How to Convert Magnification to Dioptors

Magnification can be converted to diopters using a mathematical formula.
••• lens image by Rog999 from

Magnification and diopters are actually two different measurements. Magnification is a measurement of the change in the size of the object viewed through the lens. Diopter is the measurement of the lenses ability to bend light. Because the lens’ function of bending light accomplishes the magnification, the two measurements are related and if the magnification is known the diopters can be calculated.

    Note the magnification power of the lens or lens system. A magnification power of 1x indicates a 100 percent or doubling of the perceived size of the object viewed through the lens when compared to the same object viewed with the naked eye. A 2.5x power lens would increase the size of the object by 250 percent. A 3-inch object would appear as 10 1/2 inches through the lens. The increase in the size of the object is 7 1/2 inches (3 inches times 2.5) plus the original size of the object.

    Calculate the diopters of the lens by multiplying the magnification by four. The amount the light is bent by one diopter amounts to an increase of 25 percent in the size of the viewed object. A lens with a light bending capacity of four diopters, stated as 4d, would double the size of the object and have a magnification of 1x.

    Calculate the total power of the lens by adding 1 to the magnification power. This is the measurement most often quoted in binoculars or telescopes because it is easier to understand. If a 1x magnification doubles the visual size of the object adding 1 to it, the formula for total power, results in 2x total power. The relationship between how the object is perceived and the total power is a more easily understood relationship.


    • Read the information with any binocular or telescope carefully before undertaking the conversion to diopters. Be sure the quoted measurement is magnification rather than total power. If the measurement is total power subtract 1 from it to determine magnification. The formula to determine diopters can then be applied.


About the Author

Keith Allen, a 1979 graduate of Valley City State College, has worked at a variety of jobs including computer operator, medical clinic manager, radio talk show host and potato sorter. For over five years he has worked as a newspaper reporter and historic researcher. His works have appeared in regional newspapers in North Dakota and in "North Dakota Horizons" and "Cowboys and Indians" magazines.

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