Convert Radians to Degrees

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Key Ideas Easy Medium Hard

What to Remember

The conversion

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

180°π radians

Always put radians on the bottom so they cancel.

Worked conversion

Convert π3.

π radians3×180°π radians

The radians cancel, and the π cancels too. Multiply straight across:

180°3 = 60°

Level 1

Easy

Example

Convert π3 to degrees.

π radians3×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across, then reduce.

180°3 = 60°

Answer: 60°

Convert π6 to degrees.

Show Answer

π radians6×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across, then reduce.

180°6 = 30°

Answer: 30°

Convert π4 to degrees.

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π radians4×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across, then reduce.

180°4 = 45°

Answer: 45°

Convert π2 to degrees.

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π radians2×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across, then reduce.

180°2 = 90°

Answer: 90°

Convert π to degrees.

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π radians1×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across.

180°

Answer: 180°

Convert 2π to degrees.

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2π radians1×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across.

2 · 180° = 360°

Answer: 360°

Convert π8 to degrees.

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π radians8×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across, then reduce.

180°8 = 45°2 = 22.5°

Answer: 22.5°

Level 2

Medium

Example

Convert 2π3 to degrees.

2π radians3×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across, then reduce.

360°3 = 120°

Answer: 120°

Convert 3π4 to degrees.

Show Answer

3π radians4×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across, then reduce.

540°4 = 135°

Answer: 135°

Convert 5π6 to degrees.

Show Answer

5π radians6×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across, then reduce.

900°6 = 150°

Answer: 150°

Convert 5π3 to degrees.

Show Answer

5π radians3×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across, then reduce.

900°3 = 300°

Answer: 300°

Convert 7π4 to degrees.

Show Answer

7π radians4×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across, then reduce.

1260°4 = 315°

Answer: 315°

Convert 4π3 to degrees.

Show Answer

4π radians3×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across, then reduce.

720°3 = 240°

Answer: 240°

Convert 13π10 to degrees.

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13π radians10×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across, then reduce.

2340°10 = 234°

Answer: 234°

Convert −3π to degrees.

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−3π radians1×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across.

−3 · 180° = -540°

Answer: -540°

Level 3

Hard

Example

Convert 11π6 to degrees.

11π radians6×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across, then reduce.

1980°6 = 330°

Answer: 330°

Example

Convert 4 radians to degrees. Round to 2 decimal places.

4 radians1×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

There is no π on top to cancel, so π stays in the denominator.

Use a calculator.

720°π ≈ 229.1831... → 229.18°.

Answer: 229.18°

Convert −π2 to degrees.

Show Answer

−π radians2×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across, then reduce.

−180°2 = -90°

Answer: -90°

Convert 5π2 to degrees.

Show Answer

5π radians2×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across, then reduce.

900°2 = 450°

Answer: 450°

Convert π12 to degrees.

Show Answer

π radians12×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across, then reduce.

180°12 = 15°

Answer: 15°

Convert 7π6 to degrees.

Show Answer

7π radians6×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across, then reduce.

1260°6 = 210°

Answer: 210°

Convert 3π2 to degrees.

Show Answer

3π radians2×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across, then reduce.

540°2 = 270°

Answer: 270°

Convert π17 to degrees.

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π radians17×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

The π factors cancel too.

Multiply straight across. This does not reduce to a nice number, so use a calculator.

180°17 ≈ 10.59°.

Answer: 10.59°

Convert 2 radians to degrees. Round to 2 decimal places.

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2 radians1×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

There is no π on top to cancel, so π stays in the denominator.

Use a calculator.

360°π ≈ 114.5916... → 114.59°.

Answer: 114.59°

Convert 1 radian to degrees. Round to 2 decimal places.

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1 radians1×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

There is no π on top to cancel, so π stays in the denominator.

Use a calculator.

180°π ≈ 57.2958... → 57.30°.

Answer: 57.30°

Convert 3 radians to degrees. Round to 2 decimal places.

Show Answer

3 radians1×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

There is no π on top to cancel, so π stays in the denominator.

Use a calculator.

540°π ≈ 171.8873... → 171.89°.

Answer: 171.89°

Convert 0.5 radians to degrees. Round to 2 decimal places.

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0.5 radians1×180°π radians

Radians go on the bottom of the conversion so the radians cancel.

There is no π on top to cancel, so π stays in the denominator.

Use a calculator.

90°π ≈ 28.6479... → 28.65°.

Answer: 28.65°

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