Optical Magnification Calculator
Find the magnification of a lens or mirror from the image and object distances or their heights.
Input pair
cm
cm
cm
Inverted · Enlarged
- 1
Ratio of distances di ÷ do
20 ÷ 10 = 2 - 2
Magnification m = −(di ÷ do)
−2 = -2Negative sign indicates an inverted image.
How does this calculator work?
Magnification is m = −di/do = hi/ho. Enter either the image and object distances or their heights. A negative result means the image is inverted; a positive one means upright. When |m| exceeds 1 the image is enlarged, and when it is below 1 the image is reduced in size.
Formula
How this is calculated
Magnification compares the size of the image to the size of the object. Using the thin-lens (or mirror) geometry, it equals the negative ratio of image distance to object distance, m = −di/do, which is also equal to the ratio of image height to object height, m = hi/ho. Choose the input pair you know: distances (di, do) or heights (hi, ho).
The sign carries orientation information. A negative magnification means the image is inverted relative to the object, while a positive value means it is upright. The absolute value gives the scale: |m| greater than 1 means the image is enlarged, |m| less than 1 means it is reduced, and |m| = 1 means it is the same size. If you also supply the object height in distance mode, the calculator derives the image height as hi = m·ho; in height mode, supplying the object distance derives the image distance as di = −m·do.
Distances and heights must use the same length unit (cm here, but any consistent unit works since magnification is dimensionless). The object distance (or object height) cannot be zero, which would make the ratio undefined. Sign conventions follow the standard real-is-positive convention where real images have positive di and a negative magnification.
Frequently asked questions
A negative sign comes from m = −di/do and indicates the image is inverted compared to the object. A positive magnification means the image is upright.
It means the image is larger than the object (enlarged). If |m| is less than 1 the image is smaller (reduced), and if it equals 1 the image is the same size.
Pick one pair per calculation. The two formulas are equal, so distances and heights give the same magnification, but each mode solves for the matching missing quantity.
Also known as
TG we-Calculate Editorial Team. (2026). Optical Magnification Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/magnification-calculator
TG we-Calculate Editorial Team. "Optical Magnification Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/magnification-calculator.
TG we-Calculate Editorial Team, "Optical Magnification Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/magnification-calculator
@misc{wecalculate_magnification_calculator, title = {Optical Magnification Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/magnification-calculator}}, year = {2026}, note = {TG we-Calculate} }
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