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What is an Angle Converter?

An angle converter is a digital tool designed to convert angle units from one system to another. An angle is a geometric quantity that represents the amount of rotation or deviation from a straight line. In education and engineering, we encounter various angle units: degrees (°) for everyday measurements, radians (rad) for advanced mathematics and physics, gradians (gon) for surveying, and DMS (degrees-minutes-seconds) for navigation and geodesy. Kalkulab's Angle Converter is a practical solution for high school students, engineering students, navigators, surveyors, and professionals who need to convert angle units quickly and accurately. This tool supports various angle units including degrees, radians, gradians, DMS (degrees-minutes-seconds), revolutions, and angular mils.

Angle Conversion Factors

180° = π radians = 200 gradians = 200 gonFormula: 1° = π/180 rad ≈ 0.01745 rad = 60 arcmin = 3600 arcsec

Variables:

  • 1°Degrees
    1/360 of a circle, common angle unit(e.g.: 1° = π/180 rad)
    💡 Everyday use, navigation, GPS, compass
  • 1 radRadian (rad)
    Angle whose arc length equals the radius(e.g.: 1 rad = 180/π ° ≈ 57.3°)
    💡 Mathematics, physics, calculus, trigonometry
  • 1 gonGradian (gon/grade)
    1/400 of a circle, decimal system(e.g.: 1 gon = 0.9° = π/200 rad)
    💡 Surveying, geodesy, land measurement
  • DMSDegrees-Minutes-Seconds
    45°30'36" = 45 degrees 30 minutes 36 seconds(e.g.: 1° = 60' = 3600")
    💡 Navigation, astronomy, geographic coordinates
  • 1 revFull Revolution
    One complete rotation = 360°(e.g.: 1 rev = 360° = 2π rad)
    💡 Rotating machinery, shafts, turbines
  • 1 milAngular Mil
    1/6400 of a circle (military mil)(e.g.: 1 mil = 0.05625°)
    💡 Military artillery, aircraft navigation

Categories:

Common UnitsDegrees and DMS
Math UnitsRadians
Survey UnitsGradian/Gon
Other UnitsRev, Mil, Quadrant

How to Use the KalkuLab Angle Conversion Calculator

Using the KalkuLab angle conversion calculator is easy. Follow these steps:

  1. 1

    Enter Angle Value

    Type the value to convert (whole numbers or decimals).

  2. 2

    Select Source Unit

    Choose degrees (°), radians (rad), gradians (gon), DMS, revolutions, or others.

  3. 3

    View Results

    All unit conversions appear automatically.

  4. 4

    Optional: Reset

    Change units or reset to start over.

💡 Tip:

  • •Remember: 180° = π radians
  • •1 full rotation = 360° = 2π rad = 400 gon
  • •DMS: 1° = 60 minutes, 1 minute = 60 seconds

Examples

Example 1: Trigonometry (Degrees to Radians)

Problem:

Convert 60° to radians for calculus.

Solution:
  1. 1.60 × π/180 = π/3 rad
Result:π/3 rad ≈ 1.047 rad

Essential for sin/cos calculations in radians.

Example 2: Navigation DMS

Problem:

Convert 45.51° to DMS format.

Solution:
  1. 1.45° + 0.51×60 = 30.6'
  2. 2.30' + 0.6×60 = 36"
Result:45°30'36"

Standard format for GPS and nautical coordinates.

Frequently Asked Questions

How do I convert degrees to radians?
Multiply degrees by π/180. Example: 90° = π/2 rad ≈ 1.571 rad.
What are gradians used for?
Gradians (400 per full circle) are used in surveying and geodesy.
What is DMS format?
Degrees-Minutes-Seconds, e.g., 45°30'36" for navigation and geographic coordinates.

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References