Gradians To Radians Conversion


1 grad = 0.0157079633 rad

Want to convert from radians to gradians instead?

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How to convert gradians to radians (grad to rad)

The formula for converting gradians to radians is: rad = grad × 0.0157079633. To calculate the gradian value in radians first substitute the gradian value into the preceding formula, and then perform the calculation. If we wanted to calculate 1 gradian in radians we follow these steps:

rad = grad × 0.0157079633

rad = 1 × 0.0157079633

rad = 0.0157079633

In other words, 1 gradian is equal to 0.0157079633 radians.

Example Conversion

Let's take a look at an example. The step-by-step process to convert 6 gradians to radians is:

  1. Understand the conversion formula: rad = grad × 0.0157079633
  2. Substitute the required value. In this case we substitute 6 for grad so the formula becomes: rad = 6 × 0.0157079633
  3. Calculate the result using the provided values. In our example the result is: 6 × 0.0157079633 = 0.0942477798 rad

In summary, 6 gradians is equal to 0.0942477798 radians.

Converting radians to gradians

In order to convert the other way around i.e. radians to gradians, you would use the following formula: grad = rad × 63.6619771068602. To convert radians to gradians first substitute the radian value into the above formula, and then execute the calculation. If we wanted to calculate 1 radian in gradians we follow these steps:

grad = rad × 63.6619771068602

g1 = rad × 63.6619771068602

grad = 63.6619771068602

Or in other words, 1 radian is equal to 63.6619771068602 gradians.

Conversion Unit Definitions

What is a Gradian?

The gradian is a unit of measure for angles, which is used to quantify the size of an angle. One gradian is defined as 1/400th of a full rotation, which is a complete revolution around a circle.
To better understand this definition, it's important to note that a circle has 400 gradians. Therefore, an angle that spans one quarter of a circle (i.e., 100 gradians) is a right angle, while an angle that spans half a circle (i.e., 200 gradians) is a straight angle.
Gradians can be converted to degrees using the following formula: degrees = (gradians/400) x 360. Similarly, degrees can be converted to gradians using the formula: gradians = (degrees/360) x 400.

What is a Radian?

A radian is a unit of angular measure that is used to quantify the size of an angle, particularly in trigonometry and calculus. One radian is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.
To better understand this definition, it's important to note that a circle has a circumference of 2π times the radius, where π is the mathematical constant pi (approximately 3.14159). Therefore, an angle of one radian is subtended by an arc that is equal in length to the radius of the circle, which is one unit in length.
When measuring angles using radians, angles are usually denoted using the radian symbol (rad), which is often omitted for simplicity. For example, an angle of 2 radians would be written as 2 rad.

Gradians To Radians Conversion Table

Below is a lookup table showing common gradians to radians conversion values.

Gradian (grad)Radian (rad)
1 grad0.0157079633 rad
2 grad0.0314159266 rad
3 grad0.0471238899 rad
4 grad0.0628318532 rad
5 grad0.0785398165 rad
6 grad0.0942477798 rad
7 grad0.1099557431 rad
8 grad0.1256637064 rad
9 grad0.1413716697 rad
10 grad0.157079633 rad
11 grad0.1727875963 rad
12 grad0.1884955596 rad
13 grad0.2042035229 rad

Other Common Gradian Conversions

Below is a table of common conversions from gradians to other angle units.

1 gradian in degrees0.9 °