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Light Pollution Calculator

Estimate naked-eye and telescope limiting magnitude and SQM reading based on Bortle class, altitude, and moon phase.

About this calculator

This calculator estimates how faint a star you can see under a given sky, using the Bortle scale -- amateur astronomer John E. Bortle's 1-to-9 rating of night-sky darkness, published in Sky & Telescope magazine in 2001, where 1 is an excellent dark-sky site and 9 is an inner-city sky drowned in artificial light. Naked-Eye Limit reports the faintest stellar magnitude visible without optical aid; because the magnitude scale runs backwards (smaller and negative numbers are brighter, larger numbers are fainter), a higher limiting magnitude means you can see fainter, more numerous stars. Bortle Class is by far the dominant factor in that number: each step up the Bortle scale represents a real, substantial jump in sky glow, so Naked-Eye Limit responds to Bortle Class far more than to the other inputs.

Altitude adds a small bonus of roughly 0.1 magnitude per 1,000 feet of elevation, reflecting the thinner, cleaner air at higher sites -- real but modest compared to Bortle Class's effect, and small enough that it barely registers at typical altitudes even though it adds up over the calculator's full altitude range. Moon Phase subtracts up to 2 magnitudes at full illumination, since moonlight scatters through the atmosphere and raises the sky's background brightness much like light pollution does -- published estimates for how much a full moon brightens the sky vary by site and conditions (roughly 1.5 to 3 magnitudes across different sources), and this calculator's flat 2-magnitude figure is a representative middle value rather than a precise physical constant. Telescope Limit extends Naked-Eye Limit by the aperture gain of an 8-inch telescope (a common amateur aperture), using the standard formula 2.5 × log10((aperture/pupil)²) with a 7mm dark-adapted eye pupil. SQM Reading reports the same darkness in Sky Quality Meter units (magnitudes per square arcsecond), the number most amateur astronomers use to characterize a site's darkness with an actual handheld meter.

Inputs

Results

Naked-Eye Limit

5.6 mag

Telescope Limit (8")

12.9 mag

SQM Reading20.49 mag/arcsec²

Figures current as of 2001. Source: John E. Bortle, "Introducing the Bortle Dark-Sky Scale," Sky & Telescope, February 2001

How to Use This Calculator
  1. Select your Bortle Class, and enter Altitude (ft) and Moon Phase (%).
  2. Review Naked-Eye Limit and Telescope Limit (8"), both in magnitudes (mag).
  3. Use SQM Reading (mag/arcsec²) to inform your decision.
  4. Use the chart to visualize the results and explore different scenarios by adjusting inputs.

What each input means

Bortle Class
Light pollution level on the Bortle Dark-Sky Scale.
Altitude (ft)
Your elevation above sea level in feet (higher = cleaner air)
Moon Phase (%)
Moon illumination percentage (0% = new moon, 100% = full moon)

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    Bortle Class + Altitude (ft) + Moon Phase (%)
    Bortle Class = 5, Altitude (ft) = 1000, Moon Phase (%) = 0 = 3 input(s) provided
  2. Calculate Naked-Eye Limit
    Naked-Eye Limit = Bortle Base Magnitude + Altitude Bonus − Moon Penalty
    5.6 = 5.6
  3. Calculate Telescope Limit (8")
    Telescope Limit = Naked-Eye Limit + 2.5 × log10((Aperture / Pupil)²)
    12.9 = 12.9

Figures and sources

Engine last updated . Checked against 3 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why does Bortle Class matter so much more than Altitude?

Bortle Class, named for amateur astronomer John E. Bortle who published the scale in Sky & Telescope in 2001, captures the dominant driver of night-sky brightness: how much artificial light is scattering into the atmosphere from nearby towns and cities. Moving from a Bortle 5 suburban sky to a Bortle 2 rural sky changes the naked-eye limiting magnitude by roughly a full magnitude or more. Altitude's contribution is real -- thinner air scatters and absorbs less starlight -- but the calculator adds only about 0.1 magnitude per 1,000 feet, a small effect that this calculator verifies directly against the underlying formula rather than asserting from general astronomy knowledge.

Why does a fuller moon lower my limiting magnitude?

Moonlight doesn't just illuminate the ground -- it scatters through the atmosphere and raises the overall brightness of the night sky, the same physical effect as light pollution from a city. At 100% illumination (full moon), this calculator subtracts 2 magnitudes from your naked-eye limit as a representative estimate -- published figures for full-moon sky-brightening vary by site and conditions, generally falling somewhere in the range of about 1.5 to 3 magnitudes -- meaning you lose the ability to see many of the fainter stars you could otherwise pick out on a moonless night at the same location.

What does the Telescope Limit assume about my telescope?

Telescope Limit is calculated for an 8-inch (200mm) aperture telescope, a common size for amateur astronomers, using the standard aperture-gain formula that compares the telescope's light-gathering area to a dark-adapted human eye's roughly 7mm pupil. A larger telescope gathers more light and would push the limiting magnitude fainter than shown here; a smaller telescope would see less far than this estimate.

What is SQM Reading and how does it relate to Bortle Class?

SQM Reading is the darkness value a handheld Sky Quality Meter would report in magnitudes per square arcsecond -- a direct instrument measurement rather than a calculated star-visibility estimate. This calculator maps each Bortle class to a representative SQM value (roughly 21.99 at Bortle 1 down to 17.0 at Bortle 9); published Bortle-to-SQM correspondence tables vary somewhat from source to source, so treat these as typical rather than an exact one-to-one conversion. The calculator then applies the same moon-phase penalty used for Naked-Eye Limit, since both describe the same underlying sky brightness from different angles.

Why does Altitude barely change my result at typical values?

The altitude bonus is deliberately small -- about 0.1 magnitude per 1,000 feet -- because thinner air at higher elevation helps, but it's a secondary effect compared to how much artificial light is actually present in the sky. Going from sea level to a 1,000-foot site adds only 0.1 magnitude, well within the resolution most observers can even distinguish by eye; you'd need several thousand feet of elevation change to notice a meaningful difference from altitude alone.

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