Convert Degrees to Radians

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Key Ideas Easy Medium Hard

What to Remember

The conversion

1 full turn is 360° and also 2π radians. That gives the factor

π rad180°

Always put degrees on the bottom so they cancel.

Worked conversion

Convert 150°.

150°1×π rad180°

The degree symbols cancel. Multiply straight across:

150π180 = 5π6

Level 1

Easy

Example

Convert 150° to radians.

150°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

150π180 = 5π6

Answer: 5π6

Convert 30° to radians.

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30°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

30π180 = π6

Answer: π6

Convert 45° to radians.

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45°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

45π180 = π4

Answer: π4

Convert 90° to radians.

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90°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

90π180 = π2

Answer: π2

Convert 180° to radians.

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180°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

180π180 = π

Answer: π

Convert 360° to radians.

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360°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

360π180 = 2π

Answer: 2π

Convert 15° to radians.

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15°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

15π180 = π12

Answer: π12

Level 2

Medium

Example

Convert 60° to radians.

60°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

60π180 = π3

Answer: π3

Convert 120° to radians.

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120°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

120π180 = 2π3

Answer: 2π3

Convert 135° to radians.

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135°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

135π180 = 3π4

Answer: 3π4

Convert 240° to radians.

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240°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

240π180 = 4π3

Answer: 4π3

Convert 300° to radians.

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300°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

300π180 = 5π3

Answer: 5π3

Convert 315° to radians.

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315°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

315π180 = 7π4

Answer: 7π4

Convert 330° to radians.

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330°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

330π180 = 11π6

Answer: 11π6

Convert 250° to radians.

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250°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

250π180 = 25π18

Answer: 25π18

Level 3

Hard

Example

Convert 21° to radians.

21°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

21π180 = 7π60

Answer: 7π60

Convert 33° to radians.

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33°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

33π180 = 11π60

Answer: 11π60

Convert 78° to radians.

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78°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

78π180 = 13π30

Answer: 13π30

Convert 7° to radians.

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7°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across. Nothing cancels.

The answer is 7π180.

Answer: 7π180

Convert −13° to radians.

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−13°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across. Nothing cancels.

The answer is −13π180.

Answer: −13π180

Convert 450° to radians.

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450°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

450π180 = 5π2

Answer: 5π2

Convert 76° to radians.

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76°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

76π180 = 19π45

Answer: 19π45

Convert −150° to radians.

Show Answer

−150°1×π rad180°

Degrees go on the bottom of the conversion so the degrees cancel.

Multiply straight across, then reduce.

−150π180 = −5π6

Answer: −5π6

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