Hour angle from LST and right ascension calculator

Enter both coordinates as decimal hours between 0 inclusive and 24 exclusive. The calculator subtracts right ascension from LST, converts the difference at 15 degrees per hour, and normalizes the answer to the range from 0 inclusive to 360 exclusive. That result indicates how far the object has rotated westward from the observer's local meridian, using the conventional positive full-circle representation.

What local hour angle tells you

Local hour angle describes an object's angular position relative to the local celestial meridian. An object with an hour angle of zero degrees is on that meridian. As sidereal time advances, the hour angle increases, expressing how far the sky has rotated since the object crossed the meridian. This calculator uses the standard relationship in which local hour angle equals Local Sidereal Time minus right ascension. Because both inputs are entered in decimal hours, their difference is multiplied by 15 degrees per hour. The returned value is normalized into a complete positive circle from 0 inclusive to 360 exclusive. For example, a result near 15 degrees means the object is about one sidereal hour west of the meridian, while a result near 345 degrees is equivalent to minus 15 degrees and places it about one sidereal hour east of the meridian. The normalized form is convenient for software, telescope calculations, plotting, and comparisons that expect nonnegative angular coordinates.

How to enter LST and right ascension

Provide Local Sidereal Time and right ascension as decimal hours, not as degrees and not as sexagesimal text. A value such as 10 hours 30 minutes becomes 10.5 hours, while 8 hours 15 minutes becomes 8.25 hours. Each input must be a finite number at least zero and strictly less than 24. The endpoint 24 is excluded because it denotes the same position as zero hours and would create two representations for one coordinate. Negative values, values of 24 or greater, numeric strings, missing fields, infinity, and nonnumeric values are rejected as invalid input. Make sure the Local Sidereal Time applies to the observer's longitude and intended observation instant; this calculator does not derive LST from a civil date, clock time, or location. Likewise, use right ascension expressed in the same celestial reference context required by your workflow. The operation is deliberately focused: it converts two already prepared equatorial-coordinate quantities into one local angular relationship.

Reading the normalized degree result

The result is returned in the field hour_angle_degrees. Subtraction happens before normalization, so the calculator handles wraparound across zero hours correctly. Suppose LST is 1 hour and right ascension is 23 hours. Their direct difference is minus 22 hours, or minus 330 degrees; normalization produces 30 degrees, the equivalent positive angle. This convention avoids negative output and makes the result suitable for systems that represent rotations on a 0-to-360-degree circle. If your astronomy application instead expects a signed hour angle, values greater than 180 degrees can be converted to the equivalent signed angle by subtracting 360 degrees. Thus 345 degrees corresponds to minus 15 degrees. No rounding rule is imposed beyond ordinary JavaScript numeric arithmetic, so fractional inputs retain useful precision through the multiplication. The function does not account for atmospheric refraction, precession, nutation, polar motion, or topocentric parallax; those concern how the input coordinates are established, not the hour-angle subtraction itself.