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Angle Converter

Angle converter for radians, degrees, gradians, arcminutes, and related units. Enter a value, choose units, and get an instant result with formulas and examples.

Result: 1 Radian = 57.2957795131 Degree

Explain this result

The calculator converts 1 Radian to Degree and formats the result as 57.2957795131 Degree.

  1. 1 Radian x 1 = 1 Radian.
  2. 1 Radian / 0.0174532925 = 57.2957795131 Degree.
  3. The direct relationship is 1 Radian = 57.2957795131 Degree.

Formula

1 rad = 57.2957795131 deg

Angle conversions for math, navigation, and design

Angle units appear in geometry, trigonometry, navigation, surveying, machine setup, and graphics work. Degrees are common for everyday use, while radians are standard in many math and programming contexts.

When using trigonometric functions, confirm whether your calculator, spreadsheet, or code expects degrees or radians. A correct number in the wrong angle unit can produce a very wrong result.

Practical notes

  • A full circle is 360 degrees or 2 pi radians.
  • Radians are common in programming languages and calculus.
  • Degrees are easier for maps, compass headings, and visual angles.

How angle conversion works

Angle conversions use the relationship between a full circle, degrees, and radians. A full circle is 360 degrees or 2 pi radians, so radians and degrees can be converted with fixed formulas.

Example: pi radians to degrees

  1. Start with pi radians.
  2. Use the relationship degrees = radians x 180 / pi.
  3. pi x 180 / pi equals 180 degrees.

Practical notes

Practical use cases

  • Switching between degrees and radians for trigonometry, spreadsheets, and code.
  • Checking geometry, surveying, navigation, map, and graphics measurements.
  • Converting rotations, turns, arc minutes, and arc seconds for technical references.

Rounding and precision

  • Use enough decimals when small angular errors affect distance, alignment, or machining.
  • Radians often involve pi, so rounded decimal approximations can accumulate error.
  • For navigation or surveying, preserve the source format and datum conventions separately.

Common mistakes

  • Entering degrees into a function that expects radians.
  • Treating arc minutes or arc seconds as time units.
  • Rounding small angles too aggressively before using trigonometric functions.

Supported Units

UnitSymbolAlso known as
Radianrad-
Degreedeg-
Gradiangon-
Arcminutearcmin-
Arcsecondarcsec-

Common Conversion Rates

  • Degree (deg): 1 rad = 57.2957795131 deg
  • Gradian (gon): 1 rad = 63.6619772368 gon
  • Arcminute (arcmin): 1 rad = 3,437.7467707849 arcmin
  • Arcsecond (arcsec): 1 rad = 206,264.8062470964 arcsec

Example Calculations

InputResult
1 rad57.2957795131 deg
5 rad286.4788975654 deg
10 rad572.9577951308 deg
100 rad5,729.5779513082 deg

About This Converter

Use this angle converter to compare supported units, check formulas, and calculate everyday or technical values. The tool uses radian as its base reference and updates instantly when you change the amount or selected units.

Frequently Asked Questions

What is the angle converter?

The angle converter changes values between supported angle units using the conversion data in the calculator.

Which angle units are supported?

Supported units include Radian, Degree, Gradian, Arcminute, Arcsecond.

How do I convert angle units?

1 rad = 57.2957795131 deg

Calculator

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More common converters

  • radians to degrees
  • degrees to radians
  • degrees to gradians
  • gradians to degrees
  • degrees to arcminutes
  • arcminutes to degrees
  • degrees to arcseconds
  • arcseconds to degrees