Light Pollution Sky Quality Calculator
Estimate the faintest star visible through your telescope by combining sky brightness, aperture, altitude, observer age, and moon phase. Useful for planning deep-sky sessions at any site.
About this calculator
Limiting magnitude describes the faintest object the human eye or a telescope can detect under given conditions. The base value comes from sky brightness measured in magnitudes per square arcsecond (mag/arcsec²) — a darker sky (higher value, e.g. 22) allows fainter objects to be seen. Each doubling of aperture improves limiting magnitude by roughly 1.5 mag, captured by the term 5 × log₁₀(aperture / 100). Higher observation altitude thins the atmosphere, boosting transparency by ~0.1 mag per 1,000 m. An older observer's eye transmits less light, reducing limiting magnitude by 0.5 mag per decade of age above a 20-year baseline, approximated as (age / 100) × 0.5. Finally, the Moon introduces skyglow proportional to its phase (0 = new, 1 = full), penalising up to 2 magnitudes at full moon. The combined formula is: Limiting Magnitude = skyBrightness + 5 × log₁₀(aperture / 100) + (altitude / 1000) × 0.1 − (observerAge / 100) × 0.5 − moonPhase × 2.
How to use
Suppose sky brightness is 21.5 mag/arcsec², aperture 200 mm, observer age 40, altitude 500 m, and moon phase 0.25 (waxing crescent). Step 1: aperture term = 5 × log₁₀(200 / 100) = 5 × 0.301 = 1.505. Step 2: altitude term = (500 / 1000) × 0.1 = 0.05. Step 3: age term = (40 / 100) × 0.5 = 0.2. Step 4: moon term = 0.25 × 2 = 0.5. Result = 21.5 + 1.505 + 0.05 − 0.2 − 0.5 = 22.36. Objects fainter than magnitude 22.4 will likely be invisible under these conditions.
Frequently asked questions
How does sky brightness in mag/arcsec² relate to the Bortle scale?
Sky brightness in magnitudes per square arcsecond is a quantitative measure that maps closely onto the 9-level Bortle scale. A pristine Bortle 1 site measures roughly 22.0–22.5 mag/arcsec², while a typical suburban Bortle 6 sky sits around 19.0–20.0 mag/arcsec². Urban skies (Bortle 8–9) can fall below 18 mag/arcsec². You can measure your sky's value with a Sky Quality Meter (SQM), or use published Bortle-to-SQM conversion tables. Inputting a more accurate sky brightness reading significantly improves the reliability of the limiting magnitude estimate.
Why does observer age reduce the limiting magnitude you can see?
The human lens and pupil change with age: the maximum pupil diameter shrinks from about 8 mm in youth to around 5 mm by age 60, and the lens yellows, absorbing more blue and violet light. Together these effects reduce the total light reaching the retina, making faint objects harder to detect. The model used here approximates this loss as 0.5 mag per 100 years of age, which translates to roughly 0.2 mag reduction between a 20-year-old and a 60-year-old observer — a noticeable but not catastrophic difference at the eyepiece.
When is the best time to observe faint deep-sky objects to maximise limiting magnitude?
The ideal conditions combine a new Moon (moon phase = 0), high-altitude dark-sky site with a sky brightness above 21.5 mag/arcsec², low humidity, and the target object near the zenith to minimise atmospheric path length. New Moon windows last about 5–7 days around each new moon, so planning sessions in those windows is the single biggest improvement most observers can make. Combining a large aperture telescope with a moonless, transparent night at altitude can push limiting magnitude past 15–16 for visual observing and considerably deeper for astrophotography.