Radians to Degrees
Type an angle in either box and the other one follows. The difference from the converters on page one is what this page accepts and what it gives back: 3pi/4, π/2, -pi/6, 2pi and 1.5pi are read as written, and the answer keeps the exact fraction of π instead of handing back a rounded decimal, so π/6 is 30 degrees, worked out as 180 divided by 6 in whole numbers rather than through a decimal that comes back 29.999999999999996. Every angle you can write in degrees is some exact fraction of π, and the exact-form line shows it: 57 degrees is 19π/60. The angle is drawn on a unit circle as you type, sweeping the other way when it is negative, and named beneath the drawing by quadrant, by coterminal angle and by any whole turns, so a reflex angle or a minus sign is visible rather than inferred. A table of every angle the circle is drawn with sits under the tool. It runs in this tab, with no upload and no account.
degrees = radians × 180 / π, and radians = degrees × π / 180. Either box takes a multiple of π, written 3pi/4, pi/2 or 2pi, and the other box follows as you type.
- Where it lands
- second quadrant
- Measured from zero
- 135° from the positive x-axis
- Angle type
- Obtuse: past a right angle
A unit circle with an angle of 135 degrees drawn from the positive x-axis. It lands in the second quadrant.
Worked examples
Each one is converted by the same code the boxes above use. Press Use to put it in the tool.
Every angle on the unit circle
The exact column is the fraction of π in lowest terms. Every angle you can write in degrees is some exact fraction of π, not only the ones below: 57° is exactly 19π/60, which the tool writes out in full even though no unit circle is drawn with it. The circle uses denominators up to 24, and the tool says when an angle is one of those.
| Degrees | Radians, exact | Radians, decimal |
|---|---|---|
| 0° | 0 | 0 |
| 30° | π/6 | 0.523598775598 |
| 45° | π/4 | 0.785398163397 |
| 60° | π/3 | 1.0471975512 |
| 90° | π/2 | 1.57079632679 |
| 120° | 2π/3 | 2.09439510239 |
| 135° | 3π/4 | 2.35619449019 |
| 150° | 5π/6 | 2.61799387799 |
| 180° | π | 3.14159265359 |
| 210° | 7π/6 | 3.66519142919 |
| 225° | 5π/4 | 3.92699081699 |
| 240° | 4π/3 | 4.18879020479 |
| 270° | 3π/2 | 4.71238898038 |
| 300° | 5π/3 | 5.23598775598 |
| 315° | 7π/4 | 5.49778714378 |
| 330° | 11π/6 | 5.75958653158 |
| 360° | 2π | 6.28318530718 |
Common questions
- What is the formula for converting radians to degrees?
- Degrees = radians × 180 / π, and radians = degrees × π / 180 going the other way. Both are printed under the boxes. The 180/π comes from the definition of the two units: a half turn around a circle is π radians and it is also 180 degrees, so π radians and 180 degrees are two names for the same angle and dividing one by the other gives the factor 57.29577951308232... The useful part is what happens when the angle is itself a multiple of π: in 3π/4 × 180 / π the π cancels and 3 × 180 / 4 is exactly 135. This page does that step with whole numbers, which matters wherever the decimal route drifts: π/6 sent through the decimals comes back as 29.999999999999996 degrees, and through the fraction it is 30.
- How do I enter an angle like 3pi/4?
- Type it the way you write it. 3pi/4, 3π/4 and 3*pi/4 are all read the same, capitals and spaces are ignored, pi on its own is π, 2pi is a full turn, -pi/6 gives -30 degrees, and 1.5pi is read as the fraction 3π/2. A trailing rad is allowed too. A fraction with no π in it, such as 3/4, is taken at face value as three quarters of one radian, not as three quarters of π. If you type π into the degrees box the tool does not guess: it tells you that π is a radian measure and belongs in the other box.
- Why is 1 radian 57.2957795131 degrees and not a round number?
- One radian is the angle whose arc is as long as the radius, and it takes 2π of them to go all the way round. π is irrational, so no whole number of degrees ever lands exactly on a whole number of radians. 1 radian is 180/π degrees, which is 57.29577951308232... and continues forever; this page shows 57.2957795131, which is that number rounded to twelve significant digits. The round numbers live on the other side: 30, 45, 90 and 180 degrees are exactly π/6, π/4, π/2 and π.
- Is the decimal this page shows exact?
- The fraction is exact and the decimal is a rounding to twelve significant digits, which is why both are on screen. π radians is exactly 180 degrees; 3.14159 radians, the decimal people use for π, is 179.999847961 degrees, and the difference is real rather than a display artefact. When you type a decimal such as 2.356 into the radians box, the exact-form line says there is no fraction of π for it rather than inventing one, and the degrees come back as 134.988856533.
- How do I convert degrees to radians here?
- Type the degrees into the degrees box and the radians appear beside them: the conversion runs both ways in the same two fields. 30 degrees is π/6, 45 is π/4, 90 is π/2, 180 is π and 360 is 2π, and the table under the tool lists every angle the unit circle is drawn with, in both the exact form and the decimal. Degrees written with a degree sign, such as 90°, are accepted, and so is a fraction of a degree such as 1/2.
- Which angles come back as an exact fraction of π?
- All of them, when the angle starts in degrees: 57 degrees is exactly 19π/60 and the exact-form line says so. What changes is which fraction leads the answer. A denominator of 24 or less covers every angle a unit circle is drawn with, and those fractions are written straight into the radians box; past that the decimal leads, because 123.456 degrees is exactly 1286π/1875, which is true and unreadable. An angle typed as a decimal in radians, such as 2.356, is not a rational multiple of π at all, and the page says that instead.
- What do the unit circle and the lines under it tell me?
- The arm is drawn at your angle, measured from the positive x-axis, and the shaded sweep goes counterclockwise for a positive angle and clockwise for a negative one, so the sign is something you can see. Under it the page names where the angle lands, either a quadrant or the axis it sits on, the same angle measured from zero as a value between 0 and 360 degrees, and any whole turns: -90 degrees reads as 270 degrees with one turn back, and 450 reads as 90 with one turn forward. The sweep does not animate if your device asks for reduced motion.
- Is anything I type sent anywhere?
- No. The arithmetic runs in this page, in your browser, and nothing is uploaded. The angle you last converted is kept in this browser's own storage so the tool is still filled in when you come back, and that copy never leaves the device either. There is no account and no sign-in.
Degrees and radians are related by an exact definition, so a multiple of π converts exactly and this page shows that fraction when there is one. The decimal beside it is a rounding: π radians is exactly 180°, but 3.14159 radians is not.