Enter Cuboid Values
Use the responsive input grid below.
Example Data Table
This table shows sample cuboid measurements and their computed diagonals.
| Length | Width | Height | Unit | Space Diagonal | Volume | Surface Area |
|---|---|---|---|---|---|---|
| 12 | 9 | 7 | cm | 16.553 | 756 | 510 |
| 8 | 6 | 4 | m | 10.770 | 192 | 208 |
| 20 | 15 | 10 | in | 26.926 | 3000 | 1300 |
Formula Used
Space Diagonal
d = √(l² + w² + h²)This is the longest line segment inside the cuboid. It connects two opposite corners through three dimensions.
Face Diagonal
df = √(a² + b²)Each rectangular face has its own diagonal. Use length-width, length-height, or width-height pairs.
Volume
V = l × w × hVolume measures the space occupied by the cuboid. It is useful in storage, packaging, and design tasks.
Surface Area
SA = 2(lw + lh + wh)Surface area gives the total outer coverage. It helps with coating, wrapping, and material estimates.
How to Use This Calculator
- Enter the cuboid length, width, and height.
- Select the measurement unit you want displayed.
- Choose your preferred decimal precision level.
- Optionally enter density for mass estimation.
- Optionally enter cost per cubic unit.
- Click the calculate button to generate results.
- Review diagonals, area, volume, and plotted comparisons.
- Use CSV or PDF export for saving outputs.
Frequently Asked Questions
1. What does the cuboid diagonal represent?
The space diagonal is the straight distance between two opposite corners of a cuboid. It passes through length, width, and height simultaneously, making it useful for geometry checks, packaging design, and internal clearance calculations.
2. How is a face diagonal different?
A face diagonal lies on one rectangular face only. A cuboid has three unique face-diagonal values when its dimensions differ. The space diagonal is longer because it spans all three dimensions together.
3. Can I use any measurement unit?
Yes. This calculator displays results in the unit you select. Just keep all three dimensions in the same unit before calculating, otherwise the diagonal, area, and volume outputs will become inconsistent.
4. Why include volume and surface area too?
Advanced geometry work often needs more than one metric. Volume supports capacity checks, while surface area helps estimate paint, covering, sheet material, or wrapping needs for the same cuboid.
5. When is density useful here?
Density helps estimate mass from cuboid volume. This is useful for material planning, load checks, shipping estimates, and classroom exercises where geometry connects with physical properties.
6. Does decimal precision matter?
Yes. Higher precision gives more detailed results for engineering-style work or comparison studies. Lower precision is easier for quick reviews, classroom problems, or reports where rounded values are preferred.
7. What is the main formula behind the diagonal?
The cuboid diagonal uses the three-dimensional Pythagorean theorem: d = √(l² + w² + h²). It extends the familiar right-triangle rule from two dimensions into three.
8. What does the Plotly graph show?
The graph compares the three dimensions, the three face diagonals, and the space diagonal visually. It helps you quickly see scale differences and identify how one dimension influences the final diagonal.
This single-file calculator is designed for a clean white layout, responsive inputs, export options, and geometry analysis in one place.