Convert Radians to Degrees

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Key Ideas Easy Medium Hard

180°π radians

Round decimals to 1 decimal place.

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. The π cancels too. Multiply straight across, then reduce.

No π in the given angle

If the given angle is a decimal number of radians, π stays in the denominator.

Use a calculator. Round to 1 decimal place.

Easy

Exact fractions of π

The π cancels. The answer is a whole number of degrees.

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 π6 to degrees.

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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 3π4 to degrees.

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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 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 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 5π4 to degrees.

Show Answer

5π 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.

900°4 = 225°

Answer: 225°

Medium

Larger, or negative

More than one full turn is fine. Keep the sign.

Example

Convert 7π5 to degrees.

7π radians5×180°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°5 = 252°

Answer: 252°

Convert 5π12 to degrees.

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5π 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.

900°12 = 75°

Answer: 75°

Convert 11π4 to degrees.

Show Answer

11π 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.

1980°4 = 495°

Answer: 495°

Convert −2π3 to degrees.

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−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 8π5 to degrees.

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8π radians5×180°π radians

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

The π factors cancel too.

Multiply straight across, then reduce.

1440°5 = 288°

Answer: 288°

Convert 13π6 to degrees.

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13π 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.

2340°6 = 390°

Answer: 390°

Hard

Decimal radians

There is no π on top. Use a calculator and round to 1 decimal place.

Example

Convert 0.75 radians to degrees. Round to 1 decimal place.

0.75 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. Round to 1 decimal place.

135°π ≈ 43.0°

Answer: 43.0°

Convert 0.4 radians to degrees. Round to 1 decimal place.

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0.4 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. Round to 1 decimal place.

72°π ≈ 22.9°

Answer: 22.9°

Convert 1.15 radians to degrees. Round to 1 decimal place.

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1.15 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. Round to 1 decimal place.

207°π ≈ 65.9°

Answer: 65.9°

Convert 2.08 radians to degrees. Round to 1 decimal place.

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2.08 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. Round to 1 decimal place.

374.4°π ≈ 119.2°

Answer: 119.2°

Convert −1.2 radians to degrees. Round to 1 decimal place.

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−1.2 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. Round to 1 decimal place.

−216°π ≈ −68.8°

Answer: −68.8°

Convert 5.5 radians to degrees. Round to 1 decimal place.

Show Answer

5.5 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. Round to 1 decimal place.

990°π ≈ 315.1°

Answer: 315.1°

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