Unit definitions

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.

Radian

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

How to convert Arcsecond (Second Angle) to Radian

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

Examples

Example 1

Convert $45.0\ \text{′′}$ to $\text{rad}$.

$$\text{Angle}_{\text{rad}} = \frac{45.0}{648000} \cdot 3.141592653589793$$

$$\text{Angle}_{\text{rad}} = 0.000218$$

$$\therefore \ 45.0\ \text{′′} = 0.000218 \ \text{rad}$$

Example 2

Convert $80.0\ \text{′′}$ to $\text{rad}$.

$$\text{Angle}_{\text{rad}} = \frac{80.0}{648000} \cdot 3.141592653589793$$

$$\text{Angle}_{\text{rad}} = 0.000388$$

$$\therefore \ 80.0\ \text{′′} = 0.000388 \ \text{rad}$$

Example 3

Convert $115.0\ \text{′′}$ to $\text{rad}$.

$$\text{Angle}_{\text{rad}} = \frac{115.0}{648000} \cdot 3.141592653589793$$

$$\text{Angle}_{\text{rad}} = 0.000558$$

$$\therefore \ 115.0\ \text{′′} = 0.000558 \ \text{rad}$$

Example 4

Convert $150.0\ \text{′′}$ to $\text{rad}$.

$$\text{Angle}_{\text{rad}} = \frac{150.0}{648000} \cdot 3.141592653589793$$

$$\text{Angle}_{\text{rad}} = 0.000727$$

$$\therefore \ 150.0\ \text{′′} = 0.000727 \ \text{rad}$$

Example 5

Convert $190.0\ \text{′′}$ to $\text{rad}$.

$$\text{Angle}_{\text{rad}} = \frac{190.0}{648000} \cdot 3.141592653589793$$

$$\text{Angle}_{\text{rad}} = 0.000921$$

$$\therefore \ 190.0\ \text{′′} = 0.000921 \ \text{rad}$$

Arcsecond (Second Angle) to Radian conversion table

Arcsecond (Second Angle) to Radian conversion table

Arcsecond (Second Angle) [′′]	Radian [rad]
1	0.000005
2	0.00001
3	0.000015
4	0.000019
5	0.000024
6	0.000029
7	0.000034
8	0.000039
9	0.000044
10	0.000048

Convert Arcsecond (Second Angle) to other Angle units

Convert Arcsecond (Second Angle) to other Angle units

Arcsecond (Second Angle) [′′]	Other unit
1	0.000278 Degree [°]
1	0.016667 Arcminute (Minute Angle) [′]
1	0.000001 Revolution [rev]
1	0.000485 Centiradian [centiradian]
1	0.000309 Grade [grad]