
When this calculation is useful
Estimate the internal capacity of a rectangular carton, room, tank or storage compartment, then keep the result in cubic units. For liquid capacity or litres, perform the appropriate unit conversion separately.
Estimate material that covers every closed face, or check whether a straight rigid item could span between opposite corners. Real packaging flaps, wall thickness, seams, waste and openings are not included.
Input limits and common mistakes
- All dimensions must be positive, finite decimal values. Blank, zero, negative, labelled and exponent-form inputs are rejected.
- The selected unit labels the calculation; changing it does not convert numbers already typed. Use the same real unit for every edge.
- Total surface area includes all six closed faces. An open box requires subtracting the missing face after calculating.
- The diagonal is a geometric maximum line through an empty box. It does not guarantee that a thick or rigid object can be turned through the opening.
- Displayed rounding does not increase measurement accuracy. Keep suitable tolerances for cutting, construction, freight or manufacturing decisions.
Frequently asked questions
Can I calculate a cube?
Yes. A cube is a cuboid with equal length, width and height, so enter the same edge value in all three fields.
Why are the units different for each result?
Diagonal is a length, surface area covers two dimensions and volume covers three, so the unit is respectively linear, squared and cubed.
Does surface area include the inside?
No. It is the mathematical area of the six outer faces of a closed cuboid. Material thickness and inner faces are not added.
Is the space diagonal the same as a face diagonal?
No. A face diagonal crosses one rectangular face; the space diagonal crosses the three-dimensional interior and uses all three edge lengths.
Can I enter mixed units?
No. Convert every measurement to one common unit first, select that unit, and then calculate.