Unit Circle Chart & Calculator
An interactive unit circle chart enter any angle to see its position, plus sin, cos, and tan instantly.
Last updated: September 23, 2026
Common unit circle values
| Degrees | Radians | (cos, sin) | tan |
|---|
What is the unit circle?
The unit circle is a circle with a radius of exactly 1, centered at the origin of a coordinate plane. For any angle measured from the positive x-axis, the point where that angle intersects the circle has coordinates (cosθ, sinθ) which is why the unit circle is the foundation for understanding trigonometric functions.
FAQ
Why does tan sometimes show "undefined"?
Tangent is sin ÷ cos, so it's undefined wherever cosine equals zero at 90° and 270° (and their radian equivalents).
Can I enter negative angles or angles over 360°?
Yes the calculator wraps any angle around the circle automatically, so -90° and 270° give the same result.
Using the diagram to learn trig
Move through familiar angles such as 0, 30, 45, 60, and 90 and compare the point on the circle with the table. The horizontal coordinate is cosine and the vertical coordinate is sine. Tangent is sine divided by cosine, which is why it is undefined where cosine equals zero. Switching between degrees and radians helps connect the two common ways of measuring rotation.
Rounding and exact values
The displayed decimal is convenient for checking homework, but common unit-circle angles also have exact values involving fractions and square roots. Use the decimal to confirm direction and approximate magnitude, then use the exact form when your class or calculation requires it. Remember that angles differing by a full rotation share the same terminal point and therefore the same sine and cosine.