Telescope Resolution Calculator
Enter your telescope's aperture to see the closest double stars it can split, how much more light it collects than your eye and roughly how faint a star it can show.
Telescope resolution
Dawes, Rayleigh and Sparrow limits, light grasp and faintest stars.
Diameter of the main lens or mirror.
550 nm is green light, where the eye is most sensitive. Use 650 for red, 450 for blue.
Dawes limit
0.89″
The closest pair of equal stars this aperture can just split.
- Rayleigh limit
- 1.06″
- Sparrow limit
- 0.83″
- Light gathering vs the eye
- 345x
- Limiting magnitude (approx.)
- 12.6
- Smallest detail on the Moon
- about 1.7 km
Typical seeing of 1 to 3″ usually blurs detail before this aperture reaches its limit, so steady air matters more than the figures above on most nights.
Limiting magnitude assumes a dark sky and a trained eye. City light pollution can cost 2 to 3 magnitudes.
How this is calculated
- 1
Dawes limit
An observed rule for two equal stars of about 6th magnitude: resolution in arcseconds = 116 ÷ aperture in mm. A 130 mm telescope gives 116 ÷ 130 = 0.89″.
- 2
Rayleigh and Sparrow limits
These come from the physics of diffraction. Rayleigh = 1.22 × λ ÷ D and Sparrow ≈ 0.947 × λ ÷ D, in radians, then × 206,265 for arcseconds. With λ = 550 nm and D = 130 mm, Rayleigh is 1.06″ and Sparrow 0.83″.
- 3
Light gathering power
Light collected grows with the area of the aperture, so the gain over a 7 mm dark-adapted pupil is (D ÷ 7)². A 130 mm telescope collects about 345 times more light than your eye.
- 4
Limiting magnitude
A common approximation is 2 + 5 × log10(D in mm), which gives about 12.6 for 130 mm. It assumes a dark sky; city glow and haze cut it noticeably.
Frequently asked questions
What is the Dawes limit?
It is the smallest separation, in arcseconds, at which two equal stars can just be seen as two points. William Dawes found it by observation, and it works out to 116 divided by the aperture in millimetres, or 4.56 divided by the aperture in inches.
What is the difference between the Dawes and Rayleigh limits?
Rayleigh is based on diffraction theory: the centre of one star's image sits on the first dark ring of the other. Dawes is a practical figure from experienced observers and is a little tighter. Sparrow is tighter still: it marks the point where the dip in brightness between the two stars just disappears.
Does a bigger telescope always show more detail?
In theory yes, as resolution scales with aperture. In practice the atmosphere usually blurs stars to 1 to 3 arcseconds, so above about 100 mm the seeing, not the telescope, is normally the limit. Larger apertures still show fainter objects.
How faint can my telescope see?
Roughly 2 + 5 × log10(aperture in mm) under a dark sky, so about 12.6 for 130 mm and 13.5 for 200 mm. Light pollution, haze and your experience can change this by a magnitude or more either way.