Degrees to Radians Calculator Symbolab
'/%3E%3Ccircle cx='48' cy='39' r='19' fill='%23f2c9a5'/%3E%3Cpath d='M27 35c3-16 39-17 42 2-8-8-27-9-42-2z' fill='%23374151'/%3E%3Cpath d='M21 86c5-24 49-28 56 0z' fill='%232563eb'/%3E%3Ccircle cx='41' cy='41' r='2' fill='%23111827'/%3E%3Ccircle cx='55' cy='41' r='2' fill='%23111827'/%3E%3Cpath d='M42 52c4 3 9 3 13 0' stroke='%2392400e' stroke-width='3' fill='none' stroke-linecap='round'/%3E%3C/svg%3E)
Reviewed by Calculator Editorial Team
Convert degrees to radians with our Symbolab-compatible calculator. Learn the conversion formula, see worked examples, and understand radians in practical applications.
Conversion Formula
The relationship between degrees and radians is defined by the formula:
Radians = Degrees × (π / 180)
This formula comes from the fact that a full circle is 360 degrees or 2π radians. Therefore, one degree equals π/180 radians.
For example, to convert 90 degrees to radians:
90° × (π / 180) = π/2 radians ≈ 1.5708 radians
How to Use This Calculator
- Enter the angle in degrees in the input field
- Click the "Calculate" button
- View the result in radians
- Use the "Reset" button to clear the form
The calculator will show both the exact value in terms of π and the decimal approximation.
Practical Applications
Radians are commonly used in:
- Trigonometry and calculus
- Physics (especially rotational motion)
- Engineering (especially in electrical engineering)
- Computer graphics
For example, in physics, angular velocity is often measured in radians per second.
Common Mistakes
When converting between degrees and radians, common errors include:
- Forgetting to multiply by π/180 when converting degrees to radians
- Assuming π is 3.14 instead of using the more precise value
- Mixing up the order of conversion (degrees to radians vs radians to degrees)
Tip: Remember that 180 degrees is equal to π radians to help remember the conversion factor.
Frequently Asked Questions
Why do we need radians when we have degrees?
Radians are used in calculus and higher mathematics because they provide a more natural way to express angles in terms of the unit circle. The derivative of sine and cosine functions is simpler when using radians.
How precise should my radian conversion be?
For most practical purposes, a decimal approximation to 4 decimal places (e.g., 1.5708) is sufficient. However, for precise calculations in physics or engineering, you may need more decimal places.
Can I convert radians back to degrees?
Yes, the inverse formula is Degrees = Radians × (180/π). Our calculator can perform both conversions.