Coterminal Angle Calculator
With this coterminal angle calculator you'll find some positive and negative coterminal angles, as well as the coterminal angle in the 0-360° (0-2π) range. Moreover, this tool is useful for checking if two angles are coterminal.
Smallest positive coterminal angle45°0.785398 rad
Adding turns405°, 765°, 1,125°, 1,485°
Subtracting turns-315°, -675°, -1,035°, -1,395°
Negative coterminal angle-315°
The rule
add or subtract whole turns: θ ± 360°n
Degrees and radians
A full turn is 360° or 2π radians, so:
radians = degrees × π/180 and degrees = radians × 180/π
Degrees are convenient because 360 divides so many ways. Radians are the natural choice in mathematics because arc length becomes simply rθ and the calculus of sine and cosine comes out clean — derivatives pick up stray factors of π/180 in degrees.
Names worth knowing
- Acute — under 90°. Right — exactly 90°. Obtuse — between 90° and 180°.
- Straight — 180°. Reflex — over 180°.
- Complementary pairs add to 90°; supplementary pairs add to 180°.