Magnifying Power Calculator

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.

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.