Degrees to Radians & Radians to Degrees Converter

Degrees to Radians

Formula: Radians (rads) = Degrees (°) x 0.0174533

Degrees :

Radians :

Clear

Degrees	Radians
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Radians to Degrees

Formula: Degrees (°) = Radians (rads) x 57.2958

Radians :

Degrees :

Clear

Radians	Degrees
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Conversion Factors:

• Degrees to Radians: 1° = 0.0174533 rad
• Radians to Degrees: 1 rad = 57.2958°

How to Convert Degrees to Radians:

A degree divides a full circle into 360 equal parts, while a radian is based on the radius of a circle, with a full circle equal to 2π radians. Because π is an irrational number, the exact conversion factor (π/180) is a non-repeating decimal, so it is rounded to 0.0174533 for practical use.

To convert degrees to radians, multiply the number of degrees by 0.0174533.

Radians = Degrees × 0.0174533

Example: Convert 90 degrees to radians.

Radians = 90 × 0.0174533

Radians = 1.570797 rad

How to Convert Radians to Degrees:

To convert radians to degrees, multiply the number of radians by 57.2958. Like the forward conversion, this factor is also a rounded approximation of the exact value (180/π), since it too involves the irrational number π.

Degrees = Radians × 57.2958

Example: Convert 2 radians to degrees.

Degrees = 2 × 57.2958

Degrees = 114.5916°

Degrees to Radians Conversion Table

Radians to Degrees Conversion Table

Difference Between Degrees and Radians

1. Solved Examples on Converting Degrees to Radians

Example 1

Problem: Convert 1 degree into radians.

Solution:

Radians = 1° × 0.0174533 rad/°

Radians = 0.0174533 rad

Example 2

Problem: Convert 30 degrees into radians.

Solution:

Radians = 30° × 0.0174533 rad/°

Radians = 0.523599 rad

Example 3

Problem: Convert 45 degrees into radians.

Solution:

Radians = 45° × 0.0174533 rad/°

Radians = 0.7853985 rad

Example 4

Problem: Convert 60 degrees into radians.

Solution:

Radians = 60° × 0.0174533 rad/°

Radians = 1.047198 rad

Example 5

Problem: Convert 90 degrees into radians.

Solution:

Radians = 90° × 0.0174533 rad/°

Radians = 1.570797 rad

Example 6

Problem: Convert 180 degrees into radians.

Solution:

Radians = 180° × 0.0174533 rad/°

Radians = 3.141594 rad

Example 7

Problem: Convert 360 degrees into radians.

Solution:

Radians = 360° × 0.0174533 rad/°

Radians = 6.283188 rad

2. Solved Examples on Converting Radians to Degrees

Example 1

Problem: Convert 1 radian into degrees.

Solution:

Degrees = 1 rad × 57.2958 °/rad

Degrees = 57.2958°

Example 2

Problem: Convert 2 radians into degrees.

Solution:

Degrees = 2 rad × 57.2958 °/rad

Degrees = 114.5916°

Example 3

Problem: Convert 3 radians into degrees.

Solution:

Degrees = 3 rad × 57.2958 °/rad

Degrees = 171.8874°

Example 4

Problem: Convert 4 radians into degrees.

Solution:

Degrees = 4 rad × 57.2958 °/rad

Degrees = 229.1832°

Example 5

Problem: Convert 5 radians into degrees.

Solution:

Degrees = 5 rad × 57.2958 °/rad

Degrees = 286.479°

Example 6

Problem: Convert 6 radians into degrees.

Solution:

Degrees = 6 rad × 57.2958 °/rad

Degrees = 343.7748°

Example 7

Problem: Convert 10 radians into degrees.

Solution:

Degrees = 10 rad × 57.2958 °/rad

Degrees = 572.958°

How accurate is the conversion between degrees and radians?

The conversion is an approximation in both directions, since it involves π, an irrational number with an infinite, non-repeating decimal expansion. The factors 0.0174533 and 57.2958 are rounded to 6-7 significant figures, which is precise enough for nearly all practical and academic purposes, but a small rounding difference means a round-trip conversion (degrees to radians and back to degrees) may not land on exactly the original number.

Are there any tools or calculators available for converting degrees to radians?

Yes, the calculator above converts between degrees and radians instantly in both directions. Enter a value in either field and the other field updates automatically, with the result also shown in the table below the calculator.

Can I use this conversion for any angle, including decimals?

Yes, this conversion works for any angle, whole numbers or decimals, and for angles greater than 360° or 2π radians as well. Simply multiply the number of degrees by 0.0174533 to get the equivalent number of radians.

Why do mathematicians and physicists prefer radians over degrees?

Radians are the natural unit for measuring angles in calculus and physics because they directly relate an angle to the arc length and radius of a circle, which simplifies many formulas involving trigonometric functions, derivatives, and integrals. Degrees, by contrast, are an arbitrary historical division of the circle into 360 parts and don’t carry this direct geometric relationship.

Is 180 degrees exactly equal to π radians?

Yes, 180 degrees is exactly equal to π radians by definition. However, since π itself cannot be written as a finite decimal, any numeric approximation of π radians (such as 3.141594, as used in this calculator’s rounded factor) is necessarily a rounded value rather than the true, infinitely precise figure.

How many radians are in 90 degrees?

90 degrees equal approximately 1.570797 radians, which is close to π/2. To calculate this, multiply 90 by 0.0174533, the approximate number of radians in one degree.