Altitude and Azimuth Calculator

Altitude and Azimuth Calculator

Convert right ascension and declination into local horizon coordinates using UTC time, observer position, sidereal time, and a north-based azimuth.

🔭Real Sky Presets
Calculator Inputs
0 to 24 hours. Convert degrees to hours by dividing by 15.
Use positive north and negative south of the celestial equator.
Enter the observing date in Coordinated Universal Time.
Use UTC, not local civil time or daylight saving time.
North latitude is positive; south latitude is negative.
East longitude is positive; west longitude is negative.
The visibility card compares corrected altitude with this limit.
Standard correction uses Bennett refraction above about -1 degree.
Corrected Altitude -- degrees above horizon
Azimuth From North -- compass bearing
Hour Angle -- LST minus RA
Airmass / Visibility -- line-of-sight path
🧭Observation Comparison Grid
30°+ Best Height Usually cleaner air, less extinction, and easier telescope pointing.
15° Usable Low Works for bright targets when trees, rooftops, and haze are limited.
Horizon The geometric boundary between visible sky and below-horizon positions.
-6° Civil Limit Useful for twilight geometry and rough rise or set context.
📐Formula Breakdown

Sidereal step: Julian Date is computed from the UTC date and time, GMST is found from days since J2000.0, and local sidereal time is GMST plus longitude divided by 15.

Hour angle: HA = LST - RA. Positive hour angle means the target is west of the local meridian; negative hour angle means it is east of the meridian.

Altitude: sinAlt = sinDec sinLat + cosDec cosLat cosHA, then altitude = asin(sinAlt).

Azimuth: azimuth is normalized from north using atan2(-sinHA, tanDec*cosLat - sinLat*cosHA), then wrapped into 0 to 360 degrees.

📋Bright Object Coordinate Table
Object Right Ascension Declination Sky Notes Preset Match
Sirius6.7525 h-16.7161°Bright winter starNew York
Polaris2.5303 h+89.2641°Near north celestial poleSeattle
Vega18.6156 h+38.7837°Summer Triangle starLondon
Antares16.4901 h-26.4320°Low for many north sitesSydney
Betelgeuse5.9195 h+7.4071°Orion shoulderTokyo
Canopus6.3992 h-52.6957°Deep southern starCape Town
Deneb20.6905 h+45.2803°Northern Milky WayChicago
Alpha Centauri14.6601 h-60.8339°Southern circumpolar for some sitesSantiago
Rigel5.2423 h-8.2016°Blue star in OrionReykjavik
🧭Azimuth Compass Reference
Bearing Direction Telescope Meaning Rise or Set Context
NorthAiming toward the north pointNorthern circumpolar reference
45°NortheastBetween north and eastCommon rising quadrant
90°EastAiming at the east pointMost objects rise near this side
135°SoutheastBetween east and southGood for southern winter targets
180°SouthLocal meridian for north observersOften highest for many targets
225°SouthwestBetween south and westCommon setting quadrant
270°WestAiming at the west pointMost objects set near this side
315°NorthwestBetween west and northNorthern setting quadrant
📊Altitude and Airmass Table
Altitude Zenith Distance Approx Airmass Observing Quality Practical Note
80°10°1.02ExcellentVery short atmospheric path
60°30°1.15StrongGood for imaging and visual checks
45°45°1.41GoodTypical comfortable observing height
30°60°2.00FairMore haze and extinction
15°75°3.81LowBright objects only in many skies
85°10.3DifficultHorizon clutter and refraction matter
📘Method Reference Table
Quantity Symbol Units Calculator Use
Right ascensionRAhoursObject east-west coordinate on the celestial sphere
DeclinationDecdegreesObject north-south coordinate on the celestial sphere
Local sidereal timeLSThoursRight ascension crossing the local meridian now
Hour angleHAhours or degreesLST minus RA, converted to angle for trig
AltitudeAltdegreesAngle above or below the horizon
AzimuthAzdegreesCompass bearing normalized clockwise from north
LatitudeLatdegreesObserver north-south position on Earth
LongitudeLondegreesObserver east-west position; east positive here
💡Practical Tips
Coordinate tip: Most catalogs list RA in hours, minutes, and seconds. Convert to decimal hours as h + m/60 + s/3600 before entering the value.
Time tip: If your local time zone is west of Greenwich, UTC is usually later than local clock time. A one-hour time error moves the sky about 15 degrees.

A lot of times you get your telescope out, line up on the stars, look around and find the object you wish to observe is now behind some fence. That’s what happens to many an observer. It’s typically a matter of failing to consider how setup of your own situation will affect that night. The fact is the sky turns around and you can’t just guess at angles involved. You may remember that this or that constellation “should” be there, but the Earth turned while you weren’t looking. That means that you need to take those fixed coordinates from the heavens and convert them to what you see in your own back yard’s view of the horizon.

Enter the calculator. It takes Right Ascension and Declination and converts them to Azimuth and Altitude. Right Ascension is similar to longitude except it’s measured in hours. And Declination is similar to latitude except it’s a measure of how far north or south something are. These numbers stays the same for any observer on Earth. Azimuth and Altitude is local to you. Altitude is how high thing will be. Azimuth is compass direction from true North. There is a difference between global and local.

How to Use the Star Calculator

The biggest mistake people make is getting the time wrong. Because the earth both orbits the sun and spins around its axis, solar time differ from sidereal time. Our planet’s spin cause the stars to move roughly four minutes per day westward. That means that if you don’t use Coordinated Universal Time but instead reference local clock time, you’ll be incorrect. To calculate things correctly, tool needs to know UTC for one thing (to base itself on). Then it will take your longitude into account and arrive at your Local Sidereal Time. Next, it computes the Hour Angle. An Hour Angle with a plus sign indicates that the target is already past your meridian, moving west. A minus sign mean it hasn’t yet climbed over the eastern horizon. You want to intercept objects when they’re high, not when they’re low in twilight.

Your perspective on things depends on where you are. Your line of sight has to pass through some amount of air to get from your eyes to the object you’re looking at. How much depends on Airmass. The calculator guesses this number. If thing you’re looking at is directly over head, then you’re looking through one unit of atmosphere. If it’s close to the horizon, then you’re looking through a lot more. It might be ten times more if it is ten degrees up from the horizon. That light gets scattered around and makes it harder to see details. As the seeing altitude goes down, so does quality of your observations (see table). Ideally, try to point your scope above thirty degrees for sharp images. Below that, you’ll start losing detail because of atmospheric extinction.

Another variable is refraction. As light travels toward the ground, it moves into denser air at or close to the horizon which causes light to bend. That means that things seem higher on the horizon then they really are. The calculator corrects for refraction. It’s only a slight adjustment in the zenith direction and quite large around the horizon. Without correcting for refraction, the rise time you calculate would of been incorrect. When math says that a star should already be out, you may find yourself looking up and seeing nothing.

Use the pre-set buttons and play with the calculator. Calculate Canopus from Cape Town, and compare that to Polaris from Seattle. Latitude alters what you’re able to see, some stars simply never set, while others is always obscured from view. It prepares you, and makes the sky into something schedulable. No more wandering around wondering where to point. Where is highest thing? What direction should I go? How high should I tip my scope? And yes, you even make allowances for the fact that the globe rotates and there might be things in the way locally.

This thing plugs that gap. It provides you with a map for the evening. It is a chance to catch the best of what’s out there.

Altitude and Azimuth Calculator