What is this angle in other units?
Type an angle and pick its unit. The angle calculator converts it to every other unit and finds its reference angle, quadrant, complement, supplement and trig values.
- Radians
- 2.617993878
150° is 2.617993878 radians.
- Degrees°
- 150
- Radians as a multiple of ππ rad
- 0.8333333333
- Gradians
- 166.6666667
- Turns
- 0.4166666667
- Degrees, minutes, seconds
- 150° 0′ 0″
- Coterminal angle in [0°, 360°)°
- 150
- Reference angle°
- 30
- Quadrant
- Quadrant II
- Type
- Obtuse
- Supplement°
- 30
- Sine
- 0.5
- Cosine
- -0.8660254038
- Tangent
- -0.5773502692
Radians: 2.617993878. 150° is 2.617993878 radians.
Where does the angle end on the unit circle?
How to calculate
Converts an angle between degrees, radians, multiples of π, gradians, turns and degrees-minutes-seconds, and finds its coterminal and reference angles, quadrant, type, complement, supplement, and sine, cosine and tangent.
Example with the default inputs (Angle 150, Unit Degrees (°)): 150° is 2.617993878 radians.
Method: radians = degrees × π ÷ 180; gradians = degrees × 10 ÷ 9; turns = degrees ÷ 360; coterminal = degrees mod 360; reference angle from the quadrant; complement = 90° − angle; supplement = 180° − angle.
- An angle typed in degrees, multiples of π, gradians or turns is converted exactly; one typed in radians uses π to double precision.
- Negative angles turn clockwise; coterminal angles differ by whole turns of 360°.
- The complement is shown for angles from 0° to 90°, the supplement for angles from 0° to 180°, and the type for angles from 0° to 360°.
- Seconds are rounded half up to 2 decimal places, carrying into minutes and degrees.
Worked examples
Each example is checked against the calculator on every build.
- Angle 150, Unit Degrees (°) gives Radians 2.617994, Radians as a multiple of π 0.833333, Gradians 166.666667, Degrees, minutes, seconds 150° 0′ 0″, Coterminal angle in [0°, 360°) 150, Reference angle 30, Quadrant Quadrant II, Type Obtuse, Supplement 30, Sine 0.5, Cosine -0.866025, Tangent -0.57735.Source: OpenStax Algebra and Trigonometry 2e, section 7.1, Angles (radians = degrees × π ÷ 180; coterminal and reference angles), CC BY 4.0 (https://openstax.org/books/algebra-and-trigonometry-2e/pages/7-1-angles, retrieved 2026-10-01)
- Angle -405, Unit Degrees (°) gives Coterminal angle in [0°, 360°) 315, Reference angle 45, Quadrant Quadrant IV, Turns -1.125, Degrees, minutes, seconds −405° 0′ 0″.Source: OpenStax Algebra and Trigonometry 2e, section 7.1, Angles: coterminal angles differ by multiples of 360° (https://openstax.org/books/algebra-and-trigonometry-2e/pages/7-1-angles)
- Angle 12.5125, Unit Degrees (°) gives Degrees, minutes, seconds 12° 30′ 45″, Complement 77.4875, Type Acute.Source: NIST Special Publication 811, Appendix B: 1° = 60′, 1′ = 60″ (https://www.nist.gov/pml/special-publication-811)
- Angle 0.5, Unit Multiples of π radians gives Degrees 90, Quadrant On the positive y-axis, Type Right, Sine 1, Cosine 0, Complement 0.Source: OpenStax Algebra and Trigonometry 2e, section 7.1, Angles: π ÷ 2 radians = 90° (https://openstax.org/books/algebra-and-trigonometry-2e/pages/7-1-angles)
- Angle 1, Unit Radians gives Degrees 57.29578, Radians 1, Degrees, minutes, seconds 57° 17′ 44.81″.Source: NIST Special Publication 811, Appendix B: 1 rad = 57.295 78° (https://www.nist.gov/pml/special-publication-811)
How it works
Type the angle (from −1,000,000,000 to 1,000,000,000) and pick its unit. The calculator first finds the angle in degrees:
| Unit | Degrees |
|---|---|
| Degrees | the value |
| Radians | value × 180 ÷ π |
| Multiples of π radians | value × 180 |
| Gradians | value × 9 ÷ 10 |
| Turns | value × 360 |
For every unit except radians, the degrees and everything worked from them are exact fractions of the decimal you typed. An angle typed in radians uses π to double precision, and its degrees are that floating-point value read as its shortest decimal.
From the degrees d:
- Radians = d × π ÷ 180 (or the value typed, when it is in radians). Radians as a multiple of π = d ÷ 180. Gradians = d × 10 ÷ 9. Turns = d ÷ 360.
- Degrees, minutes, seconds: the size of d in hundredths of a second, rounded half up, split into whole degrees, whole minutes (60 to a degree) and seconds (60 to a minute), written like 12° 30′ 45″ with the seconds to at most 2 decimals and no trailing zeros. A negative angle starts with a minus sign, unless it rounds to 0° 0′ 0″, which shows with no sign.
- Coterminal angle c = d − 360 × ⌊d ÷ 360⌋, so 0 ≤ c < 360.
- Reference angle: c when c ≤ 90; 180 − c when 90 < c ≤ 180; c − 180 when 180 < c ≤ 270; 360 − c otherwise.
- Quadrant of c: on the positive x-axis (0), quadrant I (0 to 90), on the positive y-axis (90), quadrant II (90 to 180), on the negative x-axis (180), quadrant III (180 to 270), on the negative y-axis (270), quadrant IV (270 to 360).
- Type, for 0 ≤ d ≤ 360 only: zero angle (0), acute (below 90), right (90), obtuse (below 180), straight (180), reflex (below 360), full turn (360).
- Complement = 90 − d, shown only when 0 ≤ d ≤ 90. Supplement = 180 − d, shown only when 0 ≤ d ≤ 180.
- Sine, cosine, tangent of c. First c is split exactly, in degrees, into the nearest axis and a rest: c = 90k + r, with k = c ÷ 90 rounded half up and −45 ≤ r ≤ 45. Then, with s = sin r and t = cos r (r in radians, r × π ÷ 180, to double precision): k = 0 or 4 gives sine s, cosine t; k = 1 gives sine t, cosine −s; k = 2 gives sine −s, cosine −t; k = 3 gives sine −t, cosine s. On an axis (r = 0) the values are exact: sine 0, 1, 0, −1 and cosine 1, 0, −1, 0. The tangent is sine ÷ cosine and is left out where the cosine is 0.
What the calculator shows
Degrees, the coterminal angle, the reference angle, the complement and the supplement with at most 6 decimal places, except that a value below 0.0001 (and not 0) shows 6 significant figures, so 0.0000005° shows as 0.0000005; radians, multiples of π, gradians, turns, sine, cosine and tangent to 10 significant figures. All are rounded half up for display only. Each value is shown from the nearest double-precision number, so past about 15 significant figures (for example degrees beyond 100,000,000,000 with decimals) the last digits shown can differ from the exact value.
Worked examples by hand
150°. Radians = 150 × π ÷ 180 = 5π ÷ 6 = 2.617993878; as a multiple of π, 150 ÷ 180 = 0.8333333333; gradians = 150 × 10 ÷ 9 = 166.6666667. It is in quadrant II, so the reference angle is 180 − 150 = 30°. It is obtuse, with supplement 30° and no complement. sin 150° = 0.5, cos 150° = −0.8660254038, tan 150° = −0.5773502692.
−405°. −405 ÷ 360 = −1.125, so ⌊−1.125⌋ = −2 and the coterminal angle is −405 + 720 = 315°, in quadrant IV, with reference angle 360 − 315 = 45°. In turns it is −1.125; in DMS, −405° 0′ 0″.
12.5125°. 0.5125 × 60 = 30.75′, and 0.75 × 60 = 45″: 12° 30′ 45″. It is acute; its complement is 90 − 12.5125 = 77.4875°.
0.5π radians. 0.5 × 180 = 90°: a right angle on the positive y-axis, with sine 1, cosine 0, no tangent, and complement 0°.
1 radian. 180 ÷ π = 57.29577951°. In seconds, 57.29577951 × 3,600 = 206,264.806; that is 57° (205,200″) plus 1,064.806″ = 17′ 44.81″.
Other questions people ask
How do I convert degrees to radians?
Multiply by π and divide by 180. 150° is 150 × π ÷ 180 = 5π ÷ 6 ≈ 2.618 radians. To go back, multiply radians by 180 and divide by π: 1 radian ≈ 57.2958°.
What is a coterminal angle?
Two angles are coterminal when they end on the same side after turning from the positive x-axis. They differ by whole turns of 360°. The calculator gives the coterminal angle from 0° up to (not including) 360°: −405° is coterminal with −405 + 2 × 360 = 315°.
What is a reference angle?
It is the acute angle between the angle’s terminal side and the x-axis, from 0° to 90°. In quadrant II it is 180° minus the angle, in quadrant III the angle minus 180°, and in quadrant IV 360° minus the angle. The reference angle of 150° is 30°.
What are complementary and supplementary angles?
Two angles are complementary when they add up to 90° and supplementary when they add up to 180°. The complement of 12.5125° is 77.4875°; the supplement of 150° is 30°.
How do I write an angle in degrees, minutes and seconds?
Keep the whole degrees, multiply the decimal part by 60 for minutes, then multiply the decimal part of the minutes by 60 for seconds. 12.5125° is 12° and 0.5125 × 60 = 30.75′, so 12° 30′ 45″.
What is a gradian?
A unit that divides a right angle into 100 parts, so a full turn is 400 gradians (also called gons). Degrees × 10 ÷ 9 gives gradians.
What kinds of angles are there?
A zero angle is 0°, an acute angle is between 0° and 90°, a right angle is exactly 90°, an obtuse angle is between 90° and 180°, a straight angle is 180°, a reflex angle is between 180° and 360°, and a full turn is 360°.