Degrees to Radians Converter

The formula is: radians = degrees × π/180. Because π/180 is about 0.0174533, you can also multiply by that decimal, but keeping π in the answer gives exact values such as π/4 instead of 0.785398.

Worked example: 135° × π/180 = 3π/4 rad, which is about 2.356194 rad.

Once the angle is in radians, the Sine Calculator and the Cosine Calculator take it directly, and the Exact Value of Trig Functions Calculator gives exact sine, cosine, and tangent values for 0°, 30°, 45°, 60°, and 90°.

1. Write down the angle in degrees, for example 60°.
2. Multiply it by π/180: 60 × π/180 = 60π/180.
3. Simplify the fraction: 60π/180 = π/3.
4. If you need a decimal, replace π with 3.14159: π/3 is about 1.0472 rad.

Degrees to Radians in Terms of π

To keep the answer exact, write it as a fraction of π instead of a decimal: put the degrees over 180, reduce the fraction, and attach π. For 225°, 225/180 reduces to 5/4, so 225° = 5π/4 rad. For 10°, 10/180 reduces to 1/18, so 10° = π/18 rad. The In Terms of π result above does this reduction for you.

Why Mathematicians Prefer Radians

The radian is the SI unit of angle, while the degree is only accepted for use alongside it. Radians make calculus clean: the derivative of sin(x) is cos(x) only when x is in radians, and in degrees an extra π/180 factor appears in every formula. That is why many math functions in software expect radians: Math.sin in JavaScript takes its angle in radians, and so does the SIN function in Excel.

Degree Mode vs Radian Mode

A calculator in the wrong mode is the most common cause of a wrong trig answer: sin(90°) is exactly 1, but sin(90) in radian mode is about 0.894, because 90 radians is a very different angle. Check the mode before trusting a result.

Every standard angle on the unit circle (sometimes called the radian circle), in exact π form and as a decimal:

Trigonometry and calculus classes switch between the two units constantly. Software is the other big reason: a trig function that expects radians gives a wrong answer for an angle typed in degrees, so the degrees are converted first. The Microsoft documentation for the Excel SIN function says exactly that: convert a degree value before taking the sine. The same conversion comes up in physics for angular velocity and in engineering for rotation.

Radians also keep circle formulas short: an arc is the radius times the angle in radians, and the Sector Area Calculator returns the arc length and sector area for a given radius and angle. To switch a whole calculation between degree and radian mode, use the Scientific Calculator.

Every converter in the angle family, starting with the reverse of this one:

• Radians to Degrees Converter: multiply by 180/π (1 rad ≈ 57.2958°)
• Degrees to Arcminutes Converter: 1° = 60 arcminutes
• Degrees to Arcseconds Converter: 1° = 3,600 arcseconds
• Decimal Degrees to DMS Calculator: turn 30.51° into 30° 30′ 36″, with N/S/E/W
• Angle Converter: every angle unit at once, including gradians, turns, and milliradians