Degrees to radians, multiply by π ÷ 180.

Radians = degrees × π ÷ 180. For 90° that is 90 × π ÷ 180 = 1.5708, which is exactly π/2. For 45° it is 0.7854, which is π/4. To go back, multiply radians by 180 ÷ π: 60° for π/3. One radian is 57.2958° and one degree is 0.017453 radians. NIST Special Publication 811, Appendix B.8 lists the degree as 1.745 329 E-02 radian (checked 24 Oct 2026).

How to use the converter

1. Choose Convert: degrees to radians, or radians to degrees.
2. Type the angle in the box, or press one of the angle buttons. For radians you can type a number such as 1.5, or a multiple of π such as pi/3, 3π/4 or 2pi.
3. Read the big result and The working. The first card gives the angle as a multiple of π when it is a simple fraction.
4. Use Copy result or Copy link to keep it.

Why it is π ÷ 180

A full turn is 360° and it is also 2π radians, since the circumference is 2π times the radius. Half a turn is 180° and π radians, so 180° = π radians. Divide both sides by 180 and 1° = π ÷ 180 radians. A fraction of a turn is the same fraction of 2π: a quarter turn is 2π ÷ 4 = π/2.

Common angles

The same table is built into the converter: type any of these degrees and the first card shows the π form.

Worked examples

• 100°. 100 ÷ 180 reduces to 5/9, so the angle is 5π/9 radians, which is 1.7453.
• 225°. 225 ÷ 180 reduces to 5/4, so 5π/4 radians, which is 3.9270.
• 2 radians to degrees. 2 × 180 ÷ π = 114.592°.
• 3π/4 to degrees. 3 × 180 ÷ 4 = 135°. The π cancels, so no decimals are needed.
• 57.3°. That is about one radian: 57.3 × π ÷ 180 = 1.0001.

Where radians show up

Many programming languages, such as JavaScript and Python, expect radians in their sine and cosine functions, so an angle written in degrees has to be converted first: 0.523599 for 30°. Formulas for arc length and sector area are also simplest in radians, because the radius times the angle is the arc length with no extra factor.

Radians back to degrees, a quick table

To go the other way multiply by 180 ÷ π, which is about 57.2958.

Degrees, minutes and seconds

Maps and surveys often write angles as degrees, minutes and seconds. A degree has 60 minutes (′) and a minute has 60 seconds (″), so a degree has 3,600 seconds. To change 40° 26′ 46″ to a decimal, add 40 + 26 ÷ 60 + 46 ÷ 3,600 = 40.44611°. Then multiply by π ÷ 180 for radians: 0.705918 rad. Type the decimal degrees into the converter.

Spinning speed in radians per second

A full turn is 2π radians, and a minute has 60 seconds. So revolutions per minute become radians per second by multiplying by 2π ÷ 60. At 60 rpm that is 6.2832 rad/s, and 1 rpm is 0.10472 rad/s.

Small angles: sin x is almost x

For small angles in radians, sin x is close to x. That is why radians are handy in physics. The error is the last column.

Why the calculator mode matters

In degree mode sin(30) is 0.5. In radian mode sin(30) is -0.98803 because 30 is read as 30 radians, which is 1,718.87° and many turns round the circle. Check the DEG or RAD sign on the screen before you read a result.

Mistakes to avoid

• Calculator in the wrong mode. sin(90) is 1 only in degree mode. In radian mode sin(90) is 0.8940. Check the mode before you read a result.
• Cutting π to 3.14 too early. For 180° that gives 3.14 rather than 3.14159, an error of 0.051 percent.
• Dividing instead of multiplying. Degrees to radians multiplies by π ÷ 180. The result is a small number, under 6.3 for one turn.
• Leaving the π off. 1.5708 is the number and π/2 is the same angle. Both are right, but 1.5708° is a very small angle in degrees.

The unit circle chart shows these angles on the circle with their sine and cosine, and the arc length calculator uses radians to find a curved length.