Unit circle calculator
Enter an angle in degrees or radians to see its point on a circle of radius 1, the basic picture behind the signs of the trig functions.
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How to use it
- Enter angle θ and angle unit.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Point (x, y) = (cos θ, sin θ). The angle is first reduced to the range 0° up to 360°, and exact values are shown for multiples of 30° and 45°.
Example
Inputs: Angle θ = 30, Angle unit = Degrees. Result: Point (cos θ, sin θ): (√3/2, 1/2); x = cos θ: 0.8660254038; y = sin θ: 0.5.
Limits and caveats
- Exact forms are shown only for multiples of 30° and 45°. Other angles show decimals rounded to 6 places in the point field.
Questions about this tool
What is the unit circle?
A circle centred at the origin with radius 1. The coordinates of any point on it are the cosine and sine of its angle.
How do I read the signs of sin and cos from the quadrant?
Both are positive in quadrant I, only sine in II, both negative in III, and only cosine in IV.
Why is 450° the same as 90°?
450 = 360 + 90, a full turn plus 90 degrees, so it lands on the same point.