Magnification Calculator
Enter an image height and an object height in the same unit to get the linear magnification — plus its percentage — and see whether the image is enlarged, reduced, or the same size.
Ratio and percentage at once
Enter the image height and object height and the calculator returns the linear magnification (m = image / object) and the same value as a percentage.
Match the units
The two heights must use the same length unit — millimetres, centimetres, or inches all work, as long as both sides match.
What is magnification?
How big the image is versus the object
Magnification is the ratio of the size of an image to the size of the real object that produced it. The magnification calculator turns two measurements — the image height and the object height, both in the same length unit — into a single dimensionless number that tells you how many times larger or smaller the image is. It is the figure behind a microscope's "10×" eyepiece, the framing of a camera lens, and the projection scale of a slide on a screen. Because it is a ratio of two lengths, the units cancel out, so the answer is just a number (and the same number expressed out of 100 as a percentage).
Enter an image height and an object height in the same unit to get the magnification and its percentage instantly.
Linear magnification is the image height divided by the object height, and the percentage is simply that ratio multiplied by 100.
m = image height / object heightBoth heights must be in the same length unit so that the units cancel and the result is a pure ratio. Multiply the ratio by 100 to read it as a percentage: a magnification of 4 is 400 %, and a magnification of 0.25 is 25 %.
Suppose a projector forms an image 20 mm tall of an object that is 5 mm tall.
Divide image by object
20 / 5 = 4 — the image is four times the height of the object.
Read the magnification
The linear magnification is 4× — the image is enlarged.
Convert to a percentage
4 × 100 = 400 % — the image is 400 % of the object's size.
The magnification tells you at a glance how the image compares to the object. A value greater than 1 means the image is enlarged — bigger than the object, as with a magnifying glass, microscope, or projector throwing 4× onto a wall. A value less than 1 means the image is reduced — smaller than the object, which is what a camera does when it shrinks a whole landscape onto a tiny sensor (a magnification of 0.25, or 25 %). A value of exactly 1 means the image is the same size as the object, neither enlarged nor reduced. The percentage says the same thing on a familiar scale: 400 % is four times life size, 100 % is life size, and 25 % is a quarter of life size. In optics a negative sign would signal an inverted (upside-down) image, while a positive value means it is upright — so the sign carries information too, not just the size.
The ratio is exact, but a couple of practical points are worth keeping in mind.
Linear magnification with matching units
This calculator gives the linear (transverse) magnification — the ratio of two heights — not angular magnification, which is what a telescope or magnifying glass is rated by when no real image is formed. Keep both heights in the same length unit, or the ratio will be meaningless, and remember the object height cannot be zero because dividing by it is undefined.