Diopter to mm Calculator

What a Diopter Measures

A diopter is one divided by the focal length in meters. Flip it into millimeters and you get the formula this page runs on: focal length in mm = 1000 / diopters. A +1.00 lens focuses parallel light at 1,000 mm, a +2.00 lens at 500 mm, a +4.00 lens at 250 mm.

The unit is not one of the named units in the International System. NIST's SI units page lists the meter as the base unit of length and the 22 derived units with special names, and the diopter is not among them, so optical power is formally inverse meters, m^-1.

Sign matters. A plus lens converges light and has a real focus. A minus lens diverges it, and the focus sits behind the glass where no screen can catch it, so the focal length is written negative. A -2.00 D lens has a focal length of -500 mm.

The Formula, Both Directions

Go the other way with D = 1000 / f. A 300 mm lens is 3.33 D, a 250 mm lens is 4.00 D, a 40 mm eyepiece is 25.00 D. The two directions are exact inverses.

The relation is a hyperbola, not a line. Doubling power halves distance: +2.00 D sits at 500 mm, +4.00 D at 250 mm. Halving power doubles it: +0.50 D sits at 2,000 mm. That is why a step from +2.00 to +3.00 moves the near point from 500 mm to 333.3 mm, while +1.00 to +2.00 moves it from 1,000 mm to 500 mm.

The error in forum posts is averaging focal lengths. A +1.00 and a +4.00 filter together average 1,000 mm and 250 mm into 625 mm, which would be 1.60 D. The real answer is 5.00 D, or 200 mm, because powers add and focal lengths do not. For thin lenses in contact, D total = D1 + D2 + D3, the rule Michigan Technological University gives for stacked close-up filters. Two +2.00 filters make +4.00 D and 250 mm, not 500 mm.

Reading Glasses: What the Number on the Rack Means

Over-the-counter readers run from +1.00 D to +3.00 D, according to the Mayo Clinic's presbyopia treatment page. The label is a lens power, not a magnification factor, so a +2.00 pair is not 2x anything. It is a lens that focuses parallel light at 500 mm.

That number sets the distance where the lens leaves the eye with nothing to do. Hold a page at 500 mm through a +2.00 lens and the print arrives as parallel rays. Move it to 400 mm and the page sends 1000 / 400 = 2.50 D into the lens; the lens adds 2.00 D, so the eye supplies the last 0.50 D.

Two cautions. The rack power is the same for both eyes, and a spherical reader cannot correct astigmatism. The number also assumes the lens sits about 12 mm from the cornea, the vertex distance described below. Magnifying spectacles are Class I devices under 21 CFR 886.5840, a category the FDA exempts from premarket notification.

Close-Up Filters: Stacking Adds Diopters

Screw-in close-up filters for cameras are sold by diopter: +1, +2, +4, often as a set of three. The filter does not change the camera lens, it adds power in front of it.

With the host lens at infinity, working distance comes from the filter alone: 1000 / D millimeters. A +4 filter puts the subject at 250 mm and a +2 at 500 mm. Stack a +1 on a +2 and the pair acts as +3 D, so the distance drops to 333.3 mm. That sum rule is the one in Michigan Technological University's close-up lens guide, with the caveat that the filters need to sit close together.

Put the stronger filter closest to the camera lens, and stop at two in most cases, since three or more cost contrast. A +7 stack leaves 142.9 mm of room, about 5.6 in, close enough to shade the subject with the lens hood.

Magnification and Working Distance Together

At infinity focus, magnification is host focal length in millimeters times diopters, divided by 1000: m = F x D / 1000. A 100 mm lens with +4 D gives 0.40x. A 50 mm lens with the same filter gives 0.20x. Filters do more on long lenses, which is why they pair with 85 mm to 200 mm glass rather than a wide angle.

Two setups can reach the same magnification with different room. A 100 mm lens with +4 D gives 0.40x at 250 mm. A 200 mm lens with +2 D also gives 0.40x, with 500 mm of working distance and easier light.

Combined focal length is 1000 / (1000 / F + D). A 100 mm lens with +4 D becomes 71.4 mm, with +3 D it becomes 76.9 mm, and a 50 mm lens with +3 D becomes 43.5 mm. Focusing the host lens closer than infinity adds magnification and shortens the distance.

Hand magnifiers use a different convention, M = D / 4 + 1 on a 250 mm reference: +5 D is sold as 2.25x, +10 D as 3.5x, +2 D as 1.5x. That is angular magnification, not the linear ratio a photographer means by 0.40x.

Vertex Distance: Why +10.00 D Is Not +10.00 D at the Eye

A prescription is written for a lens sitting 12 mm to 14 mm in front of the cornea. That gap is the vertex distance, and moving the lens changes the power the eye receives: F at the cornea = F at the glasses / (1 - d x F), with d in meters.

Run +10.00 D at 12 mm. The denominator is 1 - 0.012 x 10 = 0.88, and 10 / 0.88 = 11.36 D, so the eye sees 1.36 D more plus than the frame says. Run -8.00 D: 1 - 0.012 x (-8) = 1.096, and -8 / 1.096 = -7.30 D, which is 0.70 D weaker. Plus powers gain as the lens nears the eye, minus powers lose, and both grow with the square of the power.

The National Academy of Opticianry teaches the same conversion through focal length: f = 1000 / D, add the change in vertex distance, then D = 1000 / f. Its shortcut, D squared times the shift in millimeters divided by 1000, gives 0.2 D for +10.00 moved 2 mm. The exact figure for 12 mm to 14 mm is 11.63 - 11.36 = 0.27 D.

Worked Examples You Can Check

Example 1, +3.00 D on a 50 mm lens. Focal length is 1000 / 3 = 333.3 mm, or 13.1 in. Magnification is 50 x 3 / 1000 = 0.15x. The combined focal length is 1000 / (1000 / 50 + 3) = 43.5 mm.

Example 2, +1 and +4 stacked on a 100 mm lens. The powers add to 5.00 D, so the working distance is 200.0 mm, or 7.9 in. Magnification is 100 x 5 / 1000 = 0.50x, and the combined focal length is 1000 / (10 + 5) = 66.7 mm.

Example 3, +9.00 D at a 14 mm vertex. The denominator is 1 - 0.014 x 9 = 0.874, and 9 / 0.874 = 10.30 D at the cornea. At 12 mm the same glasses give 9 / (1 - 0.108) = 10.09 D, so 2 mm of standoff is worth 0.21 D in this range.

Example 4, backward. A 300 mm lens is 1000 / 300 = 3.33 D, a 167 mm lens is 5.99 D, and a 40 mm eyepiece is 25.00 D. The widget returns those same numbers in the reverse mode.

Where the Conversion Stops Being True

The formula assumes a thin lens, with all the bending in one plane. Real filters have two surfaces, a few millimeters of glass and a ring that holds them apart. Stack two and the gap pushes the true power a little below the simple sum. For +1 and +2 the error is well under a tenth of a diopter, and it grows with stronger filters and longer stacks.

Diopters say nothing about field of view, edge sharpness, fringing or transmission. Two +4 filters from different makers carry the same number and make different pictures.

For eyes, this arithmetic is a check, not a prescription. A refraction carries a sphere, a cylinder, an axis and a reading add for each eye, plus a vertex distance someone measured. Astigmatism needs a cylinder that no spherical conversion supplies. If a number here disagrees with your prescription, the prescription wins.