Enter Values
Example Data Table
| Scenario | Inputs | Key Output | Notes |
|---|---|---|---|
| Offset to prism | Offset 2 cm, Distance 1 m | 2 Δ | 1Δ equals 1 cm at 1 m. |
| Prism to offset | Prism 4 Δ, Distance 3 m | 12 cm offset | Offset grows linearly with distance. |
| Angle to prism | Deviation angle 2° | ≈ 3.49 Δ | Uses Δ = 100·tan(θ). |
| Prism to angle | Prism 10 Δ | ≈ 5.71° | Uses θ = arctan(Δ/100). |
Formula Used
- Definition: 1 prism diopter (Δ) creates a 1 cm deviation at 1 m.
- Offset method: Δ = offset(cm) / distance(m)
- Angle method: Δ = 100 × tan(θ) where θ is the deviation angle.
- Reverse angle: θ = arctan(Δ / 100)
- Offset from prism: offset(cm) = Δ × distance(m)
Tip: Use the offset method for clinic measurements and the angle method for optical geometry.
How to Use This Calculator
- Select a calculation method that matches your known values.
- Enter the required inputs and choose the correct units.
- Pick eye and base direction for clean reporting.
- Click Calculate to show results above the form.
- Use Download CSV or Download PDF for records.
Prism Diopter Guide
1) What prism diopters represent
Prism diopter (Δ) is a practical way to express how much a prism bends light. By definition, 1Δ produces a 1 cm displacement at a viewing distance of 1 meter. That simple relationship is why prism is widely used in vision testing, binocular alignment, and optical troubleshooting.
2) Offset and distance method
When you can measure a target shift, the offset method is fastest. The calculator uses Δ = offset(cm) / distance(m). For example, a 3 cm shift at 1.5 m equals 2Δ. Because distance is in meters, entering units correctly matters more than adding extra decimals.
3) Prism and expected shift
If prism power is known, you can predict displacement at any distance using offset(cm) = Δ × distance(m). A 5Δ prism causes about 2 cm shift at 0.4 m (near testing) and about 30 cm shift at 6 m (distance testing). This helps with setup checks and sanity checks.
4) Angle-based conversion
Optical geometry often reports deviation as an angle. This calculator converts using Δ = 100 × tan(θ). For small angles, Δ is close to 100θ (in radians), but the tangent formula stays accurate as the angle grows. The reverse uses θ = arctan(Δ/100).
5) Units and scaling
Offsets can be entered in cm, mm, or inches, while distance supports metric and imperial units. Internally, the tool standardizes to cm and meters before calculating. That prevents hidden scaling errors, especially when switching between near distances like 40 cm and longer setups like 10 ft.
6) Base direction for reporting
Prism is often documented with a base direction, such as Base In, Base Out, Base Up, or Base Down. The base does not change the magnitude calculation, but it is essential for communicating how the prism is oriented. Selecting it here keeps exports clean and consistent.
7) Precision and rounding
Rounding should match your measurement quality. If offsets are read to the nearest millimeter, reporting 4–6 decimals can be misleading. Use the precision selector to keep results realistic. For quick clinical notes, two decimals is commonly sufficient for comparison and trend tracking.
8) Saving results for later
After you calculate, use the CSV export for spreadsheet logs and the PDF export for sharing a single report. The saved report includes method, inputs, base direction, and timestamp, making it easier to audit repeated measurements or compare sessions across different viewing distances.
FAQs
1) What does 1Δ mean in simple terms?
It means the image shifts 1 cm when the screen is 1 m away. So, prism power scales linearly with distance for the same setup and alignment.
2) Which method should I use most often?
If you measured a displacement at a known distance, use Offset + Distance. If you only have a deviation angle from geometry, use the Angle method.
3) Why does the calculator show an angle too?
Angle is the geometric equivalent of prism power. It helps you compare prism values with angular specifications from optical components or lab instruments.
4) Does base direction change the prism diopter value?
No. Base direction describes orientation, not magnitude. The calculator reports magnitude from the numbers you enter and keeps base direction for labeling and exports.
5) What distance should I use for near measurements?
Common near testing distances are around 0.4 m (40 cm). Enter the distance you actually used, since prism and offset scale directly with distance.
6) Is the angle formula accurate for larger deviations?
Yes. Using tan(θ) avoids small-angle approximations. Very large prism values can be sensitive to input rounding, so choose a sensible precision.
7) What if my inputs are in inches or feet?
Select the matching units beside each input. The tool converts to metric internally, then returns results in prism diopters and the offset unit you selected.