Telescope Limiting Magnitude

This calculator estimates the faintest star magnitude your telescope can reveal, using the widely cited approximation m_lim ≈ 2.7 + 5×log₁₀(aperture in mm). That logarithmic relationship reflects how limiting magnitude scales with light-gathering area rather than aperture directly: doubling your telescope's diameter doesn't double how faint you can see, it adds about 1.5 magnitudes. The calculator applies that same formula to a 7mm dilated pupil to compute a naked-eye baseline (around magnitude 6.9), then reports the difference as your telescope's magnitude gain. Because the base formula assumes an idealized dark sky, the tool adjusts it for real conditions: for every mag/arcsec² your sky is darker than a reference suburban value of 20, it adds half a magnitude to the practical limit — so an excellent rural site (21.5) meaningfully outperforms the same telescope under city glow.

Light-gathering power is computed as the square of the aperture-to-pupil ratio, a direct area comparison. Two separate resolution figures are also reported: the Dawes limit (116/aperture in mm, in arcseconds), an empirical result the English astronomer William Rutter Dawes derived from testing observers on close double stars in 1867, and the slightly more conservative Rayleigh limit (138/aperture), which comes from the diffraction criterion Lord Rayleigh published in 1879. A rough star-count estimate extrapolates how many stars total should be visible at your practical limiting magnitude. Keep expectations grounded: this is a theoretical ceiling assuming excellent optics, good collimation, and steady seeing — atmospheric turbulence, eyepiece quality, and your own eye's dark adaptation can all push real-world performance below the number shown here.