Calculator Inputs
Use any supported input pair. The page resolves the missing rectangle side and then calculates the circumradius and related circle properties.
Plotly Graph
This graph shows how the circumradius changes as the rectangle length changes while the current width stays fixed.
Formula Used
A rectangle fits inside a circle whose center is the rectangle center. Every vertex lies on the same circle, so the circumradius equals half of the diagonal.
If you know one side and the diagonal, first recover the missing side with the Pythagorean relationship. Then divide the diagonal by two to get the circumradius.
How to Use This Calculator
- Select the input mode that matches the values you already know.
- Enter positive measurements for the required rectangle dimensions.
- Add a unit label such as cm, m, ft, or in.
- Choose how many decimal places you want in the output.
- Press the calculate button to show the result above the form.
- Review the table, steps, graph, and export buttons for reporting.
Example Data Table
| Length | Width | Diagonal | Circumradius |
|---|---|---|---|
| 4 | 3 | 5.0000 | 2.5000 |
| 10 | 6 | 11.6619 | 5.8310 |
| 12 | 9 | 15.0000 | 7.5000 |
| 8.5 | 5.25 | 9.9906 | 4.9953 |
FAQs
1. What is a rectangle circumradius?
It is the radius of the circle passing through all four rectangle corners. For every rectangle, that radius equals half of the diagonal length.
2. Why is the circumradius half the diagonal?
The circumcenter of a rectangle lies at the midpoint of both diagonals. Each corner is the same distance from that center, so the radius is one half of the diagonal.
3. Can I calculate the radius from length and width only?
Yes. The calculator first finds the diagonal using the Pythagorean theorem. It then divides that diagonal by two to return the circumradius.
4. Can I use the diagonal directly?
Yes. If the diagonal is known, the circumradius is simply diagonal divided by two. The tool also lets you combine the diagonal with one side to recover the missing side.
5. Which units should I enter?
You can use any consistent unit, including millimeters, centimeters, meters, inches, or feet. The calculator treats the unit label as display text and keeps every output in the same unit system.
6. What happens if the diagonal is smaller than a side?
That would not describe a valid rectangle. The diagonal must always be longer than either side, so the calculator shows a validation message instead of an incorrect answer.
7. Why does the graph change with the rectangle length?
The graph keeps the current width fixed and varies the length. As the rectangle becomes longer, its diagonal grows, and the circumradius increases accordingly.
8. What do the CSV and PDF buttons export?
They export the current result summary, including the chosen mode and calculated values. This is useful when you need to save, share, or document geometry calculations.