Angle Converter

Angle Converter is evaluated from Angle Value and From Unit. The calculation reports Degrees, Radians and Arcminutes.

Results

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About the Angle Converter

Angle Converter is treated here as a quantitative relation between Angle Value and From Unit and Degrees, Radians, Arcminutes and Arcseconds.

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:
degrees → radians: rad = deg x pi/180
radians → degrees: deg = rad x 180/pi
degrees → arcminutes: arcmin = deg x 60
degrees → arcseconds: arcsec = deg x 3600
degrees → gradians: gon = deg / 0.9

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:

degrees → radians: rad = deg x pi/180
radians → degrees: deg = rad x 180/pi
degrees → arcminutes: arcmin = deg x 60
degrees → arcseconds: arcsec = deg x 3600
degrees → gradians: gon = deg / 0.9

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: 90° Right Angle to Radians

Inputs

value: 90 from_unit: degrees (°)
Degrees: 32,400 deg. Radians: 565.486678 rad. Arcminutes: 1,944,000 ′. Arcseconds: 116,640,000 ″. Gradians: 36,000 gon. Turns: 90 rev

With Angle Value = 90 and From Unit = degrees ( deg) as the stated inputs, the result is Degrees = 32,400 deg, Radians = 565.486678 rad and Arcminutes = 1,944,000 ′. Each value corresponds to the declared output fields.

Example 2: GPS Coordinate: 40°42′46″ (NYC latitude)

Inputs

value: 46 from_unit: arcseconds (″)
Degrees: 0.012778 deg. Radians: 0.000223 rad. Arcminutes: 0.767 ′. Arcseconds: 46 ″. Gradians: 0.0142 gon. Turns: 0.000035 rev

With Angle Value = 46 and From Unit = arcseconds (″) as the stated inputs, the result is Degrees = 0.012778 deg, Radians = 0.000223 rad and Arcminutes = 0.767 ′. Each value corresponds to the declared output fields.

Example 3: Rifle Scope: 5 mrad adjustment

Inputs

value: 5 from_unit: milliradians (mrad)
Degrees: 0.286479 deg. Radians: 0.005 rad. Arcminutes: 17.189 ′. Arcseconds: 1,031.3 ″. Gradians: 0.3183 gon. Turns: 0.000796 rev

With Angle Value = 5 and From Unit = milliradians (mrad) as the stated inputs, the result is Degrees = 0.286479 deg, Radians = 0.005 rad and Arcminutes = 17.189 ′. Each value corresponds to the declared output fields.

Example 4: Construction Slope: 1 gradian

Inputs

value: 1 from_unit: gradians (gon)
Degrees: 0.9 deg. Radians: 0.015708 rad. Arcminutes: 54 ′. Arcseconds: 3,240 ″. Gradians: 1 gon. Turns: 0.0025 rev

With Angle Value = 1 and From Unit = gradians (gon) as the stated inputs, the result is Degrees = 0.9 deg, Radians = 0.015708 rad and Arcminutes = 54 ′. Each value corresponds to the declared output fields.

Common Use Cases

  • Convert trigonometry angle from degrees to radians
  • Convert GPS coordinate minutes to decimal degrees
  • Convert surveying angle from gradians to degrees