Last updated: 2026-07-01

Magnification Calculator

Magnification describes how big an image is compared with the object that produced it, and which way up it is. For a thin lens or a spherical mirror the lateral magnification is $m = -\frac{d_i}{d_o}$, where $d_o$ is the object distance and $d_i$ is the image distance. The same number is the ratio of heights, $m = \frac{h_i}{h_o}$, so once the magnification is known the image height follows from $h_i = m\,h_o$.

This calculator takes the object distance, the image distance and the object height, then returns the magnification and the image height, along with whether the image is upright or inverted and enlarged or reduced.

What the sign means

The magnification carries two pieces of information at once. Its magnitude is how many times larger or smaller the image is than the object: a value of 2 doubles the size, a value of 0.5 halves it. Its sign records the orientation. A negative magnification means the image is inverted — flipped upside down — while a positive magnification means it stays upright.

A positive image distance corresponds to a real image: for a lens it forms on the far side, for a mirror it forms in front of the reflecting surface, and it can be projected onto a screen. A real image always comes with a negative magnification, so it is inverted. A negative image distance corresponds to a virtual image on the same side as the object, like the view through a magnifying glass; it has a positive magnification and stays upright.

Formula

Worked example

A camera lens forms an image of a 5 cm tall object. The object sits 30 cm in front of the lens and the image forms 15 cm behind it, so $d_o = 30\ \text{cm}$, $d_i = 15\ \text{cm}$ and $h_o = 5\ \text{cm}$. The magnification is:

The image height is then:

The magnitude of 0.5 means the image is half the size of the object, and the minus sign means it is inverted — exactly what happens when a camera focuses a scene onto its sensor.

Lenses and mirrors

The lateral magnification has the same form for a thin lens and a spherical mirror, provided you use each one's standard sign convention for the image distance. If you only know the focal length and object distance, first find the image distance from the thin lens equation $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$ (lens) or the mirror equation of the same shape, then read the magnification here.

Limitations

The relation $m = -\frac{d_i}{d_o}$ assumes paraxial rays — those that stay close to the optical axis and make small angles with it — and a lens thin enough that its thickness can be ignored. Real optical systems suffer from aberrations that distort the size and shape of the image away from the axis, so for precise design these effects must be modelled separately. For everyday estimates the simple magnification formula is accurate and quick.