Reference Angle Calculator
Find the reference angle and quadrant of any angle.
Change the values and press Calculate to work out your own figures.
Enter an angle and choose degrees or radians.
Show the working
- Reduce to 0°–360°; then Q I: θ, Q II: 180° − θ, Q III: θ − 180°, Q IV: 360° − θ
How to use it
Enter an angle and choose degrees or radians.
Enter the values you know (decimals, fractions, surds such as 2√5, or angles such as π/3 in radians). Show the working gives the rule used at each step.
Key facts
Q I: θ; Q II: 180° − θ; Q III: θ − 180°; Q IV: 360° − θ
Why it helps
A function's value at any angle equals its value at the reference angle, with the sign of the quadrant.
Questions
What is the reference angle of 125°?
55°.
And of 200°?
20°.
Formulas
Q I: θ; Q II: 180° − θ; Q III: θ − 180°; Q IV: 360° − θ
Sources
Limitations
- Angles can be typed in degrees or radians; radians may be written with π (π/3, 2pi/3).