Diopter ↔ Focal Length Converter
The optical power P of a thin lens (in dioptres, symbol D) is the reciprocal of its focal length when the focal length is measured in metres: P = 1 / f(m). Hence 1 D = 1 m⁻¹. Positive D denotes a converging (convex) lens — reading glasses, magnifiers and camera close-up filters; negative D denotes a diverging (concave) lens — myopia spectacle correction and wide-angle attachment lenses. The tool converts in either direction between diopters and focal length expressed in m, mm or inches — useful for checking an eyeglass prescription, sizing a photographic close-up filter, or working out the focal length behind a magnifier marked "10 D".
Please enter a valid number
Optical power
+2.00 D
Focal length (m / mm / in)
0.5000 m · 500.00 mm · 19.685 in
Lens type
Converging (convex)
Positive D — reading glasses, magnifiers, camera close-up filters.
Formula
P (D) = 1 / f (m); 1 m = 1000 mm = 39.3701 in
Positive D = converging (convex) lens; negative D = diverging (concave) lens. An eyeglass prescription "+1.50 D" is a presbyopia add; "−3.50 D" is a myopia correction.
Formula
P (D) = 1 / f (m) f (m) = 1 / P 1 m = 1000 mm = 39.3701 in (1 in = 0.0254 m exactly)
- · Common landmarks: +1 D ↔ 1.000 m / 1000 mm; +2 D ↔ 500 mm (typical presbyopia reading add); +3 D ↔ 333 mm; +10 D ↔ 100 mm (high-power magnifier); +20 D ↔ 50 mm (camera close-up filter).
- · Negative values denote concave lenses: −1 D ↔ −1 m focal length; −3.50 D ↔ −0.286 m, a common myopia spectacle correction.
- · Eyeglass prescriptions are normally quantised to 0.25 D steps (e.g. +1.50 D, −2.75 D) — the minimum surface power required by ISO 8980-1 and ANSI Z80.1.
- · A magnifier marked "10×" is NOT the same as 10 D. Two widely used conventions exist: the trade convention "× = D / 4 + 1" (so 10 D ≈ 3.5×) and the Edmund Optics convention "× = D / 4". To be sure, check the actual focal length quoted by the manufacturer.
- · Photographic close-up ("plus") filters are sold in positive diopters: +2 D (500 mm focal length) for mild macro, +4 D (250 mm) stronger, +10 D (100 mm) for tiny subjects; they stack additively (two +2 D = +4 D).
- · References: ISO 11979-2:2024 (intraocular lens optical properties); ISO 8980-1:2017 (uncut finished spectacle lenses); ANSI Z80.1-2020 prescription tolerances; NIST SP 811 (the inch is defined as 0.0254 m exactly).
Frequently asked
Why does the diopter formula need focal length in metres, not mm?
The diopter is defined as the reciprocal focal length expressed in metres — 1 D = 1 m⁻¹. The choice of metres is deliberate: human eyes, camera lenses, magnifiers and other optical kit usually have focal lengths between 0.05 m (50 mm) and 5 m, so the diopter values they map to (roughly 0.2 D to 20 D) are tidy numbers that fit neatly on a prescription. Expressing reading glasses (focal length 500 mm) as "0.002 mm⁻¹" would be ugly. This tool accepts D, m, mm or inches as input and handles the unit conversion internally.
My reading-glasses prescription says "+2.00 D" — what focal length is that?
A +2.00 D add has a focal length of 1 / 2 = 0.5 m = 500 mm (≈ 19.7 in). Physically: in the relaxed eye state, this lens focuses parallel light 500 mm behind it; functionally, it lets a presbyopic eye view near print as if the page were optically pushed out to about 0.5 m. +1.00 D is a 1 m focal length (good for computer-distance work); +3.00 D is 333 mm (typical for ordinary print at 60+). Note: a full spectacle prescription also includes cylinder (astigmatism) and axis, so converting a D number to a focal length alone is not enough to grind glasses — only a qualified optometrist / ophthalmologist can prescribe.
A close-up filter is marked "+4". How does that interact with my 50 mm camera lens?
A photographic close-up filter is rated in diopters: "+4" means +4 D, i.e. focal length 1 / 4 = 0.25 m = 250 mm. Screwed onto a 50 mm prime, the thin-lens approximation just adds the powers: 50 mm lens = 1 / 0.05 = 20 D, plus 4 D → 24 D, combined focal length ≈ 1 / 24 = 41.7 mm. The practical payoff is closer focusing: a 50 mm lens that normally focuses to 0.45 m, with a +4 D filter and the lens set to infinity, now focuses at exactly 1 / 4 = 0.25 m — giving it macro-like reach. Close-up filters stack additively (+2 D + +4 D = +6 D), but each extra element adds aberrations (chromatic, field curvature); the usual advice is not to stack more than two.
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