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Math Practice

Radians and Degrees Practice Problems

Multiply by 180/π to get degrees and by π/180 to get radians. The later problems use radians in arc length and sector area.

  1. 1.

    Convert radians to degrees.

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  2. 2.

    Convert radians to degrees.

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  3. 3.

    Convert to radians. Give an exact answer using pi.

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  4. 4.

    Convert to radians. Give an exact answer.

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  5. 5.

    Convert to radians. Give an exact answer.

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  6. 6.

    Convert to radians. Give an exact answer.

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  7. 7.

    Convert 2.5 radians to degrees, to two decimal places.

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  8. 8.

    Convert 1.2 radians to degrees, to two decimal places.

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  9. 9.

    Convert radians to degrees.

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    The sign carries through: .

  10. 10.

    How many degrees is 1 radian, to two decimal places?

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  11. 11.

    A circle has radius 8 cm. How long is the arc cut off by a central angle of radians, in cm? Give a decimal to two places.

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    cm.

  12. 12.

    A sector of a circle with radius 6 has central angle . What is its area? Give a decimal to two places.

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MPhil in Mathematics, Founder of Mathovia
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Radians and Degrees Practice Problems

These problems follow the radians and degrees lesson. Remember: radians .

The conversions

Common mistakes to watch for

  • Multiplying by the wrong fraction. Degrees to radians: multiply by . Radians to degrees: multiply by . The unit you want goes on top.
  • Not simplifying. should be written .
  • Treating as 180 when it is a number. radians equals 180 degrees, but itself is about ; a decimal answer in radians uses that value.
  • Calculator mode. Trig values of a radian angle need radian mode, or the answer will be wrong.

Frequently Asked Questions

How do I type an answer with π?+

Type pi or π, for example 3pi/2 or 5π/4. Decimal answers within rounding are accepted too.

Why are some answers left with π?+

In calculus, exact radian values such as 5π/4 are preferred to decimals like 3.927, because they keep the answer exact.

More practice problems

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