A +10 diopter lens magnifies 2.5x or 3.5x depending on how you hold it. Enter the power, the focal length or the X on the label to see where to keep the page and how large fine print looks.
How much does a +20 diopter lens magnify?
A +10 diopter lens magnifies 2.5x or 3.5x depending on how you hold it. Enter the power, the focal length or the X on the label to see where to keep the page and how large fine print looks.
A lens of +20 diopters has a focal length of 1 / 20 of a meter, and how much it magnifies depends on how you hold it. The calculator below is set to lens power with 20 typed in and lengths in inches (in), and compares the view with the page seen without the lens at the standard near point of 25 cm, or 9.84 in.
You get two numbers. With the page at the focal point and a relaxed eye, magnification is 250 mm divided by the focal length, which works out to the diopters divided by 4. With the lens held right at the eye and the page brought closer, it rises by exactly 1. Labels can quote either figure, so one lens may be sold under two ratings, and below +4 diopters the relaxed-eye figure drops under 1x.
Know your own near point? Type it in to see the magnification for your eyes, add a lens-to-page distance to check that the view will be sharp, or a letter height to see how large the print will look.
Parameters
Enter data for calculations
💡 Fill in all required fields to unlock the calculate button
What the label promises and what the lens delivers
A magnifier marked +10 D does not have one magnification. With the page at its focal point, 10.00 cm away, and a relaxed eye it shows everything 2.50x larger; with the lens held at the eye and the page moved in to 7.14 cm it reaches 3.50x. This calculator starts from the diopters, the focal length or the X printed on the box and returns both numbers, the range of distances that gives a sharp view, and how large a small detail will look.
Before: "3x" on the box
Nothing tells you which formula the maker used, so you cannot know the lens or where to hold it.
After: both readings worked out
Counted as 250 mm / f + 1, it is a 12.50 cm, +8.00 D lens giving 2.00x to 3.00x. Counted as 250 mm / f, it is 8.33 cm, +12.00 D, giving 3.00x to 4.00x.
Six boxes, three of them optional
- You know the - diopters, focal length or the magnification on the label.
- Lengths in - millimeters, centimeters or inches, used for every distance and size.
- The value itself - for a label, also pick how it is counted: 250 mm / f + 1 or 250 mm / f.
- Your near point (optional) - the closest distance you read sharply without the lens. Empty means 25 cm.
- Lens to object (optional) - checks one holding distance for sharpness and magnification.
- Size of a detail (optional) - a letter or hallmark, to see how big it looks through the lens.
A 1 mm detail, before and after the lens
Without a lens, a detail 1 mm across looks like 1 mm at the standard near point of 25 cm. Through four common strengths it looks as large as:
| Lens | Focal length | Relaxed eye | Lens at the eye | Hold the object |
|---|---|---|---|---|
| +8 D | 125.00 mm | 2.00 mm | 3.00 mm | 83.33 to 125.00 mm |
| +16 D | 62.50 mm | 4.00 mm | 5.00 mm | 50.00 to 62.50 mm |
| +40 D | 25.00 mm | 10.00 mm | 11.00 mm | 22.73 to 25.00 mm |
| +80 D | 12.50 mm | 20.00 mm | 21.00 mm | 11.90 to 12.50 mm |
The stronger the lens, the narrower the band of sharp distances: 41.67 mm of play at +8 D, only 0.60 mm at +80 D. That is why strong loupes are held against the eye and brought to the object, not the other way round.
Where to hold a +10 D lens
The same lens at six distances from the page, lens close to the eye, near point 25 cm.
| Lens to page | Image forms at | Magnification | What you see |
|---|---|---|---|
| 12 cm | 60.00 cm, real | none | upside down, beyond the focal length |
| 10 cm | infinity | 2.50x | sharp, relaxed eye |
| 9 cm | 90.00 cm | 2.78x | sharp |
| 8 cm | 40.00 cm | 3.13x | sharp |
| 7.14 cm | 24.97 cm | 3.50x | sharp, the most this lens gives |
| 5 cm | 10.00 cm | none | blurred, image nearer than the near point |
One lens, two near points
Magnification compares the view through the lens with the best view you get without it, at your own near point. The same 10 cm lens gives 2.50x to 3.50x against the standard 25 cm, and 5.00x to 6.00x for an eye whose near point is 50 cm: the page is not larger, but that eye had to hold it twice as far away before. In inches, a +8 D lens with a 10 in near point gives 2.03x to 3.03x, held 3.30 to 4.92 in from the page, and a 0.06 in letter looks like 0.12 in to 0.18 in.
Magnifier questions with short answers
Related tools
Thin Lens Calculator
Image distance and magnification for any lens, including cameras and projectors - Open the calculator
Refractive Index Calculator
Glass, acrylic or polycarbonate: the material behind the lens - Open the calculator
Snell's Law Calculator
How light bends at each surface of the glass - Open the calculator
Scale Calculator
Enlargement ratios for drawings, maps and models - Open the calculator
Length Unit Converter
Millimeters, centimeters and inches for lens and loupe specifications - Open the calculator
See also
Calculator verified by the LiczGrupa.pl team
Content, formulas and results have been reviewed for accuracy and relevance by our team of specialists.
Reviewed by: Natalia Skrzek