Optical Magnification Calculator
Find the total magnification of a microscope or telescope from objective and eyepiece focal lengths. Use it when selecting lens combinations or checking whether a setup meets a target magnification.
About this calculator
For a refracting telescope the angular magnification is M = f_objective / f_eyepiece, where both focal lengths are in the same units. A long objective and short eyepiece yield high magnification. For a compound microscope the formula is M = (L / f_objective) × (250 / f_eyepiece), where L is the optical tube length (distance between objective rear focal point and eyepiece front focal point) and 250 mm is the conventional near-point distance of the human eye. The first factor gives the lateral magnification of the objective and the second gives the angular magnification of the eyepiece acting as a loupe. Total magnification is therefore the product of these two independent stages, making it easy to upgrade one component without recalculating the entire system.
How to use
Microscope example: objective focal length = 4 mm, eyepiece focal length = 10 mm, tube length L = 160 mm. Step 1: Objective magnification = L / f_obj = 160 / 4 = 40×. Step 2: Eyepiece magnification = 250 / f_eye = 250 / 10 = 25×. Step 3: Total = 40 × 25 = 1000×. Telescope example: f_obj = 900 mm, f_eye = 25 mm. Total = 900 / 25 = 36×. Swapping to a 10 mm eyepiece gives 900 / 10 = 90×.
Frequently asked questions
How do I calculate the total magnification of a compound microscope?
Use M = (L / f_objective) × (250 / f_eyepiece), where L is the mechanical tube length in mm, f_objective is the objective focal length in mm, and 250 mm is the standard near-point distance. For a 40× objective (f = 4 mm, L = 160 mm) paired with a 10× eyepiece (f = 25 mm) you get (160/4) × (250/25) = 40 × 10 = 400×. Most modern infinity-corrected microscopes include the tube lens in the stated objective magnification, so you simply multiply the marked objective power by the eyepiece power.
Why does telescope magnification only depend on focal lengths and not tube length?
A telescope forms an image at infinity (for a relaxed eye), so the objective focal length alone determines where parallel rays converge and the eyepiece focal length determines how those rays are re-collimated. The tube length cancels out in the angular magnification derivation, leaving M = f_obj / f_eye. This is different from a microscope, which must form a real intermediate image at a finite distance, making tube length essential to the calculation.
What limits the maximum useful magnification of a telescope or microscope?
Optical magnification is ultimately constrained by diffraction and, for telescopes, by atmospheric seeing. Increasing magnification beyond the diffraction limit just enlarges a blurry image without revealing finer detail — known as empty magnification. For a telescope the practical limit is roughly 50× per inch of aperture (about 2× per mm). For microscopes the resolution limit is set by the numerical aperture of the objective, typically allowing useful magnification up to about 1000× NA. Beyond that, detail cannot be resolved no matter how powerful the eyepiece.