Unit Circle Calculator
Enter an angle — get its sin, cos, tan values on the unit circle; exact surd form is also given at standard angles (0, 30, 45, 60...), along with quadrant and reference angle. The radius is always 1, so the point is (cos, sin).
How to use
- Enter the angle in degrees — negative or larger than 360 is fine, the tool will bring it into 0-360.
- Exact values are only given for standard angles; others will show decimal values.
- Read the sin, cos and tan values together with the quadrant and reference angle shown in the result.
Note: On the unit circle the point (x, y) = (cos theta, sin theta). The reference angle is the acute angle made with the x-axis. Signs by quadrant: Q1 all +, Q2 sin +, Q3 tan +, Q4 cos + (ASTC rule).
Good to know
- Exact surd forms (like root 2 over 2) appear only at standard angles: 0, 30, 45, 60, 90 and so on.
- Angles larger than 360 degrees or negative ones are folded into the 0–360 range automatically.
- The reference angle is the acute angle to the x-axis — it decides the sign of the trig value.
- Remember ASTC: all functions are positive in quadrant 1, sin in 2, tan in 3 and cos in 4.
Frequently Asked Questions (FAQ)
What does the unit circle calculator show?
The sin, cos and tan values for an entered angle on the unit circle, with exact surd form at standard angles like 0, 30, 45 and 60 degrees, plus quadrant and reference angle.
Can I enter negative or large angles?
Yes — angles outside 0 to 360 degrees are converted into the 0-360 range automatically.
When do I get exact values?
Exact values are shown only for standard angles; other angles show decimal values.
Is it free?
Yes — it is free with no signup.