How to calculate Water Vapor Pressure? So, we know that
$$\text{Relative Humidity(%)}=\frac{\text{Actual Water Vapor Pressure}}{\text{Saturation Vapor Pressure}}$$
Now, we can find saturation vapor pressure only from the ambient temperature [1]:
$$e_S=0.6113\text{ exp}\left(5423\left(\frac{1}{273.15-T}\right)\right)$$
The problem for me begins when I want to find the relative humidity or the Actual Water Vapor Pressure to "complete" the triangle since it seems that in order to find one I need to know the other one. The same source says that to calculate the actual water vapor pressure we can use the same formula but with dew point temperature:
$$e=0.6113\text{ exp}\left(5423\left(\frac{1}{273.15-T_d}\right)\right)$$
But in order to find the dew point temperature I need to know both ambient temperature and Relaitve Humidity, as for example Wiki offers the Magnus Formula for dew point in terms of both RH and ambient temperature [2]:

Question:
Is there some other equation that calculates the dew point without the need to know the relative humidity? Or is there one that calculates the relative humidity without the dew point and actual water vapor pressure?
 A: 
Is there some other equation that calculates the dew point without the need to know the relative humidity?

No.

Or is there one that calculates the relative humidity without the dew point and actual water vapor pressure?

No.
The dew point is the temperature at which the air is saturated (vapour pressure equals saturation vapour pressure).  Therefore, to calculate the dew point, you fundamentally need to know both the temperature and some measure for the amount of water vapour contained by the air, be it relative humidity, specific humidity, water vapour partial pressure, or water vapour mixing ratio, which can all be converted to each other if you know the temperature.
A: The equation is transcribed incorrectly, it should be:
$$
e_S=0.6113 exp\left(5423\left(\frac{1}{273.15}−\frac{1}{T}\right)\right)
$$
For the record, $e_S$ in kPa, T in Kelvin.
From day to day, even at the same temperature, the relative humidity varies because the amount of water in the air varies. Therefore, as the previous answer says, you need two values to find the third value.
