Convert angles between degrees, radians, gradians, turns, and arcminutes. Uses the exact formula radians = degrees × π/180.
The Angle Converter converts between degrees, radians, gradians (gons), turns (revolutions), and arcminutes/arcseconds. Enter an angle in any unit and see all equivalents instantly with precise mathematical accuracy.
Angles are measured in different units depending on the field. Degrees (0–360) are used in everyday geometry, navigation, and engineering. Radians (0–2π) are the mathematical standard used in calculus, physics, and programming. Gradians (0–400) are used in surveying and some European countries. Turns (0–1) represent full revolutions.
The core relationship is: radians = degrees × π/180. Our converter applies this precisely using JavaScript's Math.PI constant for maximum accuracy. It's essential for students, engineers, programmers, and scientists working across different angle conventions.
By calculating this metric accurately, professionals gain actionable insights that support smarter work habits, more realistic scheduling, and improved work-life balance over time. Understanding this metric in precise terms allows professionals to set achievable targets, measure progress objectively, and continuously refine their approach to time and task management.
Math libraries use radians, textbooks use degrees, surveyors use gradians. This converter bridges all systems with exact mathematical precision for instant cross-unit reference. Precise quantification supports meaningful goal-setting and accountability, ensuring that improvement efforts are focused on areas with the greatest potential impact on output. Data-driven tracking enables proactive schedule management, helping professionals protect focused work time and reduce the cognitive overhead of constant task-switching throughout the day.
radians = degrees × π / 180 gradians = degrees × 400 / 360 turns = degrees / 360 arcminutes = degrees × 60 arcseconds = degrees × 3600 1 full circle = 360° = 2π rad = 400 grad = 1 turn
Result: π/2 rad ≈ 1.5708 rad
90 degrees = 90 × π/180 = π/2 ≈ 1.5708 radians. Also equals 100 gradians, 0.25 turns, 5,400 arcminutes, and 324,000 arcseconds. This is a right angle.
Degrees originated in ancient Babylon (base-60 system). Radians were formalized by mathematicians for their elegant properties in calculus. Gradians were introduced during the French Revolution as part of the metric push. Each unit serves its field optimally.
JavaScript's Math.sin(), Math.cos(), Math.atan2() all expect radians. Python's math module is the same. Always convert degrees to radians before calling trig functions: Math.sin(degrees * Math.PI / 180). Some libraries provide toRadians() and toDegrees() helpers.
0° = start, 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2 (right angle), 180° = π (straight line), 270° = 3π/2, 360° = 2π (full circle). Memorizing these is essential for trigonometry and physics.
Multiply the degree value by π/180 (approximately 0.01745). For example, 45° × π/180 = π/4 ≈ 0.7854 radians. To go from radians to degrees, multiply by 180/π.
Radians simplify calculus formulas. The derivative of sin(x) is cos(x) only when x is in radians. In degrees, the derivative includes a π/180 factor. Radians make formulas cleaner because they measure arc length on the unit circle directly.
A gradian (also called gon or grad) divides a right angle into 100 equal parts. A full circle = 400 gradians. This makes percentage calculations easy: a 1% slope = 1 gradian. Gradians are used in surveying, particularly in Europe.
One turn (or revolution) equals 360 degrees = 2π radians = 400 gradians. It's the most intuitive unit for full rotations. 0.5 turns = 180° (half turn), 0.25 turns = 90° (quarter turn).
A full circle contains exactly 2π radians (≈ 6.2832). A half circle = π radians. A quarter circle (right angle) = π/2 radians. One radian ≈ 57.296 degrees.
One degree = 60 arcminutes (60'), and one arcminute = 60 arcseconds (60"). They provide finer angular resolution. Used in astronomy (star positions), navigation (latitude/longitude), and optics.