Unit Circle Calculator
Find the (x, y) coordinates on the unit circle for any angle.
Enter Angle
Degrees from positive x-axis
Coordinates
Enter an angle and click calculate.
About the unit circle
The unit circle is a circle of radius 1 centered at the origin. Every point on it can be written as (cos θ, sin θ), where θ is the angle measured counter-clockwise from the positive x-axis.
It's the foundation for extending trig functions beyond right triangles to all real numbers.
Frequently Asked Questions
What is the unit circle?▾
A circle of radius 1 centered at the origin. Every point on it has coordinates (cos θ, sin θ), where θ is the angle from the positive x-axis.
Why is the unit circle important?▾
It extends trig functions from right-triangle ratios to all real numbers, including negative and obtuse angles. Most identities are easiest to prove on the unit circle.
What are the "famous" unit circle points?▾
At 0°: (1, 0). At 30°: (√3/2, 1/2). At 45°: (√2/2, √2/2). At 60°: (1/2, √3/2). At 90°: (0, 1). The same numbers repeat in every quadrant with sign changes.
How does the unit circle define cos and sin?▾
For any angle θ, draw a ray from the origin. Its intersection with the unit circle has x = cos θ and y = sin θ. This works for any real θ, positive or negative.