Degrees to Radians Calculator with Pi Fractions

Degrees to Radians Calculator

Degrees to radians Radians to degrees

Angle in degrees

Common angles:

Drag on the circle to change the angle. The orange arc is the part of the circumference the angle sweeps.

Result:

Radians (decimal):

Radians as a multiple of π:

Degrees:

Degrees, minutes and seconds:

Full turns:

Calculation:

Enter an angle in degrees or in radians and the calculator converts it instantly. When the result is an exact multiple of π you see it as a fraction, for example 150° = 5π/6, along with the decimal. The angle is drawn on a circle with the arc highlighted, so you can see how much of a turn it represents.

Below you will find the formulas, worked examples, a conversion table and the most common questions.

How to use the degrees to radians calculator

Step 1: Choose Degrees to radians or Radians to degrees.

Step 2: Enter the angle, move the slider, drag on the circle or tap a common angle. In radians you can type pi/6, 3pi/4 or a decimal.

Step 3: It calculates instantly, and also with the Calculate button or the Enter key.

Step 4: Read the result as a multiple of π, as a decimal and in degrees, minutes and seconds. The Calculation box shows each step with your numbers.

Formulas to convert degrees and radians

A full turn is 360° or 2π radians, so 180° equals π radians. The two formulas come from that:

radians = degrees × π ÷ 180

degrees = radians × 180 ÷ π

One radian is the angle that cuts off an arc equal to the radius of the circle, and it measures 57.2958°. To leave the answer as a fraction of π, simplify the ratio degrees ÷ 180. For example, 150 ÷ 180 = 5/6, so 150° = 5π/6 radians.

Degrees to radians examples

Example 1: 150° to radians

150 × π ÷ 180 = (150 ÷ 180) × π = 5/6 × π = 5π/6 ≈ 2.618 rad

First simplify the fraction by dividing by 30, then multiply by π.

Example 2: 22.5° to radians

22.5 ÷ 180 = 1/8, so 22.5° = π/8 ≈ 0.3927 rad

Angles with decimals can also give an exact fraction of π. The calculator detects it on its own.

Example 3: 3π/4 radians to degrees

3π/4 × 180 ÷ π = 3/4 × 180 = 135°

When you multiply by 180 ÷ π, the π cancels and only the fraction times 180 is left.

Example 4: 2 radians to degrees

2 × 180 ÷ π ≈ 114.591559°, which is 114° 35′ 29.61″

Since 2 is not a rational multiple of π, the result in degrees is a decimal.

Degrees to radians table

Degrees	Radians (multiple of π)	Radians (decimal)
0°	0	0
30°	π/6	0.5236
45°	π/4	0.7854
60°	π/3	1.047
90°	π/2	1.571
120°	2π/3	2.094
135°	3π/4	2.356
150°	5π/6	2.618
180°	π	3.142
210°	7π/6	3.665
225°	5π/4	3.927
240°	4π/3	4.189
270°	3π/2	4.712
300°	5π/3	5.236
315°	7π/4	5.498
330°	11π/6	5.76
360°	2π	6.283

Frequently asked questions

How many degrees are in one radian?

One radian is 57.2958°, because 180 ÷ π = 57.2958. It is the angle whose arc is as long as the radius.

Why does 180° equal π radians?

Because the circumference of a circle is 2π times the radius, and an angle in radians is the arc length divided by the radius. Half a turn sweeps an arc of π radii, which is π radians.

What is the fastest way to convert degrees to radians?

Multiply by π and divide by 180. To keep it exact, simplify the fraction degrees ÷ 180: 45° is 45 ÷ 180 = 1/4, so π/4.

How do I type π in the calculator?

Type pi or the symbol π, for example pi/6 or 2pi/3. You can also type a decimal such as 0.5236, but then the result in degrees will be approximate.

What about negative angles or angles larger than 360°?

They convert the same way, and the circle shows the equivalent angle within one turn. For example, -45° = -π/4 radians, and 450° is one turn plus 90°.

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