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Radian - Degree Converter

Enter either radian or degree and calculate the equivalent

## How to convert Degree to Radians. How Many Degrees In Radians?

**Degrees to Radians Formula**

### To convert **1 degree to radians**, use the equation below

### 1 ° = 0.01745329252 rad

radians = 90° * π / 180°

radians = π / 2

**90 degrees is equal to π / 2 radians.**

**'rad'**.

**6.28 (2 * 3.14) radians in a circle (radian unit circle)**.

**3.14 radians in half circle.**

**Radians to Degrees Formula**

### To Convert

**1 radian to degrees**use the equation below### 1 rad = 57.295779513 ° (1 radian is 57.29 degrees)

- Radians × 180 / π
- For example, to convert 0.5 radians to degrees, you would use the following formula:
- degrees = 0.5 * 180 / π
- This would give you a result of 0.5 radians = 28.65 degrees.

## Introduction to Radians and Degrees

### Radians and Degrees are

**units of measurement of an angle.****A radian**is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.**A degree**is defined as the angle subtended at the center of a circle by an arc whose length is equal to 1/360th of the circumference of the circle.### The central angle of 1 radian subtends an arc length that is equal to the radius of the circle.

This means that**1 radian is equal to 57.2958 degrees.**

In other words, a radian angle measure is 57 degrees**1 radian**is equal to**180/π, or about 57.29578°.****Angles are measured in degrees.**One revolution is divided into 360 equal parts and each part is known as a degree.### Multiply the degree value with π / 180 ° to convert to radians and multiply radian value with 180 / π to convert to degrees

. An angle of 1 radian subtends an arc length of 1 unit on the unit circle. This makes the unit circle a convenient tool for visualizing angles in radians.**The unit circle is a circle with a radius of 1 unit**

## Degrees vs Radians

### The

. This is because it is based on the circumference of a circle, which is a fundamental geometric concept. Degrees, on the other hand, are an arbitrary unit of angle measurement that is based on the number of days in a year.**radian is the natural unit of angle measurement**### Degrees are the more common unit of measurement,

and are used in everyday life and in many industries, such as**construction and engineering.****Degrees**are often used in measuring**angles on a compass or when setting the time on a clock.****Degrees are not as precise as radians**and can lead to errors when performing calculations but they are easier to visualize, more common and intuitive.**Radians are difficult to visualize but more precise**and therefore more convenient to use in**mathematics and physics and in computer graphic applications.**Many trigonometric functions, such as sine and cosine, are defined in terms of radians.- The radian is named after the
**French mathematician François Viète.**Viète was a pioneer in the use of trigonometric functions in mathematics. - The degree is named after
**the Greek astronomer Hipparchus.**Hipparchus was the first person to divide the circle into 360 degrees. - The radian is the preferred unit of angle measurement in the International System of Units (SI).
- The degree is still widely used in many fields, such as engineering, surveying, and navigation.
**Degrees:**- Measuring the angle of a turn on a steering wheel.
- Measuring the angle of a roof pitch.
- Measuring the angle of a mountain slope.
**Radians:**- Calculating the circumference of a circle.
- Calculating the area of a sector.
- Calculating the velocity of an object moving in a circular path.

**when to use degrees and radians:**

* Note: This content has inputs from both the AI language model developed by OpenAI and by Bard, the Google AI model. *

## Degrees to Radians calculator table (Angle to Radians)

## Angle in Degree (deg) | ## In Radians (rad) |
---|---|

## 1 degrees in radians | ## 0.017 rad |

## 2 degrees in radians | ## 0.034 rad |

## 5 degrees in radians | ## 0.087 rad |

## 10 degrees in radians | ## 0.174 rad |

## 30 degrees in radians | ## 0.523 rad |

## 45 degrees in radians | ## 0.785 rad |

## 57.3 degrees in radians | ## 1 rad |

## 60 degrees in radians | ## 1.047 rad |

## 90 degrees in radians | ## 1.57 rad |

## 135 degrees in radians | ## 2.3561 rad |

## 180 degrees in radians | ## 3.14 rad |

## 240 degrees in radians | ## 4.2 rad |

## 270 degrees in radians | ## 4.71 rad |

## 360 degrees in radians | ## 6.28 rad |

## 450 degrees in radians | ## 7.85 rad |

## 540 degrees in radians | ## 9.42 rad |

## 630 degrees in radians | ## 10.99 rad |

## 720 degrees in radians | ## 12.56 rad |

## 810 degrees in radians | ## 14.13 rad |

## 900 degrees in radians | ## 15.7 rad |

## 990 degrees in radians | ## 17.27 rad |

## 1080 degrees in radians | ## 18.84 rad |

## 1170 degrees in radians | ## 20.42 rad |

## 1260 degrees in radians | ## 21.99 rad |

## 1350 degrees in radians | ## 23.56 rad |

## 1440 degrees in radians | ## 25.13 rad |

## 1530 degrees in radians | ## 26.7 rad |

## 1620 degrees in radians | ## 28.27 rad |

## 1710 degrees in radians | ## 29.84 rad |

## 1800 degrees in radians | ## 31.41 rad |

## 1890 degrees in radians | ## 32.98 rad |

## 1980 degrees in radians | ## 34.55 rad |

## 2070 degrees in radians | ## 36.12 rad |

## 2160 degrees in radians | ## 37.69 rad |

## 2250 degrees in radians | ## 39.26 rad |

## 2340 degrees in radians | ## 40.84 rad |

## 2430 degrees in radians | ## 42.41 rad |

## 2520 degrees in radians | ## 43.98 rad |

## 2610 degrees in radians | ## 45.55 rad |

## 2700 degrees in radians | ## 47.12 rad |

## 2790 degrees in radians | ## 48.69 rad |

## 2880 degrees in radians | ## 50.26 rad |

## 2970 degrees in radians | ## 51.83 rad |

## 3060 degrees in radians | ## 53.4 rad |

## 3150 degrees in radians | ## 54.977 rad |

## 3240 degrees in radians | ## 56.54 rad |

## 3330 degrees in radians | ## 58.11 rad |

## 3420 degrees in radians | ## 59.69 rad |

## 3510 degrees in radians | ## 54.97 rad |

## 3600 degrees in radians | ## 62.83 rad |

## Pi Radians to Degrees (Rad to Degrees Conversion) Table

## Pi Radians (rad) | ## In Degrees (deg) |
---|---|

## 0.25 Pi / Quarter Pi rad | ## 45 degrees |

## 0.5 Pi / Half Pi / 0.5 rad | ## 90 degrees (Quarter Circle) |

## 1 Pi Radian / 1 rad | ## 180 degrees (Half Circle) |

## 2 Pi Radians / 2 rad | ## 360 degrees (One Circle) |

## 3 Pi Radians / 3 rad | ## 540 degrees (One and Half Circle) |

## 4 Pi Radians / 4 rad | ## 720 degrees (Two Circle) |

## 5 Pi Radians / 5 rad | ## 900 degrees (Two and Half Circle) |

## 6 Pi Radians / 6 rad | ## 1080 degrees (Three Circle) |

## 7 Pi Radians / 7 rad | ## 1260 degrees (Three and Half Circle) |

## 8 Pi Radians / 8 rad | ## 1440 degrees (Four Circle) |

## 9 Pi Radians / 9 rad | ## 1620 degrees (Four and Half Circle) |

## 10 Pi Radians / 10 rad | ## 1800 degrees (Five Circle) |

### FAQ on Degree to Radian and Radian to Degree conversion

1 circle = 360 degrees. A circle multiplied by 360 gives the angle in degrees. 2 circle = 720 degrees. 10 circle = 3600 degrees.

1 circle = 360 degrees. A circle multiplied by 360 gives the angle in degrees. 2 circle = 720 degrees. 10 circle = 3600 degrees.

Multiply radian by 57.29 degrees to convert from radian to degree

Multiply radian by 57.29 degrees to convert from radian to degree

Multiply degree by 0.0174 to convert degree to radian. 180 degrees is 3.14 radians.

Multiply degree by 0.0174 to convert degree to radian. 180 degrees is 3.14 radians.

3.14 radians to a degree

3.14 radians to a degree

6.28 radians

6.28 radians

180 degrees

180 degrees

360 deg

360 deg

0.785 radians

0.785 radians

1.57 rad

1.57 rad

3.14 rad

3.14 rad

23.56 rad

23.56 rad

6.28 radians

6.28 radians

7.85 radians

7.85 radians

4.1887 radians

4.1887 radians

It is a circle of radius 1

It is a circle of radius 1

The length of an arc divided by radius is a radian measure. 1 radian measure is a unit cicle of arc length 1 and radius of 1.

The length of an arc divided by radius is a radian measure. 1 radian measure is a unit cicle of arc length 1 and radius of 1.

Since Unit circle is a circle of radius = 1 unit. It is 2 Pi or 6.28 radians. A degree is a unit of measurement of an angle. One rotation around a circle is equal to 360 degrees.

Since Unit circle is a circle of radius = 1 unit. It is 2 Pi or 6.28 radians. A degree is a unit of measurement of an angle. One rotation around a circle is equal to 360 degrees.

Both Radian and Degree are units of measurement of an angle. Radian is the SI unit for angle. Radian is defined as the distance travelled in an arc divided by the radius angle in radians (theta)= (distance travelled / radius ) Θ = s/r. Degree measures the angle of displacement from original to new position

Both Radian and Degree are units of measurement of an angle. Radian is the SI unit for angle. Radian is defined as the distance travelled in an arc divided by the radius angle in radians (theta)= (distance travelled / radius ) Θ = s/r. Degree measures the angle of displacement from original to new position

Radian is a bigger unit than Degree. 1 Radian = 57.3 degrees 3.14 Radian (1 Pi) = 180 degrees 6.28 Radian (2 Pi) = 360 degrees

Radian is a bigger unit than Degree. 1 Radian = 57.3 degrees 3.14 Radian (1 Pi) = 180 degrees 6.28 Radian (2 Pi) = 360 degrees

Angle of full circle = 360 degrees. Radian of full circle = (distance covered by arc/ Radius) = Perimeter of the circle / Radius = 2 Pi * R / R = 2 * Pi . This implies, 2 * Pi Radians = 360 Degrees Therefore, 1 Radian = 57.3 Degrees 1 Degree = 0.017 Radians

Angle of full circle = 360 degrees. Radian of full circle = (distance covered by arc/ Radius) = Perimeter of the circle / Radius = 2 Pi * R / R = 2 * Pi . This implies, 2 * Pi Radians = 360 Degrees Therefore, 1 Radian = 57.3 Degrees 1 Degree = 0.017 Radians

Theta (θ) is simply a variable to indicate an angle and is typically used in mathematical equations. . It can be represented in radians or in degrees.

Theta (θ) is simply a variable to indicate an angle and is typically used in mathematical equations. . It can be represented in radians or in degrees.

Pi (π) is the ratio of circumference to the diameter π = C/D It has a constant value of 3.1415 (equal to 22/7) Radian is the ratio of arc length to the radius and it can be expressed in terms of Pi. 2 * Pi Radians = 360 Degrees

Pi (π) is the ratio of circumference to the diameter π = C/D It has a constant value of 3.1415 (equal to 22/7) Radian is the ratio of arc length to the radius and it can be expressed in terms of Pi. 2 * Pi Radians = 360 Degrees

There are 6.28 (2 * 3.14) radians in a circle There are 3.14 radians in half circle.

There are 6.28 (2 * 3.14) radians in a circle There are 3.14 radians in half circle.

Half of Pi is Quarter Circle. 1 Pi is half circle. 2 Pi is full circle

Half of Pi is Quarter Circle. 1 Pi is half circle. 2 Pi is full circle

2.3561 rad

2.3561 rad

10313.24 degrees

10313.24 degrees

Since Unit circle is a circle of radius = 1 unit. It is 2 Pi or 6.28 radians

Since Unit circle is a circle of radius = 1 unit. It is 2 Pi or 6.28 radians

171.88 degrees

171.88 degrees

20626.48 degrees

20626.48 degrees

6875.49 degrees

6875.49 degrees

0.6108 rad

0.6108 rad

1.0471 rad

1.0471 rad

57.29 degrees

57.29 degrees

2578.31 degrees

2578.31 degrees

1718.87 degrees

1718.87 degrees

229.18 degrees

229.18 degrees

5156.62 degrees

5156.62 degrees

3437.74 degrees

3437.74 degrees

0 rad

0 rad

7.8539 rad

7.8539 rad

0.0349 rad

0.0349 rad

3.8397 rad

3.8397 rad

6875.49 degrees

6875.49 degrees

5156.62 degrees

5156.62 degrees

458.36 degrees

458.36 degrees