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Unit Circle Calculator.

Find Cartesian coordinates on the unit circle for an angle in degrees.

On-device calculationNo signup
01

Set your values

Results update as you type.

x: 0.707107

x

0.000000
y: 0.707107

y

0.000000
Angle (radians): 0.785398

Angle (radians)

0.000000

Results update automatically as you type.

Use Cases

Trigonometry Homework Help

Quickly verify sine, cosine, and tangent values for any angle, especially common angles like 30°, 45°, 60°, and 90°.

Example: Check that sin(30°) = 0.5 and cos(60°) = 0.5.

Graphing and Function Analysis

When plotting trigonometric functions or analyzing periodic behavior, use the calculator to get precise values for specific angles.

Example: Find tan(120°) to understand the function's behavior in the second quadrant.

Frequently Asked Questions

What does the Unit Circle Calculator do?
It takes an angle in degrees and instantly computes the sine, cosine, and tangent values using the unit circle definitions. It uses deterministic formulas, so you get exact trigonometric ratios for any angle.
How do I use the calculator?
Simply enter the angle in degrees in the 'Angle' field. The calculator will output the corresponding sine, cosine, and tangent values based on the unit circle. No other inputs are needed.
Can I use this calculator for angles greater than 360°?
Yes, the calculator works for any angle in degrees. It will reduce the angle modulo 360° to find the equivalent position on the unit circle, then compute the trigonometric values.

Tips & Common Mistakes

Tips

  • Remember that the unit circle has a radius of 1, so sine and cosine values are between -1 and 1.
  • For angles in degrees, you can enter any real number, including negative angles, which correspond to clockwise rotation.
  • Use the calculator to memorize common angle values: 0°, 30°, 45°, 60°, 90°, and their multiples.
  • Check your work by verifying that sin²θ + cos²θ = 1 for any angle you input.

Common Mistakes to Avoid

  • Forgetting to convert degrees to radians when using other tools, but this calculator handles degrees directly.
  • Assuming tangent is always positive; it's negative in the second and fourth quadrants.
  • Mixing up sine and cosine for complementary angles (e.g., sin(30°) = cos(60°)).

Last updated: August 13, 2026