Radians & Degrees Converter
Convert angles between radians and degrees
Conversion Type
Quick Reference
Result
Enter a value to convert
The conversion result will appear here
Conversion
Formula & Calculation
When to Use Angle Converter
Trigonometry Homework
Convert angles for trigonometry problems. Many textbooks use degrees while calculators default to radians. Quickly convert between units to verify your answers and understand the relationships.
Physics Calculations
Solve circular motion, wave, and oscillation problems. Physics formulas often require radians for angular velocity, frequency, and phase angles. Convert degrees from diagrams to radians for calculations.
Programming
Most programming languages (JavaScript, Python, C++) use radians for trigonometric functions. Convert user-friendly degree inputs to radians for Math.sin(), Math.cos(), and other functions.
Engineering Design
Convert angles for mechanical design, robotics, and CAD software. Engineering drawings use degrees, but calculations for gear ratios, linkages, and rotations often require radians.
Calculator Mode Switching
Verify calculations when switching between degree and radian modes on scientific calculators. Ensure you're using the correct unit for your problem and convert results as needed.
Calculus & Analysis
Work with derivatives and integrals of trigonometric functions. Calculus requires radians for correct results in limits, derivatives (d/dx sin(x) = cos(x) only in radians), and Taylor series.
Frequently Asked Questions
How do you convert radians to degrees?
To convert radians to degrees, multiply the radian value by 180/π (approximately 57.2958). The formula is: degrees = radians × (180/π). For example, π radians = π × (180/π) = 180 degrees. Our calculator performs this conversion instantly with high precision.
How do you convert degrees to radians?
To convert degrees to radians, multiply the degree value by π/180 (approximately 0.0174533). The formula is: radians = degrees × (π/180). For example, 90 degrees = 90 × (π/180) = π/2 radians ≈ 1.5708 radians. Our converter handles this calculation automatically.
Is this radians and degrees converter free?
Yes, our radians and degrees converter is completely free to use with no registration required. You can perform unlimited conversions, adjust decimal precision, and get instant results without any cost. There are no hidden fees, premium features, or usage limits.
What is the difference between radians and degrees?
Radians and degrees are two different units for measuring angles. A full circle is 360 degrees or 2π radians. Degrees divide a circle into 360 equal parts, while radians are based on the radius of the circle. Radians are preferred in mathematics and physics because they simplify many formulas. 1 radian ≈ 57.2958 degrees.
Why do we use radians instead of degrees?
Radians are used in advanced mathematics, calculus, and physics because they simplify formulas and calculations. In radians, arc length = radius × angle, making circular motion and trigonometric derivatives much simpler. Radians are the natural unit for angles in mathematical analysis, while degrees are more intuitive for everyday use.
What are common angle conversions?
Common conversions include: 0° = 0 rad, 30° = π/6 ≈ 0.524 rad, 45° = π/4 ≈ 0.785 rad, 60° = π/3 ≈ 1.047 rad, 90° = π/2 ≈ 1.571 rad, 180° = π ≈ 3.142 rad, 270° = 3π/2 ≈ 4.712 rad, 360° = 2π ≈ 6.283 rad. Our calculator handles all these and any custom values.
Can I adjust the decimal precision?
Yes! You can set the number of decimal places from 0 to 10. This is useful for different needs: use 2-4 decimals for general calculations, 6-8 for scientific work, or 10 for maximum precision. The calculator maintains accuracy throughout the conversion process.
When should I use this converter?
Use this converter for: trigonometry homework, physics problems involving circular motion, engineering calculations, programming (many functions use radians), calculus problems, converting between calculator modes, verifying manual calculations, and any situation requiring angle unit conversion.
No comments yet. Be the first to share your thoughts!