Unit Circle Calculator

About this calculator

The unit circle is a circle of radius 1 centered at the origin of a coordinate plane, and it is the geometric foundation for defining sine and cosine: for any angle θ measured from the positive x-axis, the point where the angle’s ray crosses the circle has coordinates (cos θ, sin θ) by definition, and the tangent follows as tan θ = sin θ / cos θ (undefined where cos θ = 0).

Because the unit circle makes trigonometric values visual and geometric rather than abstract ratios memorized from a right triangle, it is a core teaching tool in trigonometry and precalculus for understanding why sine and cosine repeat every 360°, why they range only between −1 and 1, and how special angles like 30°, 45°, 60° and 90° produce clean, memorable coordinate values. Enter an angle in degrees to find its coordinates and trig values.