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Night Sky & Celestial Coordinates Calculator

Convert equatorial celestial coordinates (Right Ascension & Declination) into local Altitude and Azimuth for any observer location and sidereal time.

InputsChange a value to recalculate instantly
ResultUpdates as you type
Target Altitude56.23°
Target Azimuth191.29°
Hour Angle (H)0.42 h
Culmination Peak Altitude56.70°
Visibility StatusAbove Horizon (Visible)
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 & STEPSNight Sky & Celestial Coordinates Calculator — Mathematical Derivation & Steps
2 StepsSequential Calculation Breakdown
1
Hour Angle Calculation
Angular distance from the local celestial meridian along celestial equator.
2
Altitude Coordinate Derivation
Target is currently elevated above the local horizon.
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 Night Sky & Celestial Coordinates Calculator

Convert equatorial celestial coordinates (Right Ascension & Declination) into local Altitude and Azimuth for any observer location and sidereal time.

01Set inputsChoose values, units and assumptions.
02Apply the modelsin(Alt) = sin(φ)sin(δ) + cos(φ)cos(δ)cos(H); H = LMST - RA
03Read the resultCheck the output against the assumptions before using it.
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What this calculator does

Enter observer latitude, target celestial object Right Ascension and Declination, and local hour angle. Calculates instantaneous pointing coordinates.

functions

Formula & method

sin(Alt) = sin(φ)sin(δ) + cos(φ)cos(δ)cos(H); H = LMST - RA

fact_check

Assumptions & notes

  • Local Sidereal Time corresponds to the Right Ascension currently crossing the local celestial meridian.
  • Objects below 0° altitude are currently below the local horizon.
  • Circumpolar stars never set below the local horizon for given observer latitude.
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