How the Telescope Limiting Magnitude Calculator works
Limiting magnitude is an estimate of the faintest point-like star that may be detected. Aperture matters strongly, but the sky often matters just as much. The core relationship used here is Aperture-based limiting magnitude is an estimate; practical reach shifts with sky brightness, transparency, observer experience and optical throughput. If you are building a complete observing or imaging setup, use the Light Gathering Calculator alongside this page rather than treating one number in isolation.
Worked example and interpretation
Moving from a 100 mm to a 200 mm aperture increases collecting area by four times, corresponding to roughly 1.5 magnitudes of point-source gain before sky and throughput losses.
For broader physical context, the NASA Stars is a useful external reference.
When this calculator is useful
Use the result to compare apertures and to understand why the same telescope reaches different stellar limits under a dark rural sky and an urban sky.
When the result involves angular size, field, observing conditions or a current target, continue with Exit Pupil Calculator. For a different but related perspective, Night Sky Tonight can connect the formula to an actual observing, telescope or Solar System context.
Diagrams
Assumptions, accuracy and practical limits
Extended objects do not behave like point stars, and a simple formula cannot fully model sky glow, extinction, eyesight, magnification, coatings or detector performance.
A second external cross-check is available from Celestron optical reference. Not for operational or published work.
Reference table: gain over the unaided eye
| Aperture | Light gathering vs eye | Magnitude gain |
|---|---|---|
| 50 mm | 51× | +4.27 |
| 100 mm | 204× | +5.77 |
| 200 mm | 816× | +7.28 |
| 300 mm | 1,837× | +8.16 |
Doubling aperture always adds about 1.5 magnitudes in the ideal case, but light pollution, optics transmission and observer experience decide how much of that you actually see.
Related SpaceTracker.live tools
Continue with Light Gathering Calculator, Exit Pupil Calculator and Night Sky Tonight.
Worked scenarios: from your sky to the telescope’s reach
If the faintest star you can see by eye is magnitude 4.5 (a suburban sky), a 150 mm telescope adds about 5 × log₁₀(150 ÷ 7) = 6.7 magnitudes in the ideal case, reaching roughly magnitude 11.2. Under a dark sky with a naked-eye limit of 6.5, the same telescope would reach about 13.2.
Each extra magnitude means a brightness ratio of 2.512, so a gain of 6.7 magnitudes lets you see objects about 459 times fainter than the unaided eye. Real limits are lower because of optics losses, sky brightness and the observer’s eye.
Common mistakes and sky-quality reference
- Using one naked-eye limit everywhere. The limit depends on your sky; a city sky may give magnitude 4, a dark site 6.5 or more.
- Forgetting the dark-adapted pupil. The formula assumes your eye’s 7 mm pupil, but the pupil shrinks with age and the real gain is a little smaller.
- Ignoring magnification. The limiting magnitude assumes a suitable power; very low power on a bright background hides faint stars.
| Bortle class | Sky | Naked-eye limit |
|---|---|---|
| 1 | Excellent dark site | 7.6–8.0 |
| 3 | Rural | 6.6–7.0 |
| 4 | Rural/suburban transition | 6.1–6.5 |
| 5 | Suburban | 5.6–6.0 |
| 6 | Bright suburban | 5.1–5.5 |
| 7 | Suburban/urban transition | 4.6–5.0 |
| 8–9 | City | below 4.5 |
More questions answered
Why do two observers with the same telescope report different limits?
Eyesight, dark adaptation, sky brightness and the object’s colour all differ. The formula is an average, so treat it as an estimate rather than a measurement.
Does a bigger aperture help under city light?
Yes, but less than in the dark. Sky glow adds a bright background, so the gain in faint stars is smaller than the calculated one.
Frequently asked questions
Why is my real limiting magnitude lower than the calculated one?
Sky brightness, optical losses, magnification choice and eyesight all reduce it. Treat the calculation as an upper estimate under dark skies.
What is the naked-eye limit?
Roughly magnitude 6 at a dark site, and 3–4 in a bright city.
Does a bigger telescope help in light-polluted skies?
It still reaches fainter stars, but the gain is smaller because the background glow also grows with aperture for extended objects.