Reference angle calculator
A reference angle turns the trig values of any angle into those of an acute angle, with the sign set by the quadrant.
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How to use it
- Enter angle and angle unit.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
After reducing θ to [0°, 360°): quadrant I gives θ, II gives 180° - θ, III gives θ - 180°, IV gives 360° - θ.
Example
Inputs: Angle = 150, Angle unit = Degrees. Result: Reference angle: 30 °; Reduced angle: 150 °; Position: Quadrant II.
Limits and caveats
- For angles on an axis the reference angle is given as 0° or 90°.
Questions about this tool
What is a reference angle?
The positive acute angle between the terminal side of an angle and the x-axis, between 0° and 90°.
How does it help with sin 150°?
The reference angle is 30° and sine is positive in quadrant II, so sin 150° = sin 30° = 1/2.
What about a negative angle?
Reduce it first by adding 360°. So -45° becomes 315°, whose reference angle is 45°.