Telescope Resolving Power & Light-Gathering Calculator

Kaava

How this is calculated

The single input is the aperture D, the clear diameter of the telescope's objective lens or primary mirror, given in millimetres. Aperture is the dominant factor in a telescope's performance, far more than magnification.

Resolution is the smallest angle between two stars the optics can still separate. The Dawes limit (116/D arcseconds) is an empirical rule for double-star splitting, while the Rayleigh criterion (138/D arcseconds) is the stricter diffraction-theory value; both shrink as aperture grows, so larger scopes resolve finer detail. Light-gathering power compares the objective's collecting area to a 7 mm dark-adapted human pupil, scaling as (D/7)² since area grows with the square of diameter. The limiting magnitude, 7.5 + 5·log₁₀(D_cm) with D converted to centimetres, estimates the faintest star visible under dark skies; magnitude is a reverse logarithmic scale, so higher numbers mean fainter stars.

These are idealised values assuming perfect optics, good collimation, and steady, transparent skies. Real performance is limited by atmospheric seeing (often around 1–2 arcsec), light pollution, optical quality, and the observer's eye. Use the results for comparison rather than as guaranteed observing thresholds.