Angular Separation Calculator
Measure the shorter great-circle angle between two right-ascension and declination positions.
Calculate locally
No account, API or uploaded inputs. All calculations run in this browser.
Worked example
At declination 0° for both objects, right ascensions 0 h and 6 h are 90° apart. Right ascensions 23 h and 1 h are only 30° apart across the wrap boundary.
Method and units
Convert right ascension hours to degrees by multiplying by 15. Rotate the two spherical unit directions, then calculate θ = atan2(length of their cross product, their dot product). This avoids acos precision loss for close pairs.
What this result means
Use coordinates in the same reference frame and epoch. This is apparent angular proximity on a sphere, not physical distance or position angle. Proper motion, precession, parallax, aberration and refraction are not applied. 24 h is equivalent to 0 h.