Magnification of a Lens Calculator

Lens magnification (m) represents the ratio of the image size projected onto the sensor compared to the actual size of the subject. The underlying physics relies on thin lens equations and geometry. First, an intermediate radial factor r is calculated using the focal distance (F) and focal length (f): r = sqrt(focusDistance^2 / 4 - focalDistance * focalLength). Next, object distance and sensor distance are derived to find how far the light travels. Finally, magnification is computed as the ratio of the effective sensor distance (including any extension tubes) to the object distance: m = (sensorDistance + extTube) / objectDistance.

Imagine you are configuring a macro photography setup using a lens with a focal length of 50 mm. You set your focus distance to 200 mm and attach a 12 mm extension tube to achieve closer focusing. Using our governing equations, the intermediate factor r evaluates to approximately 86.6 mm. The object distance computes to 186.6 mm, while the baseline sensor distance computes to 13.4 mm. Adding the 12 mm extension tube gives an effective sensor distance of 25.4 mm. Dividing this by the object distance (25.4 / 186.6) yields a final magnification ratio of approximately 0.136x, meaning the projected image on your camera sensor is about 13.6% the size of the actual subject.

When measuring distances for your calculation, always measure from the principal planes of the lens rather than the outer barrel or front element. If you use extension tubes, remember that they increase the effective sensor-to-lens distance, which boosts magnification but reduces your maximum focus distance to infinity. Always account for cropping factors if you are comparing different digital sensor sizes in photography.