Angle Drawer Calculator
Type an angle in degrees or radians and see it drawn in standard position, with its quadrant, reference angle, coterminal angles and sin, cos and tan.
Type π or “pi” for radians, e.g. 5pi/6. The drawing updates as you type.
135° = 3π/4 rad · counterclockwise
Quadrant II
Reference angle 45° (π/4 rad).
Black: initial side on the positive x-axis. Blue: terminal side and the rotation. Dashed: reference angle.
| Coterminal angle in 0°–360° | 135° |
| Positive coterminal | 135° (3π/4) |
| Negative coterminal | -225° (−5π/4) |
| More coterminal angles | 495°, -225° — add or subtract 360° |
| sin θ | 0.707107 |
| cos θ | -0.707107 |
| tan θ | -1 |
How to draw an angle in standard position
- Enter the angle. Type the angle in degrees, or switch to radians and type a value such as 3π/4, -pi/6 or 2.1.
- Start on the positive x-axis. The initial side always lies along the positive x-axis with the vertex at the origin.
- Rotate. Positive angles turn counterclockwise and negative angles clockwise; angles beyond 360° make full turns, shown as a spiral.
- Read the results. The drawing shows the terminal side; the card gives the quadrant, reference angle, coterminal angles and trig values.
10 situations where drawing an angle helps
Checking trig homework
A student can confirm that −210° ends in quadrant II before working out its sine, avoiding a sign error on every later step.
Finding a reference angle
The reference angle is drawn and given in degrees and radians.
Listing coterminal angles
The positive and negative coterminal angles are shown, plus how to get more.
Converting degrees to radians exactly
135° shows as 3π/4, not just a decimal.
Seeing large angles
An angle like 750° is drawn as two full turns plus 30°.
Preparing class slides
A teacher can draw any angle quickly for an example.
Understanding negative angles
The drawing makes the clockwise rotation visible.
Spotting quadrantal angles
Angles on an axis are labelled, and the tool says why they have no reference angle.
Checking sin, cos and tan signs
The values show which are positive or negative in each quadrant.
Studying for a placement test
Rapid practice with many angles, each drawn instantly.
Definitions used
The definitions are from OpenStax Precalculus 2e, section 5.1 'Angles' (CC BY-NC-SA 4.0). An angle is in standard position when its vertex is at the origin and its initial side lies along the positive x-axis. Counterclockwise rotation is positive and clockwise is negative.
Quadrantal angles have their terminal side on an axis (0°, 90°, 180°, 270°). Coterminal angles share a terminal side and are found by adding or subtracting 360° (2π). The reference angle is the smallest positive acute angle between the terminal side and the horizontal axis — so a quadrantal angle has none. Degrees and radians are related by θ/180 = θ_R/π.
Radians are written as an exact multiple of π when the angle in degrees is a whole or half number; otherwise as a decimal. Sine, cosine and tangent are computed numerically; tangent is undefined when the terminal side is on the y-axis. Everything runs in your browser.
Limits: decimal results are rounded for display. The drawing is to scale for direction; the spiral used for multiple turns grows slightly each turn so the turns can be told apart.
Sources
- OpenStax — Precalculus 2e, 5.1 Angles — Standard position, coterminal and reference angles, degree–radian conversion
Frequently asked questions
How do you draw an angle in standard position?
Put the vertex at the origin and the initial side along the positive x-axis, then rotate counterclockwise for a positive angle or clockwise for a negative one to reach the terminal side.
What is a reference angle?
The smallest positive acute angle between the terminal side and the x-axis. For 135° it is 45°; for 210° it is 30°.
How do I find coterminal angles?
Add or subtract 360° (or 2π radians). 135° is coterminal with −225° and 495°.
What quadrant is a negative angle in?
Rotate clockwise from the positive x-axis. −45° ends in quadrant IV, −120° in quadrant III.
How do I convert degrees to radians?
Multiply by π/180. 135° × π/180 = 3π/4.
Why doesn't 90° have a reference angle?
Its terminal side lies on an axis. A reference angle must be acute, and the angle to the x-axis here is 90°, so quadrantal angles have none.
Can I enter radians with π?
Yes. Switch the unit to radians and type values like 5pi/6, -π/4 or 2pi.
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