Telescope Resolving Power & Light-Gathering Calculator
Enter your telescope's aperture to estimate its angular resolution, how much light it collects versus the naked eye, and the faintest stars it can show.
mm
Smallest separation of two stars this aperture can split (Rayleigh: 0.69 arcsec)
- 1
Aperture
D = 200 mm = 200 - 2
Dawes resolution limit
116 ÷ 200 = 0.580Empirical rule: 116 / D arcseconds for equal-brightness double stars.
How does this calculator work?
Enter your telescope's aperture in millimetres to get its resolution and reach. Dawes limit is 116/D and Rayleigh is 138/D arcseconds, light-gathering power is (D/7)² times the naked eye, and limiting magnitude is about 7.5 + 5·log₁₀ of the aperture in centimetres. Larger apertures resolve finer detail and reveal fainter stars.
Formula
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.
Frequently asked questions
Aperture sets both resolution and light grasp. A larger objective collects more light and resolves finer detail, letting you use higher magnification usefully. Over-magnifying a small aperture only yields a dim, blurry image with no extra detail.
Both describe resolution. The Dawes limit (116/D) is an empirical figure for splitting equal-brightness double stars and is slightly more optimistic. The Rayleigh criterion (138/D) comes from diffraction theory and is the more conservative, formally defined limit.
Often not. The 7.5 + 5·log₁₀(D_cm) estimate assumes dark, transparent skies and good optics. Light pollution, atmospheric haze, and seeing typically make the practical limit a magnitude or more brighter than the calculated value.
Also known as
TG we-Calculate Editorial Team. (2026). Telescope Resolving Power & Light-Gathering Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/telescope-resolving-power-calculator
TG we-Calculate Editorial Team. "Telescope Resolving Power & Light-Gathering Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/telescope-resolving-power-calculator.
TG we-Calculate Editorial Team, "Telescope Resolving Power & Light-Gathering Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/telescope-resolving-power-calculator
@misc{wecalculate_telescope_resolving_power_calculator, title = {Telescope Resolving Power & Light-Gathering Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/telescope-resolving-power-calculator}}, year = {2026}, note = {TG we-Calculate} }
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