Diopter & Lens Power Calculator
Convert Focal Length to Diopters or Diopters to Focal Length
Calculate the optical power of a lens in diopters (D) from its focal length, or find the focal length from a given diopter value. Supports multiple units and lens combinations.
Diopter & Lens Power Calculator
Convert Focal Length to Diopters or Diopters to Focal Length
About the Diopter & Lens Power Calculator
The diopter (symbol: D) is the SI unit of optical power, defined as the reciprocal of the focal length in metres: D = 1/f(m). A lens with a focal length of 1 metre has a power of 1 D; a lens with a focal length of 0.5 m has a power of 2 D; and a lens with a 250 mm focal length has a power of 4 D. Diopters are additive, which makes them extremely convenient for describing lens combinations and prescriptions: the total power of two thin lenses in contact is simply D_total = D₁ + D₂.
Converging (convex) lenses have positive focal lengths and positive diopter values. They bring parallel rays of light to a focus and are used in reading glasses, magnifying lenses, and correcting farsightedness (hyperopia). Diverging (concave) lenses have negative focal lengths and negative diopter values. They spread parallel rays outward and are used in correcting nearsightedness (myopia). A plano-convex lens and a plano-concave lens of equal magnitude, placed together, cancel each other out to a total power of zero diopters.
In optometry and ophthalmology, the diopter is the standard unit for prescribing spectacles, contact lenses, and intraocular lenses. A typical myopia prescription might read –2.50 D, meaning the corrective lens must diverge light with an optical power of –2.5 diopters. Bifocal and progressive lenses are described by an addition power (Add) that expresses the extra converging power added to the lower portion of the lens for near vision.
Photographic and microscopy lenses are more commonly described by focal length in mm, but converting to diopters is useful when calculating depth of field, close-up lens power, or combining supplementary lenses. For example, attaching a +4 D close-up lens to a camera lens shifts the near focus to 25 cm from the front of the close-up lens. Knowing the diopter power of each element allows you to stack close-up lenses and predict the combined result without measuring.
This calculator supports single and multiple lens inputs in metres, centimetres, millimetres, or inches. Enter comma-separated values to find the combined diopter power of a lens stack, or convert an optometry prescription back to a physical focal length to understand what it means geometrically.
Diopter Calculator Examples
See how to use the Diopter & Lens Power Calculator in real-world scenarios.
| Input | Result | Application |
|---|---|---|
| Focal Length = 50 mm (single lens) | D = 20 D | A 50 mm camera lens has an optical power of 20 diopters. This is relevant when choosing close-up supplementary lenses. |
| Diopter = 2 D (single lens) | f = 500 mm (0.5 m) | A +2 D reading glass brings the near point to 50 cm (500 mm) from the lens — comfortable for arm's-length reading. |
| Focal Lengths = 100 mm + 200 mm (combined) | D_total = 15 D (f ≈ 66.7 mm) | Two converging lenses of 100 mm and 200 mm give a combined power of 10 D + 5 D = 15 D, with an equivalent focal length of about 66.7 mm. |
| Diopters = 1 D, −2 D, 3 D (three lenses) | D_total = 2 D (f = 500 mm) | Three thin lenses in contact: a +1, −2, and +3 D lens stack gives a total of +2 D, equivalent to a 500 mm focal length. |
How to Use the Diopter Calculator
- Select the calculation type: 'Focal Length → Diopter' to convert a focal length to optical power, or 'Diopter → Focal Length' to convert in the opposite direction.
- Choose the focal length unit (m, cm, mm, or inches) if you are entering focal lengths.
- Type your value or a comma-separated list of values into the input field. Negative values represent diverging (concave) lenses.
- Click Calculate to see the total optical power in diopters or the equivalent focal length.
- Click Reset to clear the fields, or use the example buttons to load a preset scenario.
Diopter FAQ
What is a diopter?
A diopter (D) is the SI unit of optical power, equal to the reciprocal of the focal length in metres: D = 1/f. A 1 D lens focuses parallel light at 1 metre; a 4 D lens focuses it at 25 cm. Diopters are additive, making them convenient for combining lenses or prescribing corrective eyewear.
What does a negative diopter mean?
A negative diopter value indicates a diverging (concave) lens that spreads light outward rather than converging it. Negative-power lenses are used to correct myopia (nearsightedness). The magnitude of the number indicates the strength: –5 D is a stronger myopia correction than –1 D.
How do I combine multiple lenses?
For thin lenses in contact (touching), the total diopter power is the algebraic sum: D_total = D₁ + D₂ + … This additive rule is exact only when the lenses are physically touching. When lenses are separated by a distance t (in metres), use the more general formula: D_total = D₁ + D₂ − t × D₁ × D₂.
How does a close-up lens affect camera focus?
Adding a close-up lens of power D to a camera lens shifts the minimum focus to 1/D metres from the front of the close-up lens. A +4 D close-up lens brings focus to 1/4 = 0.25 m (25 cm), enabling macro photography without a macro lens.
What is the relationship between focal length and diopters?
The relationship is f (m) = 1/D and D = 1/f, so they are simply reciprocals of each other. To convert from millimetres: D = 1000/f(mm). A 250 mm telephoto lens has a power of 4 D, while a 28 mm wide-angle lens has about 35.7 D.
Can I use this calculator for eyeglass prescriptions?
Yes. Enter the sphere power from a prescription (e.g. −2.50) as a diopter value to find the equivalent focal length. Note that prescriptions also include cylinder and axis values for astigmatism, which this calculator does not handle; it covers only the spherical (sphere) component.