Calculator
Example data table
| Focal length (mm) | Focal length (m) | Optical power (D) | Typical use |
|---|---|---|---|
| 25 | 0.025 | 40 | Short focal lens systems |
| 50 | 0.050 | 20 | Standard optics reference |
| 100 | 0.100 | 10 | Longer focal setups |
| 250 | 0.250 | 4 | Reading lens range |
| -250 | -0.250 | -4 | Diverging correction example |
Formula used
- Diopters: D = 1 / f(m)
- From millimeters: f(m) = f(mm) / 1000, so D = 1000 / f(mm)
- Reverse conversion: f(mm) = 1000 / D
The sign of D follows the sign of the focal length.
How to use this calculator
- Select the conversion mode you need.
- Enter your value in millimeters or diopters.
- Choose decimal places and rounding method.
- Click Calculate to view results above.
- Use CSV or PDF buttons to save outputs.
Notes and limits
- Zero is not allowed because it implies infinite power.
- Negative values model diverging lenses and myopia correction.
- Small focal lengths can produce large diopter values.
Millimeters and diopters in one view
Millimeters describe focal length, while diopters describe optical power. The relationship is reciprocal, so shorter focal lengths produce higher diopters. This calculator converts both ways and also displays focal length in meters and centimeters for quick unit checks. As a quick scale, 1000 mm equals 1 D.
Primary conversion data points
The key rule is D = 1000 / f(mm). Using this, 25 mm equals 40 D, 50 mm equals 20 D, and 100 mm equals 10 D. A mid value like 75 mm gives about 13.33 D. These checkpoints help confirm that inputs are truly millimeters, not centimeters.
Reverse conversion checkpoints
When starting with diopters, the calculator uses f(mm) = 1000 / D. Common values are 1.00 D → 1000 mm, 2.00 D → 500 mm, 2.50 D → 400 mm, and 4.00 D → 250 mm. At 8.00 D, focal length is 125 mm.
Sign convention and real meaning
Negative values are supported because sign indicates lens behavior. A positive focal length produces positive diopters and typically represents a converging lens. A negative focal length produces negative diopters and represents a diverging lens, such as -250 mm producing -4 D. In prescriptions, “minus” power usually indicates a diverging correction.
Precision controls for reporting
Rounding options help match how you publish or compare results. Two decimals are common for summaries. More decimals help during bench testing, especially when small mm changes matter. Ceiling rounding gives a conservative higher power, while floor rounding gives a conservative lower power. Example: 333 mm is 3.003 D, shown as 3.00 D or 3.01 D.
Where these numbers are used
Millimeter to diopter conversion is useful when comparing lens datasheets, verifying close-up filters, selecting magnifiers, and translating between “strength” language and focal length. For example, a 5 D lens corresponds to 200 mm, often referenced for near-vision aids.
Common mistakes and quick validations
Avoid zero because it implies infinite focal length or infinite power. If your result looks ten times off, you likely entered centimeters. Use the example table as a sanity check, then export CSV or PDF to keep a record with your chosen rounding. Doubling focal length halves diopters, a reliable sanity check every time always.
FAQs
1) What does “diopter” measure?
A diopter measures optical power as the reciprocal of focal length in meters. A 2 D lens has a 0.5 m focal length, while a 10 D lens has a 0.1 m focal length.
2) How do I convert millimeters to diopters?
Use D = 1000 / f(mm). Enter the focal length in millimeters, and the calculator returns diopters plus focal length in meters and centimeters for verification.
3) Can this tool convert diopters back to millimeters?
Yes. Select the reverse mode and use f(mm) = 1000 / D. The calculator also shows the equivalent in meters and centimeters to reduce unit errors.
4) Why are negative values allowed?
Negative focal length represents a diverging lens, so the diopter result is also negative. This matches common optics sign conventions and is useful for modeling minus-power corrective lenses.
5) What decimal setting is best?
Two decimals work well for summaries and quick comparisons. Use more decimals for lab measurements or design checks. Choose ceiling or floor rounding when you need conservative results.
6) Why is zero rejected as an input?
Zero diopters implies infinite focal length, and zero millimeters is physically impossible. Blocking zero prevents divisions by zero and avoids misleading “infinite power” outputs.