Lens Magnification Calculator
Lateral magnification tells you how large an image is relative to the object, and whether the image is upright or inverted. The formula is m = -di/do, where di is the image distance from the lens and do is the object distance. A negative value of m means the image is inverted; a positive value means it is upright. The magnitude tells you the size ratio: |m| = 2 means the image is twice the object height. Enter the object and image distances (using consistent units) along with the object height to find the magnification and the actual image height. Sign conventions: object distance is positive for a real object (standard), image distance is positive for a real image on the far side of the lens and negative for a virtual image.
Magnification formula
m = -di / do
The image height is: hi = m x ho. A negative m means the image is inverted. The magnitude |m| is the size ratio of image to object.
Interpreting magnification
- m = -2: real, inverted image that is twice as large as the object.
- m = +0.5: virtual, upright image that is half the size of the object (diverging lens or object inside focal point).
- m = -1: real, inverted image exactly the same size as the object (object placed at 2f from a converging lens).
- Large |m| (telescope or microscope eyepiece) arises when the image distance greatly exceeds the object distance.
Lens magnification: frequently asked questions
What does the magnification formula m = -di/do mean?
The lateral magnification m equals negative image distance divided by object distance. The negative sign means that a real image (positive di) formed by a single lens is inverted relative to the object. A virtual image (negative di) produces positive m, meaning the image is upright.
What does a negative magnification value mean?
A negative magnification means the image is inverted (upside down) compared to the object. This happens when the object is beyond the focal point of a converging lens, producing a real image on the other side.
What does a magnification greater than 1 mean?
A magnitude greater than 1 (|m| > 1) means the image is larger than the object. A magnitude less than 1 means the image is smaller. A magnification of exactly 1 (or -1) means the image is the same size as the object.
How do I calculate the image height from magnification?
Image height hi = m x ho, where ho is the object height. If the object is 5 cm tall and m = -2, the image is 10 cm tall and inverted. If m = 0.5, the image is 2.5 cm tall and upright (virtual image).
Does this formula apply to mirrors as well?
Yes. The lateral magnification formula m = -di/do applies to both thin lenses and spherical mirrors, using the same sign conventions. For mirrors, object and image distances are measured from the mirror surface rather than a lens.
Official sources
- OpenStax University Physics Volume 3, Chapter 2: Geometric Optics and Image Formation. openstax.org.
- NIST Physical Measurement Laboratory. physics.nist.gov.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.