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Stargazing & Dark Sky Calculator

Evaluate night sky darkness using the Bortle scale, naked-eye limiting magnitude (NELM), artificial sky brightness, and deep-sky visibility.

InputsChange a value to recalculate instantly
ResultUpdates as you type
Effective NELM at 22:00Mag 6.5
Sky Twilight ConditionNight (Astronomical Dark) (Sun -41.9°)
Sky Surface Brightness20.96 mag/arcsec²
Telescope Limiting MagMag 13.4
Max Useful Telescope Magnification300x
Milky Way VisibilityClear structure with great detail
PHYSICAL SIMULATOR

Night Sky & Dark-Sky Planetarium Observatory Simulator

LIVE ENGINE 60FPS
M42 OrionM31 GalaxyM45 PleiadesM57 Ring♄ Saturn♃ JupiterPolaris (N)SiriusVegaBetelgeuseRigelAldebaranDenebE (90°)NE (45°)N (0° - POLARIS)NW (315°)W (270°)OBSERVATORY TIME22:00 LSTBORTLE 3 • NELM 6.50mClass 3: Rural Sky
DEEP SKY TARGETS:
TIME OF NIGHT (EARTH ROTATION):22:00 LST
BORTLE LIGHT POLLUTION CLASS:CLASS 3
OPTICAL APERTURE:150 mm
NELM (Naked Eye Limit): 6.50 magScope Limit: 13.6 magSky Brightness: 20.68 mag/arcsec²Milky Way: Bulbs of Sagittarius & Cygnus sharp
FORMULA & STEPSStargazing & Dark Sky Calculator — Mathematical Derivation & Steps
2 StepsSequential Calculation Breakdown
1
Observer Time & Twilight Solar Altitude
Calculates the Sun elevation below the local horizon to determine sky brightness.
2
Effective Naked-Eye Limiting Magnitude (NELM)
Faintest star magnitude visible after factoring in atmospheric light pollution and twilight.
λ DooMathWork with this calculation
Local · deterministic · optional
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Quick mathNatural-language-style shortcuts for deterministic arithmetic.
Calculator guide

How to use the Stargazing & Dark Sky Calculator

Evaluate night sky darkness using the Bortle scale, naked-eye limiting magnitude (NELM), artificial sky brightness, and deep-sky visibility.

01Set inputsChoose values, units and assumptions.
02Apply the modelNELM = 7.93 - 0.714 × (Bortle - 1); Sky brightness: m_sq = 21.58 - 5 log10(10^((Bortle-1)/2))
03Read the resultCheck the output against the assumptions before using it.
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What this calculator does

Select or input your local light pollution Bortle class (1: pristine dark sky to 9: inner-city sky). The calculator computes naked-eye limiting magnitude and deep-sky contrast visibility.

functions

Formula & method

NELM = 7.93 - 0.714 × (Bortle - 1); Sky brightness: m_sq = 21.58 - 5 log10(10^((Bortle-1)/2))

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Assumptions & notes

  • Bortle 1 sites reveal the zodiacal light and zodiacal band.
  • Human dark adaptation takes 20 to 30 minutes in the absence of white light.
  • Atmospheric seeing can limit telescope resolution regardless of dark sky quality.
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