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Convert between degrees, radians, gradians, arcminutes, and arcseconds with formula display.
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All Conversions
Angle is a measure of rotation between two lines or rays. Different fields use different units to measure angles. Degrees are common in everyday use, radians are standard in mathematics and physics, gradians are used in surveying and engineering, while arcminutes and arcseconds are used in astronomy and navigation.
This converter supports conversion between all five common angle units with formula display. The conversion uses exact mathematical relationships: π radians = 180°, 90° = 100 gradians, 1° = 60 arcminutes = 3600 arcseconds.
A degree (1/360 of a full circle) is the most common unit for measuring angles. A radian is the angle where the arc length equals the radius. There are π radians in 180° (about 3.14159 rad = 180°). Radians are preferred in calculus and physics because they simplify formulas involving trigonometric functions.
Gradians (or gons) divide a right angle into 100 units, making a full circle 400 gradians. They are primarily used in surveying, civil engineering, and some European countries for land measurement. The advantage is that a quarter circle is exactly 100 gradians, making decimal calculations simpler.
Arcminutes (′) and arcseconds (″) are subdivisions of degrees used when precision matters. 1° = 60′ (arcminutes), 1′ = 60″ (arcseconds). They are commonly used in astronomy (measuring star positions), navigation (GPS coordinates), optics (lens specifications), and surveying (property boundaries).
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