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Convert between degrees, radians, gradians, and turns for trigonometry and navigation
Radians to Degrees: degrees = radians × (180/π)
Gradians to Degrees: degrees = gradians × 0.9
Turns to Degrees: degrees = turns × 360
Multiply degrees by π/180. For example, 90° × (π/180) = π/2 radians ≈ 1.5708 radians. The formula is: radians = degrees × (π/180) or radians = degrees × 0.0174533.
Multiply radians by 180/π. For example, π radians × (180/π) = 180°. The formula is: degrees = radians × (180/π) or degrees = radians × 57.2958.
Gradians (also called gons or grades) divide a circle into 400 equal parts, with a right angle being 100 gradians. They're mainly used in surveying and some European countries. 1 gradian = 0.9° = 0.0157 radians.
A turn (also called a revolution or rotation) represents one complete circle, equal to 360 degrees or 2π radians. It's commonly used in mechanical engineering and angular velocity measurements. 1 turn = 360° = 2π rad = 400 grad.
Use radians in calculus, physics, and advanced mathematics because they simplify many formulas. Trigonometric derivatives and integrals work naturally with radians. Use degrees for everyday applications, navigation, and when communicating angles to non-technical audiences.
π radians equals exactly 180 degrees. This is a fundamental relationship in trigonometry. Therefore, 2π radians = 360° (full circle), π/2 radians = 90° (right angle), and π/4 radians = 45°.
Yes, all angle units (degrees, radians, gradians, turns) can be negative. Negative angles indicate rotation in the opposite direction (typically clockwise instead of counter-clockwise). The conversion formulas work the same for negative values.
The gradian system was designed during the French Revolution to fit the metric system. A right angle (quarter circle) is 100 gradians, making it decimal-friendly. While logical, gradians never achieved widespread adoption outside of surveying.