Unit definitions

Radian

The radian is the unit of angle in the SI. A full circle is $2\pi$ radians, where $\pi$ is approximately $3.141\,592\,653\,589\,793$.

Arcsecond (Second Angle)

$\frac{1}{3\,600}$ of a degree is an arcsecond. It is used in places where extremely precise measurements are required. It is said that the US dime is $1$ arcsecond wide from $2.3$ miles away.

How to convert Radian to Arcsecond (Second Angle)

$$\text{Angle}_{\text{′′}} = \frac{\text{Angle}_{\text{rad}}}{3.141592653589793} \cdot 648000$$

Examples

Example 1

Convert $30.0\ \text{rad}$ to $\text{′′}$.

$$\text{Angle}_{\text{′′}} = \frac{30.0}{3.141592653589793} \cdot 648000$$

$$\text{Angle}_{\text{′′}} = 6187944.187413$$

$$\therefore \ 30.0\ \text{rad} = 6187944.187413 \ \text{′′}$$

Example 2

Convert $70.0\ \text{rad}$ to $\text{′′}$.

$$\text{Angle}_{\text{′′}} = \frac{70.0}{3.141592653589793} \cdot 648000$$

$$\text{Angle}_{\text{′′}} = 14438536.437297$$

$$\therefore \ 70.0\ \text{rad} = 14438536.437297 \ \text{′′}$$

Example 3

Convert $110.0\ \text{rad}$ to $\text{′′}$.

$$\text{Angle}_{\text{′′}} = \frac{110.0}{3.141592653589793} \cdot 648000$$

$$\text{Angle}_{\text{′′}} = 22689128.687181$$

$$\therefore \ 110.0\ \text{rad} = 22689128.687181 \ \text{′′}$$

Example 4

Convert $140.0\ \text{rad}$ to $\text{′′}$.

$$\text{Angle}_{\text{′′}} = \frac{140.0}{3.141592653589793} \cdot 648000$$

$$\text{Angle}_{\text{′′}} = 28877072.874593$$

$$\therefore \ 140.0\ \text{rad} = 28877072.874593 \ \text{′′}$$

Example 5

Convert $195.0\ \text{rad}$ to $\text{′′}$.

$$\text{Angle}_{\text{′′}} = \frac{195.0}{3.141592653589793} \cdot 648000$$

$$\text{Angle}_{\text{′′}} = 40221637.218184$$

$$\therefore \ 195.0\ \text{rad} = 40221637.218184 \ \text{′′}$$

Radian to Arcsecond (Second Angle) conversion table

Radian to Arcsecond (Second Angle) conversion table

Radian [rad]	Arcsecond (Second Angle) [′′]
1	206264.806247
2	412529.612494
3	618794.418741
4	825059.224988
5	1031324.031235
6	1237588.837483
7	1443853.64373
8	1650118.449977
9	1856383.256224
10	2062648.062471

Convert Radian to other Angle units

Convert Radian to other Angle units

Radian [rad]	Other unit
1	57.29578 Degree [°]
1	3437.746771 Arcminute (Minute Angle) [′]
1	0.159155 Revolution [rev]
1	1E+2 Centiradian [centiradian]
1	63.661977 Grade [grad]