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Magnifying Power Calculator

Find the magnifying power of a lens.

How it is calculated

Enter the focal length f of the lens in centimetres. The tool uses the standard near point of 25 cm and gives two values. The first is M = 25 ÷ f, the magnification with the eye relaxed and the image far away (the object sits at the focal point). The second is M = 1 + 25 ÷ f, the magnification when the eye is focused so that the image appears at the near point, which is always one more. Both are shown to two decimals with a × sign. The focal length must be greater than zero, otherwise nothing is returned. The numbers describe a single thin lens held close to the eye. Compound microscopes and telescopes work differently and are not covered.

Worked example

A hand lens has a focal length of 5 cm. Relaxed-eye case: 25 ÷ 5 = 5.00×. Near-point case: 1 + 25 ÷ 5 = 1 + 5 = 6.00×. So the lens is sold as a 5× magnifier, and if you focus the image at your near point it looks about 6 times larger than the object seen by the naked eye at 25 cm. Halving the focal length to 2.5 cm would double the first figure to 10.00×.

Try this example →

Common mistakes

  • Entering the focal length in millimetres or metres; the formula needs centimetres, so a 50 mm lens is 5.
  • Entering the lens power in dioptres instead of the focal length. Convert first: f in cm = 100 ÷ dioptres.
  • Confusing the two results: the marketed value on loupes is usually 25 ÷ f, while 1 + 25 ÷ f applies when the image is placed at the near point.
  • Assuming a bigger lens diameter gives more magnification; only focal length matters here, and a shorter one magnifies more.
  • Applying the result to a viewer who is not at a 25 cm near point, such as a person who needs reading glasses, whose real magnification differs.

About this calculator

This calculator uses M = 25/f, where f is the focal length of a converging lens in centimeters and 25 cm is the standard near point — the closest distance at which a typical eye can focus comfortably. The formula compares the angular size of an object seen through the lens, held at its focal point, to the angular size it would have if viewed unaided at the near point, giving the apparent magnification of a simple single-lens magnifier.

Opticians, jewelers and hobbyists use this relationship to rate magnifying glasses and loupes, since a shorter focal length lens always yields higher magnifying power. Physics students studying geometric optics rely on the same formula to connect a lens's focal length to its practical usefulness as a simple magnifier, distinct from the higher magnifications achieved by compound microscopes and telescopes.

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Comments (1)

  • Editorial team

    Besides the number itself, a magnifier's focal length tells you how close you must hold it: the object sits near the focal point, so a lens with f = 2 cm, which gives 12.50 times for the relaxed eye and 13.50 times with the image at the near point, has to be held about 2 cm from what you are inspecting. Higher power therefore means a shorter working distance. Which loupe or magnifier are you rating, and which figure does its label quote?

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