# How to find the degrees between 2 vectors when I have $\arccos$ just in radian mode?

I'm trying to write in java a function which finds the angles, in degrees, between 2 vectors, according to the follow equation - $$\cos{\theta} = \frac{\vec{u} \cdot \vec{v}}{\|\mathbf{u}\|\|\mathbf{v}\|}$$

but in java the Math.acos method returns the angle radians, so what I have to do after I calculate $\frac{\vec{u} \cdot \vec{v}}{\|\mathbf{u}\|\|\mathbf{v}\|}$, to get it in degrees?

-
Multiply the value in radians by $\frac{360}{2\pi}$. You'll get the value in degrees. – Jonathan Y. Aug 10 '13 at 20:18

## 2 Answers

You can compute the angle, in degrees, by computing the angle in radians, and then multiplying by

$\dfrac {360}{2\pi} = \dfrac {180\; \text{degrees}}{\pi\; \text{radians}}$:

$$\theta = \arccos\left(\frac{\vec{u} \cdot \vec{v}}{\|\mathbf{u}\|\|\mathbf{v}\|}\right)\cdot \frac {180}{\pi}$$

-
$\color{blue}{great~work}\color{green}{+}^\color{red}{+}\color{orange}{+}$ @amWhy – Software Aug 10 '13 at 23:46

After calculating the value in radians, simply multiply by $\frac {180}{\pi}$ to convert it into degrees.

-