Degrees To Radians
Convert degrees to radians with this free angle converter using π/180. Enter any angle for precise radian results, ideal for trigonometry and calculus.
About This Calculator
This free online degrees to radians converter is a simple yet powerful tool that helps students, engineers, and professionals quickly convert any angle measurement from degrees to radians. Whether you are working on trigonometry homework, calculus problems, physics equations, or engineering designs, this converter handles all your angle conversion needs with precise results based on the standard mathematical formula.
The conversion follows the fundamental relationship between degrees and radians: π radians equals 180 degrees. To convert, simply multiply the angle in degrees by π/180. For example, 90° × π/180 = π/2 rad = 1.5708 rad, and 360° × π/180 = 2π rad = 6.28319 rad. Our calculator performs this computation automatically using the exact value of π (pi) for maximum precision.
Degrees and radians are the two most common units for measuring angles. Degrees divide a full circle into 360 equal parts, making them intuitive for everyday navigation, construction, and geometry. Radians, on the other hand, measure angles based on the radius of a circle — one radian is the angle formed when the arc length equals the radius. Radians are the standard unit in higher mathematics, physics, and engineering because they simplify trigonometric derivatives, integrals, and series expansions.
Common angle conversions to remember: 0° = 0 rad, 30° = π/6 rad ≈ 0.5236 rad, 45° = π/4 rad ≈ 0.7854 rad, 60° = π/3 rad ≈ 1.0472 rad, 90° = π/2 rad ≈ 1.5708 rad, 180° = π rad ≈ 3.1416 rad, and 360° = 2π rad ≈ 6.2832 rad. This converter saves you time by computing any degree-to-radian conversion instantly with a single click.
Frequently Asked Questions
How do you convert degrees to radians?
To convert degrees to radians, multiply the angle in degrees by π/180. For example, 180° × π/180 = π radians ≈ 3.14159 rad. The formula is: radians = degrees × π/180.
What is 360 degrees in radians?
360 degrees is equal to 2π radians, which is approximately 6.28319 radians. This represents a full circle or one complete rotation.
What is 90 degrees in radians?
90 degrees is equal to π/2 radians, which is approximately 1.5708 radians. This represents a right angle or one quarter of a full circle.
What is 1 radian in degrees?
1 radian is approximately 57.2958 degrees. To convert radians to degrees, multiply the radian value by 180/π. Radians and degrees are two different units for measuring angles.
Why do we use radians instead of degrees?
Radians are preferred in calculus, physics, and advanced mathematics because they simplify formulas. For example, the derivative of sin(x) is cos(x) only when x is in radians. Many scientific and engineering calculations use radians for trigonometric functions.
What is the formula to convert degrees to radians?
The formula to convert degrees to radians is: radians = degrees × π/180. Since π radians = 180°, multiplying any degree measure by π/180 gives the equivalent radian measure. For example, 45° × π/180 = π/4 rad ≈ 0.7854 rad.
Is this degrees to radians converter free?
Yes, this degrees to radians converter is completely free to use with no limitations. You can convert any angle from degrees to radians instantly and share your results with others via a unique URL.