Position Angle Calculator

Position Angle Insights

This guide explains what the calculator reports and why observers use it. Position angle (PA) is measured east of north, so 0° points north, 90° points east, 180° points south, and 270° points west.

1) What position angle describes

PA is a direction on the sky from a reference object to a target object. In astrometry, it pairs with separation to fully describe a relative position. Double-star measures, comet tail directions, galaxy major-axis orientation, and guiding corrections often rely on this simple bearing.

2) Coordinate mode data you provide

In RA/Dec mode you enter two points: a reference (α1, δ1) and a target (α2, δ2). Right ascension can be supplied as decimal hours, decimal degrees, or H:M:S, while declination can be decimal degrees or D:M:S. The calculator converts inputs to radians internally before applying trigonometry.

3) Why the RA/Dec formula uses atan2

A plain arctangent loses quadrant information, which can flip the angle by 180°. Using atan2(y, x) preserves the correct quadrant by tracking the signs of both numerator and denominator terms. The final PA is then wrapped into your chosen range (0–360° or −180° to +180°).

4) Separation output and common unit conversions

Along with PA, the tool returns angular separation using a great-circle distance. One degree equals 60 arcminutes and 3600 arcseconds. If you are comparing to detector motion, arcseconds are typically the most convenient because plate scales are often quoted in arcseconds per pixel.

5) Offset mode for fast field work

Offset mode is ideal when you already have small-angle offsets: ΔE (east) and ΔN (north). The PA is computed by atan2(ΔE, ΔN), and separation is sqrt(ΔE² + ΔN²) in your selected unit. Positive ΔE means the target lies east of the reference, and positive ΔN means north.

6) Pixel mode with scale and rotation

Pixel mode converts (x, y) differences into sky offsets using your plate scale. Rotation θ accounts for camera orientation: it maps image axes onto east and north. If your image coordinates increase downward in y (typical for images), enable the “Y increases downward” option so the direction is interpreted correctly.

7) Practical accuracy notes

For wide separations, always prefer RA/Dec mode because it uses spherical geometry. The displayed ΔEast and ΔNorth in RA/Dec mode are small-angle approximations for intuition. For high precision, supply accurate coordinates, keep units consistent, and use enough decimal places to match your measurement uncertainty.

FAQs

1) What is the position angle reference direction?

It is measured from celestial north toward the east direction. A value of 0° points north, 90° points east, 180° points south, and 270° points west.

2) Why can two methods give slightly different results?

Offsets assume a local tangent plane, while RA/Dec uses spherical geometry. For small separations they agree closely, but for larger separations spherical calculations are more accurate.

3) When should I use −180° to +180° output?

Use it when you want signed angles around north and prefer negative values for west-of-north directions. It can be easier for plotting residuals or reporting small deviations.

4) How do I interpret the quadrant label?

The label uses the signs of ΔEast and ΔNorth. NE means the target is east and north of the reference; SW means west and south, and so on.

5) What rotation angle θ should I enter in pixel mode?

Enter the angle that describes how your image +Y axis is rotated eastward from north. If your header or astrometric solution reports a position angle for “up,” use that value.

6) Why does enabling “Y increases downward” matter?

Many images store pixels with y increasing downward. If you do not correct for that, north-south direction flips and the computed position angle can be mirrored.

7) Can I export multiple runs in one CSV?

This page exports the most recent calculation stored in your session. For multiple runs, download each result or modify the script to append rows to a file.