Angle Converter
Frequently Asked Questions
How do I convert degrees to radians?
Multiply the degree value by π divided by 180 (approximately 0.017453). For example, 90 degrees equals 90 × π/180 = π/2 ≈ 1.5708 radians. The Angle Converter does this instantly — just enter your degree value, select Degrees as the source unit, and read the Radians result.
Why do programming languages use radians instead of degrees?
Radians are the natural mathematical unit for angles because they arise directly from arc length on a circle. When using radians, the derivative of sin(x) is cos(x) with no scaling factor. All standard math libraries — JavaScript, Python, C, Java — expect radians in trigonometric functions, so passing degrees produces incorrect results.
What is a gradian and when is it used?
A gradian (also called gon or grad) divides a full circle into 400 equal parts, making a right angle exactly 100 gradians. This clean decimal relationship makes gradians convenient for surveying calculations. They are used primarily in European land surveying, some civil engineering workflows, and French cadastral mapping systems.
How many arcseconds are in one degree?
One degree equals 3,600 arcseconds. A degree is divided into 60 arcminutes, and each arcminute is divided into 60 arcseconds, so 60 × 60 = 3,600 arcseconds per degree. Arcseconds are used in precision astronomy, GPS coordinates, and geodetic surveying where very small angular differences matter.
Can I convert negative angles?
Yes. Negative angles represent rotation in the opposite direction — counterclockwise vs. clockwise depending on convention. Enter a negative value such as −45 degrees and the converter outputs the equivalent negative value in every other unit: −0.7854 radians, −50 gradians, −0.125 turns, −2700 arcminutes, and −162000 arcseconds.
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