General
Degrees to Radians Calculator
Convert angles between degrees and radians with this easy-to-use calculator. Perfect for mathematics, physics, and engineering calculations.
Enter an angle value and select units to see the conversion result
Related to Degrees to Radians Calculator
The Degrees to Radians Calculator is a precise tool that converts angles between degrees and radians, two fundamental units used in mathematics, physics, and engineering. The calculator uses the mathematical relationship between degrees and radians, where a complete circle of 360 degrees equals 2π radians.
Conversion Formulas
• Degrees to Radians: rad = deg × (π/180)
• Radians to Degrees: deg = rad × (180/π)
These formulas are derived from the fact that a complete circle contains 360 degrees or 2π radians. This relationship establishes that π radians equals 180 degrees, which forms the basis for the conversion factors used in the calculator.
Both degrees and radians are essential units for measuring angles, each with their own advantages in different contexts. Understanding when to use each unit is crucial for various applications in mathematics and science.
Common Values
• 90° = π/2 radians (quarter circle)
• 180° = π radians (half circle)
• 270° = 3π/2 radians (three-quarter circle)
• 360° = 2π radians (full circle)
When to Use Each Unit
• Degrees: More intuitive for basic geometry and everyday measurements
• Radians: Preferred in calculus, physics, and advanced mathematics due to their natural relationship with circular motion and trigonometric functions
1. Why do we use radians in mathematics?
Radians are used because they provide a more natural way to describe angles in terms of the radius of a circle. In radians, the angle equals the arc length divided by the radius, making many mathematical formulas simpler. This is particularly important in calculus and physics where the derivatives of trigonometric functions become more straightforward when using radians.
2. How accurate is this calculator?
The calculator provides results with six decimal places of precision, which is sufficient for most practical applications in mathematics, engineering, and physics. The conversion uses the exact mathematical relationship between degrees and radians, ensuring high accuracy in the calculations.
3. Can I convert negative angles?
Yes, the calculator can handle both positive and negative angles. Negative angles represent clockwise rotation, while positive angles represent counterclockwise rotation. The conversion formulas work the same way for both positive and negative values.
4. What is the range of values this calculator can handle?
The calculator can handle angles from -360,000 to 360,000 degrees or their equivalent in radians. This range is more than sufficient for most practical applications, while still maintaining accuracy in the conversion process.
5. What is the scientific source for this calculator?
This calculator implements the standard mathematical relationship between degrees and radians established in fundamental geometry and trigonometry. The conversion formula is based on the mathematical constant π (pi) and the definition that 2π radians equals 360 degrees, a relationship that has been fundamental to mathematics since ancient times. This relationship is recognized by the International Bureau of Weights and Measures (BIPM) and is consistent with the International System of Units (SI). The mathematical principles behind these conversions are documented in numerous mathematical texts and are used universally in scientific and engineering applications.