What this calculator does
A diopter is the standard unit of optical power used for eyeglass and contact lens prescriptions, camera and telescope lenses, and any other optical element with a focal length. It is defined as the reciprocal of the focal length measured in metres, so a stronger, more sharply curved lens has a shorter focal length and a higher diopter value.
This diopter calculator works in both directions: enter a focal length to get its optical power in diopters, or enter a diopter value to get the equivalent focal length. The relationship is exact and does not depend on the lens material or shape, only on the focal length itself.
The formula
Optical power in diopters equals 1 divided by the focal length, with the focal length measured in metres: D = 1 / f. Working backwards, the focal length equals 1 divided by the diopter value: f = 1 / D. This calculator accepts a focal length in centimetres for convenience and converts it to metres before applying the formula.
| Term | Meaning |
|---|---|
| Diopter (D) | The unit of optical power, equal to the reciprocal of the focal length in metres. |
| Focal length (f) | The distance from a lens to the point where parallel light rays converge, or appear to diverge from. |
| Optical power | A measure of how strongly a lens bends (converges or diverges) light; higher power means a shorter focal length. |
The inputs explained
| Field | What to enter |
|---|---|
| Solve for | Choose whether you are starting from a focal length or a diopter value. |
| Focal length (cm) | The focal length, in centimetres, used when solving for diopters. |
| Diopters | The diopter value, used when solving for focal length. Positive for a converging lens, negative for a diverging one. |
When to use it
Reading an eyeglass or contact lens prescription
Prescriptions state lens power directly in diopters; converting that to a focal length in centimetres or metres gives a more intuitive sense of how strongly the lens bends light.
Working out the power of a camera or magnifying lens
Photography and optics equipment is sometimes specified by focal length rather than diopter; converting between the two lets you compare a lens against a diopter-rated close-up filter or reading lens.
Choosing reading glasses or a magnifier by strength
Off-the-shelf reading glasses are labelled in diopters (such as +1.50 or +2.50); working out the equivalent focal length shows roughly how close an object needs to be held to come into focus.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Diopters for a range of common focal lengths
A range of focal lengths, from a short macro lens to a long telephoto distance, converted to diopters.
Focal length for a range of common prescription strengths
A range of diopter values typical of reading glasses and mild prescriptions, converted to their equivalent focal length.
| Diopters (D) | Focal length |
|---|---|
| 0.5 | 2.000 m (200.0 cm) |
| 1 | 1.000 m (100.0 cm) |
| 1.5 | 0.667 m (66.7 cm) |
| 2 | 0.500 m (50.0 cm) |
| 3 | 0.333 m (33.3 cm) |
| 4 | 0.250 m (25.0 cm) |
Questions
What does a diopter measure?
A diopter measures optical power, how strongly a lens converges or diverges light, defined as 1 divided by the focal length in metres. It is the standard unit on eyeglass, contact lens and optical instrument specifications.
What is the focal length of a +2.00 D lens?
Dividing 1 by 2.00 gives a focal length of 0.500 m, or 50 cm. A higher diopter value always means a shorter, more strongly converging focal length.
Can diopters be negative?
Yes. A positive diopter value describes a converging lens, used for long-sightedness, and a negative value describes a diverging lens, used for short-sightedness. The same 1/f relationship applies with the sign carried through.
Why is diopter power additive but focal length is not?
Optical powers in diopters simply add when thin lenses are placed close together, which is why prescriptions and lens combinations are specified in diopters rather than in focal length, where combining lenses requires a less direct calculation.
For a related optics figure, see the refractive index calculator. For camera focus and sharpness range instead of lens power, see the depth of field calculator.