Convert angles between degrees, radians, gradians, arcminutes, and arcseconds with instant calculations and step-by-step formulas.
0.1666666667 Arcminute
Angles measure the amount of rotation between two intersecting rays. The sexagesimal system divides a circle into 360 degrees, which dates back to ancient Babylonian astronomy. Radians, the standard SI unit of angle measurement, relate angle directly to arc length along a circle of unit radius.
Radians are essential throughout physics and calculus because trigonometric derivatives require angles expressed in radians. Degrees, arcminutes, and arcseconds remain the primary coordinate standards for celestial navigation, cartography, and satellite guidance.
To convert degrees to radians, multiply the number of degrees by π/180 (approximately 0.0174533). For example, 180° = 180 × (π/180) = π radians (≈ 3.14159 rad).
One radian is equal to 180/π degrees, which is approximately 57.29578 degrees (57° 17′ 45″).
A gradian (symbol: grad or gon) is a metric angular unit where a full circle is divided into 400 gradians, making each right angle exactly 100 gradians (0.9 degrees per gradian).
An arcminute is 1/60th of a degree, while an arcsecond is 1/60th of an arcminute or 1/3600th of a degree. Both are used for high-precision angular measurements in astronomy and navigation.
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