Magnifier Calculator (Magnifying Glass Power from Focal Length)
Magnification of a magnifying glass or loupe from its focal length, in both common conventions, with its power in dioptres — or the focal length for a stated magnification.
Results
The dashed line marks the value you entered.
What this tool does
A magnifier's '×' rating compares the angle an object covers through the lens with the angle it covers to the naked eye at the conventional near point of 250 mm. With the object at the focal point and the eye relaxed, the magnification is 250 ÷ f; move the lens until the image sits at 250 mm and it is 1 + 250 ÷ f — one more. Makers do not always say which they quote, so a '10×' loupe means a focal length of about 25 mm. A shorter focal length gives more magnification but a smaller field of view, and the object has to be held about one focal length from the lens.
Formula
M = 250 ÷ f (relaxed eye) · M = 1 + 250 ÷ f (image at 250 mm) · power = 1000 ÷ f (dioptres) · f in mm
Variables
| Symbol | Meaning | Unit |
|---|---|---|
f | Focal length of the magnifier | mm |
mg | Magnification you want (×) | × |
MR | Magnification, relaxed eye (object at the focal point) | × |
MC | Magnification, image at the near point (250 mm) | × |
DP | Lens power | D |
FM | Focal length that gives that magnification | mm |
Worked example
- Focal length of the magnifier50 mm
- Magnification, relaxed eye (object at the focal point)5.00 ×
- Magnification, image at the near point (250 mm)6.00 ×
- Lens power20.0 D
Limitations
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.