Microscope vs telescope magnification
Why microscopes multiply powers while telescopes divide focal lengths, how to read the numbers on your gear, and when high magnification stops helping.
Two instruments, two formulas
A microscope and a telescope both build a final image from two optical stages, but they combine those stages differently. In a compound microscope the objective produces a magnified real image and the eyepiece magnifies that image again, so the total is the product of the two powers. In a telescope the objective forms an image of a distant object and the eyepiece acts as a magnifier of that image, giving a magnification equal to the objective focal length divided by the eyepiece focal length. This calculator applies the matching formula automatically once you pick the instrument.
Reading the numbers on your equipment
Microscope lenses are usually engraved with their power directly, such as 4x, 10x, 40x, or 100x on the objectives and 10x on the eyepiece. Telescope parts are labeled with focal lengths in millimeters instead, printed on the tube for the objective and on the barrel for each eyepiece. To use this tool, read those markings and drop them into the matching fields. Remember that a shorter telescope eyepiece produces a higher magnification, which often surprises newcomers.
When more magnification stops helping
Raising the magnification does not add detail beyond what the optics can resolve. In a microscope the useful ceiling is tied to the numerical aperture of the objective, and pushing past it gives empty magnification that only enlarges blur. In a telescope the aperture and atmospheric steadiness set the limit, and a common rule of thumb caps useful power at about two times the aperture in millimeters. Past that the image grows larger but dimmer and softer, so the best view often uses a moderate magnification.
Worked examples you can check
A standard school microscope with a 40x objective and a 10x eyepiece reaches 400 times, while switching to the 100x oil-immersion objective lifts it to 1000 times. A beginner telescope with a 1000 mm objective and a 25 mm eyepiece gives 40 times, and dropping to a 10 mm eyepiece raises it to 100 times. Each of these matches the number this calculator returns, so you can use them to confirm you are entering values in the right fields.