A lens’s diopter is just the reciprocal of the focal length of the lens, with units of 1/(meters); equivalently, the focal length of a lens is just the reciprocal of the diopter value, in meters. So a +1 diopter corresponds to a focal length of 1 meter; +2 diopter corresponds to 0.5 m (500 mm); +10 diopter corresponds to 0.1 m (100 mm); etc.

Diopter units are particularly convenient to use when combining lenses together: their equivalent diopter value is just the sum of the individual diopters. For example, suppose a 50 mm lens has a +2 diopter close-up lens mounted on the front. The diopter value of the lens is 1/50mm = 1/0.05m = 20. So the total equivalent diopter value is 20 + 2 = 22, which corresponds to a focal length of about 0.045 m, or 45 mm.

But wait, if the diopter of the combined lens plus close-up lens is just the sum of the diopters, does that work for more than two lenses combined? Absolutely. Adding another +3 diopter to the previous combination results in a total diopter of 25, which corresponds to a focal length of 0.04 m, i.e., 40 mm.

**How can I calculate its effect on close focusing distance?**

Roughly speaking (see note below), the close focusing distance will be reduced according to:

*x*_{new} = *x*_{old} / ( *D* ∙ *x*_{old} + 1) ,

where

*x*_{new} is the close-focusing distance with the close-up lens applied;
*x*_{old} is the original close-focusing distance (without the close-up lens);
*D* is the diopter of the close-up lens.

For example, suppose a lens can focus as closely as 500 mm. With a +4 diopter close-up lens attached, the combination can now focus as close as 500 mm / (4 m^{-1} ∙ 0.5 m + 1) = (500/3) mm ≈ 167 mm.

*Note:* The reason I say “roughly speaking” is that these distances are based on distances from the center of an idealized single *thin lens* with negligible thickness, such that the *thin lens formula* can be used. Real-world optical lens elements have thickness, and of course real-world photographic lens systems consist of several individual lens elements and lots of air space in between many of them. Additionally, when talking about a camera lens’s *Minimum Focus Distance* (MFD), the MFD is measured from the camera’s film/sensor plane. Thus, the MFD includes the image-side focus object-side focus distances in the thin lens formula, as well as the substantial length of most of the lens assembly (which is usually not constant as a lens focuses). But the “close focus distance” discussed above is merely the mathematically-described object-distance side of the then lens. Thus, this formula is a guide to judge what diopter you might need.

**Infinity focus**

With a close-up lens, you will no longer be able to focus far away. The furthest you will be able to focus is simply the focal length of the close-up lens – i.e., the reciprocal of the diopter, in meters. So with a +4 diopter you cannot focus any further away than 0.25 meters (250 mm).

**How much magnification can I get from the combination?**

Assuming you’re working at the closest focus distance possible, both before using the close-up lens, and with the new closer focus distance with the close-up lens, then the image will be magnified (*D* ∙ *x*_{old} + 1) larger than it was without the close-up lens.

For example, if a lens’s closest focus distance is 500 mm, then with a +4 diopter close-up lens and focus at the new close focus distance of *x*_{new}, the image will be (4 m^{-1} ∙ 0.5 m + 1) = 3 times larger than without the close-up lens.

Note that the imaging system’s magnification is *not* 3:1. Rather, the ratio of magnification after vs. before, *M*_{new} / *M*_{old}, is 3.