Unit Circle Calculator
Look up exact sin, cos, tan values and coordinates for standard unit-circle angles.
About Unit Circle Calculator
The unit circle is a circle of radius 1 centred at the origin. Any angle θ maps to the point (cos θ, sin θ). The reference angle is the acute angle formed with the x-axis; the quadrant determines the sign of each function.
Formula
Unit circle coordinates
(x, y) = (cos θ, sin θ) on a circle of radius 1
- θ
- Angle from positive x-axis
- x
- cos θ
- y
- sin θ
Worked example
With the default values below, Unit Circle Calculator returns sin θ of 0.7071067812. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Angle (degrees)
- 45
Results
- sin θ
- 0.7071067812
- cos θ
- 0.7071067812
- tan θ
- 1
- Quadrant
- I
- Reference angle
- 45.0000 °
- Radians
- 0.78539816
Step by step
- 1Normalised angle= 45° = 0.785398 rad
- 2Quadrant= I
- 3Reference angle= 45°
- 4Coordinates (cos θ, sin θ)= (0.7071067812, 0.7071067812)
Assumptions and limits
- The result is derived only from the single input listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 10 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What are the standard unit circle angles?
0°, 30°, 45°, 60°, 90° and their counterparts in each quadrant: 120°, 135°, 150°, 180°, 210°, 225°, 240°, 270°, 300°, 315°, 330°, 360°.
How do I find the reference angle?
In Q1: ref = θ; in Q2: ref = 180° − θ; in Q3: ref = θ − 180°; in Q4: ref = 360° − θ.