An angle converter translates between degrees, radians, gradians, arcminutes, arcseconds, and turns. Each unit serves a different field: degrees for everyday use, radians for math and programming, gradians for surveying, and arcminutes/arcseconds for astronomy and GPS navigation.
Angle Converter
Common Reference Angles
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How to Convert Angle Units
Angle unit conversion is essential in mathematics, programming, surveying, astronomy, and navigation. Different fields have adopted different standards: mathematicians and programmers work in radians, everyday users think in degrees, surveyors use gradians, and astronomers use arcminutes and arcseconds for precise celestial coordinates.
Step 1: Degrees to Radians
Multiply degrees by π/180 ≈ 0.01745. Common values: 30° = π/6 ≈ 0.5236 rad, 45° = π/4 ≈ 0.7854 rad, 60° = π/3 ≈ 1.0472 rad, 90° = π/2 ≈ 1.5708 rad, 180° = π ≈ 3.1416 rad, 360° = 2π ≈ 6.2832 rad. Radians are the natural unit for mathematics — trigonometric functions in programming languages expect radians.
Step 2: Degrees to Gradians
Multiply degrees by 10/9 (or 1.1111). A right angle is 90° = 100 gradians. The gradian makes surveying calculations cleaner because right angles equal round numbers. Used in European surveying and cartography. 1 grad = 0.9° = π/200 rad.
Step 3: Degrees to Arcminutes and Arcseconds
1 degree = 60 arcminutes = 3600 arcseconds. GPS coordinates use degrees and decimal degrees or degrees-minutes-seconds (DMS). For example, latitude 40°30'15" means 40 degrees, 30 arcminutes, 15 arcseconds. Converting: 40 + 30/60 + 15/3600 = 40.504167 decimal degrees. Arcseconds are tiny: 1 arcsecond of latitude ≈ 30 meters on Earth's surface.
FAQ
How do I convert degrees to radians?
Multiply degrees by π/180 (approximately 0.017453). Example: 90° × π/180 = π/2 ≈ 1.5708 radians. Or simply multiply by 0.0174533. To go from radians to degrees, multiply by 180/π ≈ 57.2958.
What is a gradian (grad)?
A gradian (grad or gon) divides a full circle into 400 units, so a right angle (90°) equals 100 gradians. Gradians are used primarily in surveying and civil engineering, especially in European countries. 1 gradian = 0.9 degrees = π/200 radians.
What are arcminutes and arcseconds?
Arcminutes (') and arcseconds (") are subdivisions of degrees used in navigation, astronomy, and GPS coordinates. 1 degree = 60 arcminutes = 3600 arcseconds. A 1 arcminute difference in latitude equals approximately 1 nautical mile (1.852 km) on Earth's surface.
What is a turn in angle measurement?
A turn (also called revolution or cycle) represents one complete rotation: 360 degrees, 2π radians, or 400 gradians. Turns are used in engineering and mathematics when discussing rotational quantities. Half a turn = 180° = π radians.
Is this angle converter free?
Yes, completely free with no signup required. All conversions run instantly in your browser.