BYTETOOLS

Unit Circle Calculator

See any angle drawn on the unit circle with its (cos θ, sin θ) point, radians in π form, quadrant and reference angle — updated live as you type.

-0.5
cos θ (x)
0.866025
sin θ (y)
-1.732051
tan θ
II
Quadrant

Angle forms

120°
Degrees
2.094395
Radians
2π/3
Radians (π form)
60°
Reference angle

The point where the angle's terminal side meets the unit circle is always (cos θ, sin θ) — that is the definition of sine and cosine for any angle.

What is the Unit Circle Calculator?

The ByteTools Unit Circle Calculator draws any angle on a live unit-circle diagram: the radius line, the angle arc, the terminal point and its (cos θ, sin θ) coordinates, with dashed projection lines showing how cosine is the x-coordinate and sine is the y-coordinate.

  • Live canvas diagram: radius, arc, point and projection lines
  • Coordinates shown as (cos θ, sin θ) on the diagram
  • Radians displayed as exact fractions of π for whole-degree angles
  • Quadrant and reference angle identification
  • Handles negative angles and angles beyond 360°
  • 100% local — drawn in your browser, nothing uploaded

How to use the Unit Circle Calculator

  1. 1

    Enter an angle in degrees or radians.

  2. 2

    Watch the angle drawn on the unit circle with its terminal point.

  3. 3

    Read cos θ, sin θ and tan θ — the point's coordinates and slope.

  4. 4

    Check the radians-as-π form, quadrant and reference angle.

About the Unit Circle Calculator

The ByteTools Unit Circle Calculator draws any angle on a live unit-circle diagram: the radius line, the angle arc, the terminal point and its (cos θ, sin θ) coordinates, with dashed projection lines showing how cosine is the x-coordinate and sine is the y-coordinate. The picture updates instantly as you change the angle.

Alongside the diagram you get every form of the angle: degrees, decimal radians, radians as a fraction of π (like 7π/6 for 210°), the quadrant and the reference angle, plus cos, sin and tan values. It is the fastest way to build the unit-circle intuition that trigonometry courses depend on.

The diagram is drawn on an HTML canvas entirely in your browser — no images are fetched and nothing you enter is uploaded. Works offline, ideal for revision and classroom demonstrations.

Frequently asked questions

What is the unit circle?

A circle of radius 1 centred at the origin. Its power is that the point where an angle's terminal side crosses the circle always has coordinates (cos θ, sin θ) — so every trig value becomes something you can see as a length on a picture.

How do you find coordinates on the unit circle?

Take the cosine and sine of the angle: at 120° the point is (cos 120°, sin 120°) = (−1/2, √3/2) ≈ (−0.5, 0.866). This calculator draws that point and its projections onto both axes so you can see where the numbers come from.

How do you convert degrees to radians as a fraction of π?

Multiply by π/180 and reduce the fraction. For 210°: 210/180 reduces to 7/6, so the angle is 7π/6 radians. The calculator does this reduction automatically for any whole number of degrees.

What happens with angles bigger than 360° or negative angles?

They wrap around the circle. The tool normalizes any angle to its coterminal angle between 0° and 360° — so 450° lands at 90°, and −30° at 330° — because coterminal angles share the same point and therefore identical trig values.

Why is sine the y-coordinate and cosine the x-coordinate?

Drop a perpendicular from the circle point to the x-axis and you get a right triangle with hypotenuse 1. The adjacent side (along x) is cos θ and the opposite side (along y) is sin θ by the triangle definitions — with hypotenuse 1, the ratios are the coordinates themselves.

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