Optical Magnification Calculator
Find the total magnification of a microscope or telescope from objective and eyepiece focal lengths. Useful for students, lab technicians, and amateur astronomers configuring optical instruments.
About this calculator
Total magnification depends on which type of compound optical system you are using. For a telescope, the formula is simple: M = f_objective / f_eyepiece, where both focal lengths are in the same units. A long objective paired with a short eyepiece yields high magnification. For a compound microscope the standard formula is: M = (L / f_objective) × (250 / f_eyepiece), where L is the mechanical tube length (the distance between the rear focal point of the objective and the front focal point of the eyepiece, typically 160 mm) and 250 mm is the conventional near-point distance of the human eye. The first factor gives the real intermediate magnification produced by the objective, and the second factor gives the angular magnification of the eyepiece acting as a magnifier. Both formulas assume the eye is relaxed at the eyepiece exit pupil.
How to use
Example 1 — Telescope: objective focal length = 900 mm, eyepiece focal length = 25 mm. M = 900 / 25 = 36×. Example 2 — Microscope: tube length L = 160 mm, objective focal length = 4 mm, eyepiece focal length = 10 mm. Step 1: objective magnification = 160 / 4 = 40×. Step 2: eyepiece magnification = 250 / 10 = 25×. Step 3: total M = 40 × 25 = 1000×. Select your system type in the calculator, enter those three values, and the result appears immediately — no manual multiplication required.
Frequently asked questions
Why do microscopes and telescopes use different magnification formulas?
The difference reflects their optical architectures. A telescope forms an image at infinity and you compare angular sizes, so only the ratio of focal lengths matters. A microscope forms a real, enlarged intermediate image inside the tube at a fixed distance from the objective, and that intermediate image is then further magnified by the eyepiece. The tube-length term in the microscope formula captures that first real magnification stage. Using the telescope formula for a microscope would dramatically underestimate the total magnification.
What is the standard tube length used in microscope magnification calculations?
The historical standard mechanical tube length for finite-conjugate microscopes is 160 mm, established by early German optical manufacturers and still used in many educational and laboratory instruments. Modern research-grade microscopes often use infinity-corrected objectives with no fixed tube length, instead relying on a separate tube lens (typically 165–200 mm focal length depending on the manufacturer) to form the intermediate image. When using this calculator, enter the actual mechanical tube length of your specific microscope for the most accurate result.
How do I choose the right eyepiece focal length to avoid empty magnification?
Empty magnification occurs when you magnify beyond the resolving power of the objective — you get a larger but blurrier image with no extra detail. A practical rule for telescopes is that useful magnification tops out at about 50× per inch (2× per mm) of aperture. For microscopes, total magnification beyond roughly 1000× per mm of numerical aperture yields empty magnification. To stay within useful limits, choose an eyepiece focal length that keeps the total magnification below these thresholds. Shorter eyepiece focal lengths always increase magnification, so erring toward a longer eyepiece is safer when resolution is the bottleneck.