Unit circle calculator
Type an angle in degrees, or in radians such as 5pi/6 or 3π/4. For multiples of 30° and 45° you get exact values like √3/2, and for any angle you get decimals, the quadrant, the reference angle and the point on the unit circle.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose degrees or radians and type the angle.
- Read sin, cos and tan, the quadrant and the reference angle.
- Check the point on the circle in the drawing; the faint dots are the special angles.
How it works
The point on the unit circle at angle θ is (cos θ, sin θ), and tan θ = sin θ / cos θ. The reference angle gives the size, using the first-quadrant values 0, 1/2, √2/2, √3/2, 1 for sin at 0°, 30°, 45°, 60° and 90°; the quadrant gives the signs (sin positive in I and II, cos in I and IV, tan in I and III).
Example
150° is 5π/6 in the second quadrant with reference angle 30°. So sin = 1/2, cos = −√3/2 (about −0.866025) and tan = −√3/3 (about −0.57735).
Tips
- To convert degrees to radians multiply by π/180.
- Learn the first quadrant once; every other quadrant only changes the signs.
Frequently asked questions
Which angles get exact values?
Multiples of 30° and of 45° (in radians, multiples of π/6 and π/4). Their sin and cos are 0, 1/2, √2/2, √3/2 or 1 with the right sign, and tan is 0, √3/3, 1, √3 or not defined. Other angles show decimals only.
What is the reference angle?
The acute angle between the terminal side and the x-axis. For 150° it is 30°, and sin 150° has the same size as sin 30° with the sign of the second quadrant.
When is tan not defined?
When cos is 0, at 90° and 270° (π/2 and 3π/2) and their full turns. The tool marks tan as not defined there.
Can I enter angles above 360° or negative angles?
Yes. The angle is reduced to 0° to 360°: 405° becomes 45° and −90° becomes 270°.