Convert degrees to radians and radians to degrees instantly with high precision
radians = degrees × (π / 180)
degrees = radians × (180 / π)
Degrees are a unit of angular measurement where a full circle is divided into 360 equal parts. Each degree represents 1/360 of a complete rotation.
Radians are the natural unit of angular measurement in mathematics. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius.
Many mathematical formulas become simpler when using radians
Radians are the natural unit for angular measurement
Standard in scientific and engineering applications
Trigonometry, calculus, and geometric calculations often require angle conversions between degrees and radians.
Angular velocity, rotational motion, and wave mechanics calculations use both degree and radian measurements.
Mechanical engineering, robotics, and CAD design applications frequently use angle conversions for precision.
The formula to convert degrees to radians is: radians = degrees × (π / 180). For example, 90° = 90 × (π / 180) = π/2 radians ≈ 1.571 radians.
To convert radians to degrees, use the formula: degrees = radians × (180 / π). For example, π radians = π × (180 / π) = 180°.
Radians are the natural unit for angular measurement in calculus and physics because they simplify many mathematical formulas. When angles are measured in radians, the derivative of sin(x) is cos(x) and the arc length formula becomes s = rθ without additional conversion factors.
Common angle conversions include: 0° = 0 rad, 30° = π/6 rad ≈ 0.524 rad, 45° = π/4 rad ≈ 0.785 rad, 60° = π/3 rad ≈ 1.047 rad, 90° = π/2 rad ≈ 1.571 rad, 180° = π rad ≈ 3.142 rad, 270° = 3π/2 rad ≈ 4.712 rad, 360° = 2π rad ≈ 6.283 rad.
Our angle converter provides high-precision calculations using JavaScript's built-in Math.PI constant, which is accurate to 15-17 decimal places. Results are displayed with 6 decimal places for most applications, ensuring excellent accuracy for educational, engineering, and scientific purposes.