Calculator
Enter your optical inputs below. The page uses a configurable empirical model for the main 20/x estimate and also shows a geometric far-point estimate for myopia.
Plotly graph
The graph compares the main empirical estimate against a geometric far-point estimate. The geometric curve is mainly meaningful for myopia at distance.
Formula used
The empirical output is the main estimate on this page. The geometric output is shown as a second reference because far-point behavior is intuitive for myopia, but it is not a universal clinical acuity conversion.
How to use this calculator
- Enter sphere power in diopters. Use negative values for myopia and positive values for hyperopia.
- Add cylinder if you want the page to compute spherical equivalent.
- Enter hyperopia compensation only when you want to model accommodation reducing plus blur.
- Keep slope at 0.30 for a balanced estimate, or raise it for a stricter acuity loss model.
- Choose chart distance and unit to update the secondary geometric estimate.
- Press Convert Now to show results above the form area.
- Review 20/x, 6/x, decimal acuity, logMAR, far point, and the graph.
- Use the CSV and PDF buttons to export the calculated result.
Example data table
These examples use cylinder = 0, hyperopia compensation = 0, slope = 0.30, and a 20 ft chart distance.
| Sphere (D) | Spherical Equivalent (D) | Effective Blur (D) | Approx. 20/x | Closest Line | Decimal | logMAR | Far Point (m) |
|---|---|---|---|---|---|---|---|
| -0.25 | -0.25 | 0.25 | 20/23.8 | 20/25 | 0.841 | 0.075 | 4 |
| -0.5 | -0.5 | 0.5 | 20/28.3 | 20/25 | 0.708 | 0.15 | 2 |
| -0.75 | -0.75 | 0.75 | 20/33.6 | 20/32 | 0.596 | 0.225 | 1.333 |
| -1 | -1 | 1 | 20/39.9 | 20/40 | 0.501 | 0.3 | 1 |
| -2 | -2 | 2 | 20/79.6 | 20/80 | 0.251 | 0.6 | 0.5 |
| -3 | -3 | 3 | 20/158.9 | 20/160 | 0.126 | 0.9 | 0.333 |
| -4 | -4 | 4 | 20/317 | 20/320 | 0.063 | 1.2 | 0.25 |
FAQs
1) Is diopter to 20/20 conversion exact?
No. It is an estimate. Real visual acuity depends on pupil size, contrast, illumination, accommodation, astigmatism, retinal health, and the exact chart method used during testing.
2) Why can two people with the same diopters see differently?
They may have different pupil diameters, cylinder values, tear film quality, lighting, neural adaptation, and eye health. Those differences change how blur affects readable detail.
3) Why does the calculator use spherical equivalent?
Spherical equivalent combines sphere and half the cylinder into one simple blur number. It is a common way to summarize refractive power before applying an approximate acuity model.
4) Why is hyperopia compensation included?
Some people can use accommodation to offset part of a plus prescription, especially when young. That means uncorrected distance vision may look better than the raw diopter value suggests.
5) What does 20/20 mean?
It means the observer can resolve a standard chart line at 20 feet that a reference observer is expected to resolve at 20 feet under standard conditions.
6) What is the far point distance?
For myopia, the far point is the farthest distance that appears clear without correction. A stronger minus prescription moves that clear point closer to the eye.
7) Which output should I rely on most?
Use the empirical 20/x result as the primary estimate. Use the geometric result as a secondary physical reference, mainly for understanding distance blur in myopia.
8) Can this replace an eye exam?
No. It is an educational calculator only. Prescription decisions and true acuity measurement should come from a proper refraction and a clinical vision assessment.