Magnification Calculator
Find magnification from object and image distances.
Results update as you type.
How it works
Magnification measures how much larger or smaller an image is compared to the object, and this calculator computes it from the object and image distances. You enter the object distance and image distance, and optionally the object height, and it returns the magnification, the image height, and the orientation. The magnification equals minus the image distance divided by the object distance. Its absolute value gives the scale: a magnification of 2 means the image is twice as tall as the object, while 0.5 means it is half as tall. The sign carries important information about orientation: a negative magnification indicates an inverted image, typical of a real image from a converging lens, and a positive magnification indicates an upright image, as with a virtual image. If you supply the object height, the calculator multiplies by the magnification to give the image height, including its sign to show whether it is inverted. Magnification is central to understanding cameras, telescopes, microscopes, magnifying glasses, and projectors, where the goal is often to enlarge or reduce an image by a known factor. This calculator complements the lens equation, which finds the image distance in the first place. The object distance must not be zero. Enter the object and image distances, and optionally the object height, to find the magnification and image height.
m = −di/do ; image height = m × object height
Magnification is minus the image distance divided by the object distance. Its magnitude tells you how many times larger or smaller the image is, and its sign gives the orientation: negative for an inverted image, positive for an upright one. Multiplying magnification by the object height gives the image height.
Source:Optics
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter object distance (do) and image distance (di).
- 2
Adjust the options
Adjust object height (optional) if they apply — sensible defaults are already set.
- 3
Read your result
Magnification updates instantly as you type — no button to press.
Frequently asked questions
How is magnification calculated?
Magnification equals minus the image distance divided by the object distance. The negative sign follows the standard optical convention. The magnitude tells you the scale of the image relative to the object, and the sign tells you the orientation. If you know the object height, you can multiply by magnification to find the image height.
What does a negative magnification mean?
A negative magnification means the image is inverted, or upside down, relative to the object. This is typical of a real image formed by a converging lens when the object is beyond the focal length. A positive magnification means the image is upright, as with a virtual image seen through a magnifying glass or a diverging lens.
What does a magnification greater than one mean?
A magnification with an absolute value greater than one means the image is larger than the object, an enlargement. A value between zero and one means the image is smaller, a reduction. A magnitude of exactly one means the image is the same size as the object. The sign separately indicates whether the image is upright or inverted.
How do I find the image height?
Multiply the magnification by the object height. The result is the image height, and its sign shows orientation: a negative image height means the image is inverted. For example, a magnification of minus two applied to a four-centimeter object gives an eight-centimeter image that is inverted. Enter the object height to have the calculator do this.
How does this relate to the lens equation?
The lens equation finds the image distance from the focal length and object distance, and the magnification formula then uses that image distance to determine size and orientation. Together they fully describe image formation by a lens. If you do not yet know the image distance, use the lens equation calculator first, then apply this magnification calculator.