About

Precision in angular conversion is non-negotiable for structural engineering, computer graphics, and theoretical physics. While degrees suffice for navigation, mathematical functions - specifically calculus and trigonometric analysis - operate natively in radians. A mismatch here leads to catastrophic calculation errors in wave functions or rotational dynamics.

This utility performs the conversion using high-precision floating-point arithmetic. Unlike basic calculators that obscure the process, this tool exposes the transformation logic, displaying the multiplication factor relative to π. This transparency aids verification when inputting data into simulation software or graphing utilities where the domain is strictly defined in radians.

Formulas

The relationship between degrees and radians is derived from the circumference of a unit circle C = 2πr. Since a full rotation equals 360° or 2π radians, the conversion factor is established as:

Rad = Deg × π180

Conversely, to convert radians back to degrees:

Deg = Rad × 180π

Reference Data

Degrees (°)	Radians (rad)	Exact Form in Terms of π	Quadrant
0°	0.0000	0	Axis +X
30°	0.5236	π6	I
45°	0.7854	π4	I
60°	1.0472	π3	I
90°	1.5708	π2	Axis +Y
120°	2.0944	2π3	II
180°	3.1416	π	Axis -X
270°	4.7124	3π2	Axis -Y
360°	6.2832	2π	Axis +X

Frequently Asked Questions

Decimals are approximations. In calculus, using an exact form like π3 maintains infinite precision, preventing rounding errors from compounding in subsequent integration or derivation steps.

Yes. Negative inputs (e.g., -90°) represent clockwise rotation. The tool preserves the sign, outputting −π2 radians.

The conversion remains linear and valid. An input of 720° yields 4π. For coterminal angles within the 0 to 2π range, manual modulo arithmetic is required.

No. We utilize the environment's maximum floating-point precision (typically IEEE 754 double-precision), where π ≈ 3.141592653589793.