Magnification Calculator

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.

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.