Reference Angle Calculator
Reference angle, quadrant and exact trig signs.
Enter your values
ⓘ Live results
Results
- Reference angle
- 65°
- In radians
- 1.13446
- Quadrant
- Quadrant 3
- Coterminal angle (0–360°)
- 245°
- Trig signs
- sin −, cos −, tan +
- sin / cos / tan
- -0.9063 / -0.4226 / 2.1445
Quick answer
A reference angle is the acute angle between the terminal side and the x-axis, always between 0° and 90°.
Q1: θ, Q2: 180−θ, Q3: θ−180, Q4: 360−θ
How to use the Reference Angle Calculator
- 1Enter your angle in degrees — negative and over 360 are fine.
- 2Read the reference angle and the quadrant.
- 3Apply the quadrant signs to the reference angle's trig values.
Worked example
Using the values the calculator loads with:
Inputs
- Angle245 degrees
Results
- Reference angle65°
- In radians1.13446
- QuadrantQuadrant 3
- Coterminal angle (0–360°)245°
- Trig signssin −, cos −, tan +
- sin / cos / tan-0.9063 / -0.4226 / 2.1445
Frequently asked questions
Why do reference angles help?
Every trig value comes from the first-quadrant value of the reference angle plus a sign from the quadrant — one table covers all angles.
What about negative angles?
They are converted to their coterminal angle between 0° and 360° first.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.