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Magnification Calculator

Find the magnification and image size of a lens.

How it is calculated

The tool divides the image distance by the object distance: m = dᵢ ÷ dₒ, then multiplies by the object height: hᵢ = m × hₒ. Distances should be in the same unit (cm, mm or m), and the image height comes out in the unit you used for the object height.

Note the sign convention. Textbooks write m = −dᵢ/dₒ so that a negative m means an inverted image; this tool uses dᵢ/dₒ without the minus sign. So with a positive image distance (real image) it shows a positive m, even though a single converging lens inverts a real image. If you enter a negative image distance for a virtual image, the output turns negative. The object distance must be greater than zero. The tool does not find the focal length; the thin-lens relation 1/f = 1/dₒ + 1/dᵢ does that.

Worked example

An object 6 cm tall stands 30 cm from a lens and its image forms 15 cm behind the lens.

Magnification: 15 ÷ 30 = 0.50×. Image height: 0.50 × 6 = 3.00 cm, so the image is half the size of the object. With the thin-lens relation, 1/30 + 1/15 = 1/10, so this lens has a focal length of 10 cm, and a real image from it is inverted.

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Common mistakes

  • Assuming a positive result means an upright image. This tool omits the minus sign, so a real image from a converging lens is inverted even though m is shown as positive.
  • Mixing units, such as the object distance in metres and the image distance in centimetres. The ratio is then wrong by a factor of 100.
  • Entering the focal length in place of the image distance. The tool needs where the image forms, not the lens's focal length.
  • Entering a negative object distance. It must be greater than zero, or no result appears.
  • Expecting the image height to be in a fixed unit. It follows whatever unit you used for the object height.

About this calculator

Lens magnification is m = −dᵢ / dₒ (image distance divided by object distance), which equals the ratio of image height to object height, m = hᵢ / hₒ. The minus sign only says whether the image is upright or inverted; this calculator reports the size factor dᵢ / dₒ without it, so a real, inverted image shows as a positive number. This calculator derives both the magnification factor and the resulting image height directly from the object and image distances, following from the thin-lens equation.

Optics students use magnification to connect lens theory to observable image behavior, and it's core to designing real optical instruments — telescopes and microscopes combine multiple lenses' magnifications multiplicatively, camera lenses use it to determine how large a subject appears on the sensor, and optometrists reference related magnification concepts when discussing corrective lens power.

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Comments (1)

  • Editorial team

    If you know the focal length instead of the image distance, find the image distance first with 1/f = 1/dₒ + 1/dᵢ. For f = 10 cm and an object at 25 cm, the image forms at about 16.67 cm, and entering that gives roughly 0.67×. The tool itself only takes the three measured values. Are you working on a camera, a microscope or a classroom exercise? Tell us if you would like focal length as an input.

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