Convert Grade to Arcsecond (Second Angle)
Unit definitions
Grade
A grade is defined as $\frac{1}{400}$ of a revolution. It is also known as the gon or the gradian.
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 Grade to Arcsecond (Second Angle)
$$\text{Angle}_{\text{′′}} = \text{Angle}_{\text{grad}} \cdot 3240$$
Examples
Example 1
Convert $30.0\ \text{grad}$ to $\text{′′}$.
$$\text{Angle}_{\text{′′}} = 30.0 \cdot 3240$$
$$\text{Angle}_{\text{′′}} = 97200$$
$$\therefore \ 30.0\ \text{grad} = 97200 \ \text{′′}$$
Example 2
Convert $85.0\ \text{grad}$ to $\text{′′}$.
$$\text{Angle}_{\text{′′}} = 85.0 \cdot 3240$$
$$\text{Angle}_{\text{′′}} = 275400$$
$$\therefore \ 85.0\ \text{grad} = 275400 \ \text{′′}$$
Example 3
Convert $100.0\ \text{grad}$ to $\text{′′}$.
$$\text{Angle}_{\text{′′}} = 100.0 \cdot 3240$$
$$\text{Angle}_{\text{′′}} = 324000$$
$$\therefore \ 100.0\ \text{grad} = 324000 \ \text{′′}$$
Example 4
Convert $140.0\ \text{grad}$ to $\text{′′}$.
$$\text{Angle}_{\text{′′}} = 140.0 \cdot 3240$$
$$\text{Angle}_{\text{′′}} = 453600$$
$$\therefore \ 140.0\ \text{grad} = 453600 \ \text{′′}$$
Example 5
Convert $200.0\ \text{grad}$ to $\text{′′}$.
$$\text{Angle}_{\text{′′}} = 200.0 \cdot 3240$$
$$\text{Angle}_{\text{′′}} = 648000$$
$$\therefore \ 200.0\ \text{grad} = 648000 \ \text{′′}$$
Grade to Arcsecond (Second Angle) conversion table
Convert Grade to other Angle units
| Grade [grad] | Other unit |
|---|---|
| 1 | 0.015708 Radian [rad] |
| 1 | 0.9 Degree [°] |
| 1 | 54 Arcminute (Minute Angle) [′] |
| 1 | 0.0025 Revolution [rev] |
| 1 | 1.570796 Centiradian [centiradian] |