Angle Calculator

Angle between two points, using atan2

Angle = atan2(Y2−Y1, X2−X1), measured counterclockwise from the positive X axis — the two-argument arctangent correctly places the angle in the right quadrant regardless of which direction the second point sits from the first, which a plain arctangent of rise÷run can't do on its own.

Why some prints and instruments still use DMS

Degrees-minutes-seconds (base 60, like a clock) is a holdover from surveying and older optical tooling, and it still shows up on some prints, protractors, and angle gauges — while decimal degrees are what nearly every CAM system and modern control actually wants. Converting between them by hand (dividing or multiplying by 60 twice) is an easy place to make an arithmetic slip, which is the whole reason this exists.

Reading a DMS conversion correctly

45° 30' 36" means 45 whole degrees, plus 30 minutes (each 1/60 of a degree), plus 36 seconds (each 1/60 of a minute, or 1/3600 of a degree) — convert it by adding degrees + minutes/60 + seconds/3600, exactly what this calculator does under the hood.