Magnification Calculator
Compute the optical magnification of a lens or mirror by comparing the image height to the object height. Use it to determine whether a lens enlarges, reduces, or inverts an object.
About this calculator
Magnification (m) describes how much larger or smaller an image is compared to the original object. The linear magnification formula is: m = imageHeight (hᵢ) / objectHeight (hₒ). A magnitude greater than 1 means the image is larger than the object; less than 1 means it is smaller. A negative sign indicates the image is inverted relative to the object, which occurs for real images formed by converging lenses when the object is beyond the focal point. Magnification is dimensionless because it is a ratio of two lengths. It is also related to the ratio of image distance to object distance: m = −dᵢ/dₒ, offering an alternative way to compute it when distances are known instead of heights.
How to use
Imagine a 5 cm tall flower placed in front of a converging lens. The lens forms an image that measures 15 cm tall on a screen. Enter objectHeight = 5 cm and imageHeight = 15 cm. The calculator computes: m = 15 / 5 = 3. A magnification of 3 means the image is three times the size of the object. If the image were inverted, you would enter imageHeight as −15 cm, giving m = −3, confirming a real, inverted image three times the original size.
Frequently asked questions
What does a negative magnification value mean in optics?
A negative magnification means the image is inverted — flipped upside down relative to the object. This occurs when a converging lens forms a real image with the object placed beyond the focal length. In contrast, a positive magnification means the image is upright, which is typical of virtual images produced by diverging lenses or by a converging lens used as a magnifying glass. The absolute value of magnification still tells you the size ratio regardless of orientation.
How is magnification related to object and image distances?
Magnification can be calculated from distances using m = −dᵢ/dₒ, where dᵢ is the image distance and dₒ is the object distance. This formula is equivalent to hᵢ/hₒ and is often more convenient when you know the lens setup but haven't measured image height. The negative sign in the distance formula reflects the sign convention: a real image (positive dᵢ) on the opposite side of the lens from the object produces an inverted image (negative m). Both formulas are fully consistent with the thin-lens equation.
When would you use a magnification calculator in real life?
Magnification calculators are used by photographers to understand macro lens reproduction ratios, by biologists configuring microscope eyepieces and objectives, and by engineers designing projection systems or optical instruments. In medical imaging, knowing magnification ensures structures are measured at true scale. Even in everyday life, comparing the magnification of reading glasses or binoculars helps consumers choose the right optical tool for their needs.