Diopter ⇄ Focal Length Converter

Understanding the diopter to focal length converter — concept and principle

This converter switches between a lens's optical power in diopters (D) and its focal length in metres or millimetres. Diopters are the unit used on eyeglass and contact lens prescriptions, close-up filters for cameras, magnifiers and many optics lab components, while photographers and engineers usually think in focal length. The calculator also tells you whether the lens is converging (plus) or diverging (minus).

How it is calculated

Optical power P = 1 / f, where f is the focal length in metres.

• From diopters: f (m) = 1 / P, and f (mm) = 1,000 / P.
• From millimetres: f (m) = f (mm) / 1,000, then P = 1 / f.

A positive value is a converging lens, which brings parallel light to a real focus; a negative value is a diverging lens, whose focus is virtual.

The principle

Power measures how strongly a lens bends light. A strong lens brings light to a focus over a short distance, so power is the reciprocal of focal length. The reciprocal is practical: for thin lenses placed together, powers simply add. A +2 D close-up filter on a camera lens, or a +1 D and +1.5 D lens stacked, behave like single lenses of the summed power. The relaxed human eye has a total power of roughly 60 D, and spectacles add or subtract a few diopters to move the focus onto the retina: minus lenses for short-sightedness (myopia), plus lenses for long-sightedness and presbyopia.

Worked example

Default input: 2.5 diopters.

1. f = 1 / 2.5 = 0.4 m.
2. In millimetres: 0.4 × 1,000 = 400 mm.
3. The value is positive, so it is a converging (plus) lens.

The calculator shows 2.5 D, focal length 0.4 m = 400 mm, converging, which is a typical strength for reading glasses.

How to read the result

Larger absolute diopter values mean stronger lenses and shorter focal lengths: +1 D is 1,000 mm, +4 D is 250 mm, and −4 D is −250 mm. A camera close-up filter of +P diopters lets a lens focused at infinity focus at about 1/P metres. Reading glasses are usually in the +1 to +3 D range.

Common mistakes

• Forgetting to convert millimetres to metres before taking the reciprocal (1/400 is not 2.5).
• Dropping the sign: −2 D and +2 D lenses do opposite things.
• Assuming spectacle and contact lens powers are equal. Moving a lens closer to the eye changes its effective power; a −6.00 D spectacle lens 12 mm from the eye corresponds to about −5.6 D at the cornea.
• Adding powers for lenses that are far apart; the simple sum holds only for thin lenses in contact.

Frequently asked questions

What focal length is +2 diopters?

1 / 2 = 0.5 m, or 500 mm.

What does a minus diopter mean?

The lens is diverging; it spreads light out and is used to correct short-sightedness.

Can I combine close-up filters?

Yes. A +1 and a +2 filter together act as about +3 D, but image quality usually drops with stacked filters.

Sources: E. Hecht, Optics, Pearson · ISO 13666, Ophthalmic optics — Spectacle lenses — Vocabulary