How to Convert Radians to Degrees
Learn how to convert radians to degrees using 180 divided by pi, examples, exact forms, common mistakes, troubleshooting, and FAQs.
Quick Answer
To convert radians to degrees, multiply radians by 180/pi. For example, pi/2 radians equals 90 degrees.
What You Need
- Radian measure
- Pi value
- Calculator if needed
- Fraction simplification skills
- Degree symbol if writing final answer
Safety Precautions
- Multiply by 180/pi, not pi/180.
- Keep exact pi forms when the problem asks for exact answers.
- Check calculator mode if using trigonometric functions.
- Do not round too early.
Step-by-Step Instructions
- Step 1
Write radians
Start with the radian value you need to convert.
- Step 2
Use conversion factor
Multiply by 180/pi.
- Step 3
Cancel pi if present
If the radian value contains pi, cancel it with the denominator pi.
- Step 4
Multiply numbers
Complete the remaining multiplication.
- Step 5
Simplify fraction
Reduce any fraction if needed.
- Step 6
Add degree symbol
Write the final answer in degrees.
- Step 7
Check common angles
Compare with known conversions like pi = 180 degrees.
Practical Example
Example: 3pi/4 radians x 180/pi = 3 x 180 / 4 = 135 degrees.
Common Mistakes
- Using pi/180 instead of 180/pi
- Forgetting to cancel pi
- Rounding exact angles
- Leaving radians label on final answer
- Calculator in wrong mode
- Confusing degrees to radians conversion
Troubleshooting
Answer is tiny
You may have used pi/180, which converts degrees to radians.
Pi does not cancel
Use decimal multiplication if the radian value is a decimal without pi.
Fraction looks messy
Simplify after multiplying by 180.
Trig answer seems wrong
Check calculator degree/radian mode.
Helpful Internal Links
FAQs
What is pi radians in degrees?
Pi radians equals 180 degrees.
What is pi/2 radians?
Pi/2 radians equals 90 degrees.
What is the formula?
Degrees = radians x 180/pi.
How do I convert degrees to radians?
Multiply degrees by pi/180.
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