Angle Converter
Convert between degrees, radians, gradians, and other angle units.
So funktioniert's
This converter handles angle measurement across degrees, radians, and gradians, converting your value to radians (the mathematical base unit) first, then from radians into your target unit.
Degrees are the everyday unit most people learn first, dividing a full circle into 360 equal parts â a convention dating back to ancient Babylonian astronomy, likely chosen because 360 divides evenly by many small numbers (and approximates the number of days in a year).
Radians are the standard unit in mathematics, physics, and engineering, defined so that one full circle equals exactly 2Ï radians (about 6.28319). This makes radians the natural unit for calculus and trigonometry, since many formulas (like arc length = radius Ă angle in radians) become clean and simple only when the angle is expressed in radians.
Gradians (also called gons) divide a full circle into 400 equal parts instead of 360, making a right angle exactly 100 gradians â a decimal-friendly system that was historically popular in surveying and some European engineering contexts, though it's far less common today than degrees or radians.
Common conversion factors: to convert degrees to radians, multiply by Ï/180 (â0.01745); to convert radians to degrees, multiply by 180/Ï (â57.2958); a full circle is 360°, 2Ï radians, or 400 gradians, and these three reference points anchor every other conversion between the units.
Angle conversions come up often in trigonometry homework, engineering calculations, and programming â many programming languages' built-in trig functions (sin, cos, tan) expect radians as input by default, which is a common source of bugs when a value is calculated in degrees but never converted before being passed to those functions.
Angles are also central to navigation, surveying, and computer graphics â compass bearings are expressed in degrees, 3D graphics engines frequently work internally in radians for rotation calculations, and GPS and mapping systems rely on precise angle conversions to translate between coordinate systems that may use different underlying angular units.
How do I convert degrees to radians?
Multiply degrees by Ï/180.
How do I convert radians to degrees?
Multiply radians by 180/Ï.
Why does math and physics use radians instead of degrees?
Radians make many formulas simpler and more natural â for example, arc length equals radius times angle only when the angle is expressed in radians, not degrees.
What is a gradian?
A unit that divides a full circle into 400 equal parts (rather than 360 for degrees), making a right angle exactly 100 gradians â used historically in surveying and some engineering contexts.
How many radians are in a full circle?
Exactly 2Ï radians, approximately 6.28319.
Why do programming languages expect radians for trig functions?
Radians are the mathematical standard unit for angles, so most languages' built-in sin, cos, and tan functions assume radian input by default â passing degrees directly without converting is a common bug.
How many degrees is a right angle?
90 degrees, which equals Ï/2 radians or 100 gradians.
Where does the 360-degree system come from historically?
It traces back to ancient Babylonian astronomy, likely chosen because 360 divides evenly by many small numbers and roughly approximates the number of days in a year.
Why do 3D graphics and game engines often use radians internally?
Radians integrate more naturally with the underlying trigonometric math used for rotations and transformations, even though degrees are often shown in user-facing settings for readability.
Are compass bearings measured in degrees or radians?
Degrees â compass bearings and navigation headings conventionally use a 0-360 degree system, requiring conversion to radians for use in most mathematical or programming calculations.
How many gradians are in a right angle?
100 gradians â the gradian system was specifically designed so that a right angle equals a clean, round number.
Why might a surveying instrument use gradians instead of degrees?
The decimal-friendly 400-per-circle scale simplifies certain calculations in surveying and mapping, avoiding some of the fractional awkwardness that can come with the 360-degree system in specific technical contexts.