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Reference Angle Degrees Radians Calculator

Radians: --

How this degrees to radians calculator works

Enter an angle in degrees. The calculator converts it to radians with Radians = Degrees × π ÷ 180. 180 degrees becomes 3.141593. 90 degrees becomes 1.570796. The result is labelled Radians and shown to six decimal places.

A half turn is 180 degrees and π radians, so the scale factor is π/180. 30 degrees is π/6 ≈ 0.523599. 45 degrees is π/4 ≈ 0.785398. 60 degrees is π/3 ≈ 1.047198. A full turn of 360 degrees is 2π ≈ 6.283185.

Any finite degree value is accepted, including negatives and decimals. −90 degrees is −1.570796. An empty field shows “--.” Despite the page title, this tool does not compute a separate acute reference angle; it only converts the number you type from degrees to radians.

To go back, multiply radians by 180 and divide by π. Many programming and calculus trig functions expect radians, so 90 degrees must be entered as about 1.570796 when the function is in radian mode.

Degrees to radians examples

Each row is Degrees × π ÷ 180, rounded to six decimals as on the calculator.

DegreesRadiansWhat it marks
00.000000Zero angle
10.017453One degree
300.523599π/6
450.785398π/4
601.047198π/3
901.570796π/2
1803.141593π
3606.2831852π

How to read the result

  • Degrees × π ÷ 180

    180° → 3.141593 radians.

  • Common fractions of π

    90° → π/2, 45° → π/4, 30° → π/6.

  • Six decimal places

    1° shows as 0.017453.

  • Conversion only

    Does not reduce to an acute reference angle.

Frequently asked questions

  • What does this calculator convert?

    An angle in degrees into radians. The formula is Radians = Degrees × π ÷ 180. 180 degrees becomes 3.141593 radians (π). 90 degrees becomes 1.570796 radians (π/2). The result is shown to six decimal places.

  • Why multiply by π and divide by 180?

    A full circle is 360 degrees and also 2π radians, so 180 degrees equals π radians. Scaling by π/180 converts any degree measure into that radian measure. 1 degree is about 0.017453 radians.

  • What is 30 degrees in radians?

    30 × π ÷ 180 = π/6 ≈ 0.523599. 45 degrees is π/4 ≈ 0.785398. 60 degrees is π/3 ≈ 1.047198.

  • What is 360 degrees in radians?

    360 × π ÷ 180 = 2π ≈ 6.283185. That is one full turn. 270 degrees is 3π/2 ≈ 4.712389.

  • Can the degree value be negative?

    Yes. Negative degrees convert to negative radians with the same formula. −90 degrees is −1.570796 radians. An empty field leaves the result as “--.”

  • Does this find a reference angle?

    No. Despite the page title, the calculator only converts the number you enter from degrees to radians. It does not reduce the angle to an acute reference angle in a quadrant diagram.

  • How precise is the answer?

    Radians are fixed at six decimal places. 0 degrees shows 0.000000. 180 degrees shows 3.141593. 90 degrees shows 1.570796.

  • How do I turn radians back into degrees?

    Multiply by 180 and divide by π. Degrees = Radians × 180 ÷ π. 3.141593 × 180 ÷ π ≈ 180 degrees. π/2 × 180 ÷ π = 90 degrees.

  • What inputs are accepted?

    Any finite number in the Degrees box. Decimals such as 22.5 are allowed. 22.5 × π ÷ 180 ≈ 0.392699 radians.

  • When are radians used?

    Many calculus and programming trig functions expect radians. Entering 90 when a function wants radians is wrong; use about 1.570796 instead, which is what this page prints for 90 degrees.