How this calculator works
Magnification compares two lengths: how large the image is on the sensor and how large the object is in front of the lens. A pencil 100 mm long that fills 25 mm of sensor is recorded at 0.25 times, written 1:4. The same number comes out of the lens geometry as the image distance divided by the object distance, because similar triangles make the two ratios equal. With a thin lens, the image distance for a subject at u is f x (u - f) / u for the principal plane, and the magnification simplifies to f / (u - f). Adding an extension tube moves the lens away from the sensor; at infinity focus the extra distance e gives a magnification of e / f, which is why a 25 mm tube on a 50 mm lens reaches 1:2.
Formula
magnification m = image size / object size = image distance / object distance. Thin lens at focus distance u: m = f / (u - f). Extension tube at infinity focus: m = e / f. Reproduction ratio is m written as a ratio, so 0.25 is 1:4.
Worked example
A 100 mm object fills 25 mm of the sensor, so the magnification is 0.25 and the ratio is 1:4. If the image distance is 60 mm and the object distance is 300 mm, the magnification is 60 / 300 = 0.2, or 1:5. A 50 mm lens focused at 250 mm gives 50 / (250 - 50) = 0.25, with an image distance of 50 x 1.25 = 62.5 mm. A 25 mm extension tube on the same lens at infinity focus gives 25 / 50 = 0.5, or 1:2.
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Frequently asked questions
What magnification counts as macro?
A true macro lens reaches 1:1, where the image on the sensor is the same size as the subject. Many lenses sold as macro reach 1:2 or 1:3, which is why their specifications quote a maximum reproduction ratio.
Does an extension tube change the focal length?
No, it moves the lens farther from the sensor so it can focus closer. The magnification rises, the effective aperture falls and some light is lost, which is why the marked f-number understates the working f-number.
Why is the thin lens answer slightly off for real lenses?
Real lenses have a nodal point away from the physical centre and change focal length as they focus. At close range the difference is large enough that the marked focal length is only a guide.
Does sensor size change magnification?
No. Magnification is a property of the optics and the distances. A smaller sensor records a smaller field around the subject, so the subject fills more of the frame, but the image on the sensor is the same size.