Use this degrees to radians converter to change a degree measurement into its radian equivalent. Enter a number in the calculator above and the result updates instantly.
Angle conversions are useful for geometry, trigonometry, navigation, surveying, machining, astronomy, and engineering drawings.
What is a degree?
A degree is an angle unit equal to 1/360 of a full turn. It is widely used in geometry, navigation, surveying, and everyday angle measurement.
What is a radian?
A radian is the SI angle unit used in mathematics, trigonometry, physics, and engineering calculations.
Degrees to Radians Converter formula
To convert degrees to radians, use the formula below.
1 rad = 57.2957795131 deg. This relationship is the conversion factor used by the calculator.
How to convert degrees to radians
Start with the degree value, apply the formula, and round the result only after the calculation is complete.
Example: 10 deg = 0.1745329252 rad.
- 1 deg = 0.0174532925 rad
- 10 deg = 0.1745329252 rad
- 100 deg = 1.745329252 rad
Manual conversion steps
- Write down the value in degrees.
- Use the conversion formula: radians = degrees / 57.2957795131.
- Calculate the result in radians.
- Round the answer to the number of decimal places you need.
For quick checking, the converter above performs the same calculation automatically.
Common degrees to radians use cases
This conversion is useful in practical situations where measurements need to move between different unit systems or audiences.
- Convert degrees to radians when you need equivalent measurements in another unit.
- Trigonometry, calculus, physics, and engineering often require degrees to radians conversion.
- Programming languages and math libraries frequently expect angle input in radians.
- Surveying, geometry, robotics, and navigation tasks may switch between degree notation and radian calculations.
- Technical drawings may use degrees, while formulas use radians.
Common mistakes when converting degrees to radians
These are the most common issues to watch for when doing this conversion by hand.
- Do not mix up the direction of the conversion. degrees to radians is not the same as radians to degrees.
- Avoid rounding too early. Keep the full result during the calculation, then round the final answer.
- Do not treat degrees and radians as interchangeable. They measure the same angle with different scales.
- Do not forget that 180 degrees equals pi radians.
- When using calculators or programming functions, check whether the angle mode is degrees or radians.
Degrees to radians in math and programming
Degrees are intuitive for everyday angles, but radians are the natural angle unit in many formulas. Most trigonometric functions in programming languages expect radians, which makes this conversion especially important in code.
Degrees to Radians conversion table
| Degree | Radian |
|---|---|
| 1 deg | 0.0174532925 rad |
| 5 deg | 0.0872664626 rad |
| 10 deg | 0.1745329252 rad |
| 25 deg | 0.436332313 rad |
| 50 deg | 0.872664626 rad |
| 100 deg | 1.745329252 rad |
How to convert radians to degrees
To reverse the conversion, switch the two units in the calculator or open the reverse conversion page: radians to degrees.
Reversing the units is useful when you already have a value in radians and need the equivalent value in degrees.
How to use this degrees to radians converter
- Enter the number you want to convert in the value field.
- Confirm that the from unit is Degree and the to unit is Radian.
- Read the converted result in the result box.
- Use the copy button if you want to paste the answer elsewhere.
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FAQ
What is the formula for degrees to radians?
The formula is: radians = degrees / 57.2957795131.
How do I convert degrees to radians by hand?
Write down the value in degrees, apply the formula, and round the final result in radians.
How accurate is this converter?
The converter uses standard conversion factors and shows rounded results for readability.
Can I reverse the conversion?
Yes. Use the swap button in the converter or open the related reverse conversion page.
Why do results sometimes have many decimal places?
Some unit conversions do not produce short decimal values. Keep more decimal places for technical work, and round the answer for everyday use.
How many radians are in 180 degrees?
180 degrees equal pi radians, or about 3.1415926536 radians.
How many radians are in 90 degrees?
90 degrees equal pi divided by 2 radians, or about 1.5707963268 radians.
Why do many formulas use radians?
Radians relate angle measure directly to arc length and radius, which makes many calculus and physics formulas simpler.