Degrees to Radians Calculator

Degrees to Radians is evaluated from Angle Value, Input Unit and Radius. The calculation reports Degrees, Radians and Gradians.

Results

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About the Degrees to Radians Calculator

Degrees to Radians is treated here as a quantitative relation between Angle Value, Input Unit and Radius and Degrees, Radians, Gradians and Arc Length.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
radians = degrees x pi/180
degrees = radians x 180/pi
gradians = degrees x 10/9
Arc length = r x θ (θ in radians)

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

radians = degrees x pi/180
degrees = radians x 180/pi
gradians = degrees x 10/9
Arc length = r x θ (θ in radians)

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: 45° → Radians for JavaScript Math

Inputs

angle: 45 input_unit: degrees
Degrees: 45 deg. Radians: 0.78539816 rad. Gradians: 50 grad

With Angle Value = 45 and Input Unit = degrees as the stated inputs, the result is Degrees = 45 deg, Radians = 0.78539816 rad and Gradians = 50 grad. Each value corresponds to the declared output fields.

Example 2: Arc Length — Circular Highway On-Ramp

Inputs

angle: 270 input_unit: degrees radius: 500
Degrees: 270 deg. Radians: 4.71238898 rad. Gradians: 300 grad. Arc Length: 2,356.19449 units. Sector Area: 589,048.622548 units^2

With Angle Value = 270, Input Unit = degrees and Radius = 500 as the stated inputs, the result is Degrees = 270 deg, Radians = 4.71238898 rad and Gradians = 300 grad. Each value corresponds to the declared output fields.

Example 3: Surveying with Gradians

Inputs

angle: 100 input_unit: gradians
Degrees: 90 deg. Radians: 1.57079633 rad. Gradians: 100 grad

With Angle Value = 100 and Input Unit = gradians as the stated inputs, the result is Degrees = 90 deg, Radians = 1.57079633 rad and Gradians = 100 grad. Each value corresponds to the declared output fields.

Example 4: Sector Area — Pizza Slice

Inputs

angle: 60 input_unit: degrees radius: 7
Degrees: 60 deg. Radians: 1.04719755 rad. Gradians: 66.666667 grad. Arc Length: 7.330383 units. Sector Area: 25.65634 units^2

With Angle Value = 60, Input Unit = degrees and Radius = 7 as the stated inputs, the result is Degrees = 60 deg, Radians = 1.04719755 rad and Gradians = 66.666667 grad. Each value corresponds to the declared output fields.

Common Use Cases

  • Convert degrees to radians for programming trig functions
  • Calculate arc length of a circle sector
  • Convert navigation bearings
  • Convert gradians used in surveying