Unit Circle Calculator

Unit Circle Calculator

Find coordinates and trig values for any angle on the unit circle.

Last updated: June 2026 | By Patchworkr Team

Degrees
Coordinates
(0.707107, 0.707107)
Radians: 0.785398
sin
0.707107
cos
0.707107
tan
1

Formula

The unit circle has radius 1, so every angle maps to a point with x = cos θ and y = sin θ.

x = cos θ, y = sin θ

The tangent is only defined when cos θ is nonzero.

How to Use

Choose degrees or radians, enter an angle, and read the coordinates and trig values directly from the result panel.

  1. Choose the unit system.
  2. Enter the angle value.
  3. Inspect the coordinates, sine, cosine, and tangent.

Example

At 45 degrees, the point is approximately (0.707107, 0.707107) and tan is 1.

That matches the standard 45-45-90 triangle relationship on the unit circle.

Notes

The tangent display switches to Undefined when cosine is effectively zero, which avoids giant misleading values near 90 degrees and similar angles.

Blank and malformed angles are rejected explicitly instead of being coerced to zero.

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