90° = 1.5708 rad
90 degrees equals 1.5708 radians.
Convert angles from degrees to radians using this calculator. Radians and degrees are two units for measuring angles, with radians being the standard unit in mathematics and physics. This calculator provides instant and accurate conversion for mathematical, scientific, and engineering applications.
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Mathematical Explanation
Conversion formula: radians = degrees × π / 180. Common conversions: 180° = π rad (approximately 3.14159), 90° = π/2 rad (approximately 1.57080), 360° = 2π rad (approximately 6.28318). One complete rotation equals 360 degrees or 2π radians.
Frequently Asked Questions
The formula is: radians = degrees × π / 180. To convert from degrees to radians, multiply the degree value by π (approximately 3.14159) and divide by 180.
180 degrees equals π radians (approximately 3.14159 radians). This is a fundamental conversion because a semicircle measures 180° or π radians.
90 degrees equals π/2 radians (approximately 1.57080 radians). This represents a quarter circle or a right angle.
Radians are the natural unit for measuring angles in mathematics because they simplify many formulas in calculus, trigonometry, and physics. Using radians makes derivatives and integrals of trigonometric functions cleaner and more intuitive.
A full circle is 2π radians (approximately 6.28318 radians), which equals 360 degrees. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius.
Resources & References
Encyclopedia Resources
- Radian - Wikipedia - Comprehensive guide to radians and angle measurement
- Degree (angle) - Wikipedia - Learn about degrees and their relationship to radians
Educational Resources
- Khan Academy - Radians and Degrees - Free lessons on radians and angle measurement
- Math is Fun - Radians - Interactive radians examples and explanations