Degree to Diopter Calculator
Plotly Graph
The graph shows how prism diopters rise nonlinearly as deviation angle increases.
Example Data Table
| Angle (°) | Radians | tan(θ) | Prism Diopters (Δ) |
|---|---|---|---|
| 1 | 0.0175 | 0.0175 | 1.7455 |
| 2 | 0.0349 | 0.0349 | 3.4921 |
| 5 | 0.0873 | 0.0875 | 8.7489 |
| 10 | 0.1745 | 0.1763 | 17.6327 |
| 15 | 0.2618 | 0.2679 | 26.7949 |
| 20 | 0.3491 | 0.3640 | 36.3970 |
Formula Used
This calculator uses the prism diopter relation:
Prism Diopters (Δ) = 100 × tan(θ)
Here, θ is the deviation angle in degrees. The calculator first converts degrees into radians, then applies the tangent function.
Important note: prism diopters describe image deviation through a prism. They are not the same as refractive power diopters used for lens focusing.
How to Use This Calculator
- Enter the deviation angle in degrees.
- Enter a comparison angle for side-by-side analysis.
- Select decimal precision for displayed values.
- Set chart start, end, and step values.
- Click Calculate Now to show results.
- Review the graph and example table.
- Export the results using CSV or PDF buttons.
Frequently Asked Questions
1. What does this calculator convert?
It converts angular deviation in degrees into prism diopters. This is useful in prism optics and vision measurements involving deviation angles.
2. Is prism diopter the same as lens power diopter?
No. Prism diopters measure image displacement. Lens power diopters measure focusing strength. They describe different optical behaviors.
3. Why does the formula use tangent?
Prism deviation follows geometric optics. The tangent of the angle gives displacement per unit distance, and multiplying by 100 expresses prism diopters.
4. Can negative angles be entered?
Yes. Negative values represent deviation in the opposite direction. The numeric result becomes negative as well.
5. Why do large angles produce very high values?
The tangent function rises sharply near 90 degrees. That makes prism diopters increase rapidly for large deviation angles.
6. What range is safe for this calculator?
Angles below 89.999 degrees are allowed. Values extremely close to 90 degrees create unstable tangent results.
7. What does the comparison output show?
It shows the prism diopter value for a second angle and the difference between both measurements. This helps quick optical comparison.
8. When should I use CSV or PDF export?
Use CSV for spreadsheet work and batch analysis. Use PDF when sharing a clean report or saving a printable result summary.