What is the formula for magnification?

Linear magnification M equals the image height divided by the object height (M = hi/ho). For a lens or mirror it also equals negative image distance divided by object distance (M = -di/do). A positive M means the image is upright; a negative M means it is inverted. A magnitude greater than 1 means the image is enlarged.

What does a magnification of negative 2 mean?

A magnification of negative 2 means the image is twice the height of the object and is inverted. The negative sign indicates inversion; the number 2 indicates the image is two times larger than the object.

What is angular magnification?

Angular magnification compares the angle subtended by the image seen through an optical instrument with the angle subtended by the object seen with the naked eye. For a telescope it equals the objective focal length divided by the eyepiece focal length.

Magnification Calculator

Magnification describes how much larger or smaller an image appears compared with the original object, and whether the image is upright or inverted. There are two common ways to calculate it. The first uses image and object heights: M equals hi divided by ho. A positive result means the image is upright; a negative result means it is inverted. The second uses image and object distances in the thin lens or mirror context: M equals negative di divided by do, where di is the image distance and do is the object distance, both measured from the optical centre. Both formulas give the same result when applied consistently, and both are included in this calculator so you can choose whichever values you have available. Angular magnification is a separate measure used for optical instruments such as telescopes. For a telescope it equals the objective focal length divided by the eyepiece focal length. This calculator covers all three modes: from distances, from heights, and telescope angular magnification. Enter the values that you have and choose the mode that matches your situation. The tool is used in secondary school and university physics optics, photography and microscopy. Results assume ideal thin-lens geometry and do not account for aberrations or distortion.

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Calculation mode

Image distance di (cm)

Object distance do (cm)

Image height hi (cm) - for height mode

Object height ho (cm) - for height mode

Objective focal length (cm) - for telescope

Eyepiece focal length (cm) - for telescope

-2.00x

magnification

Image size relative to object2x larger

OrientationInverted

How it works

Three modes are available. Distance mode applies M = -di/do: a negative sign means the image is inverted relative to the object. Height mode applies M = hi/ho where positive values keep the sign consistent with the distance formula. Angular magnification for a telescope applies M = f_objective / f_eyepiece. In all modes, the absolute value of M gives the size ratio: a value of 2 means the image is twice the object size; a value of 0.5 means it is half the size. A positive M indicates an upright image and a negative M indicates an inverted image.

Worked example

A converging lens produces an image at di = 60 cm when the object is placed at do = 30 cm. Using the distance formula: M = negative 60 divided by 30 = negative 2.00x. The image is inverted (negative sign) and twice the size of the object (magnitude 2). These match the default values pre-filled in the calculator above.

Related calculators

Lens and Mirror Equation Calculator: solve 1/f = 1/do + 1/di for any unknown distance.
Refractive Index Calculator: calculate how light bends when passing between media of different densities.
Percent Error Calculator: compare your experimental magnification result with the theoretical value.
Velocity Calculator: calculate the speed of light in a medium from the refractive index.

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