Relative Humidity (RH)

Follow the instructions and get the Humidity Ratio from the below link.

Calculation for Humidity Ratio OR Specific Humidity.

Assume the calculated value W = 0.0131 lb/lb @ 75°F DBT, 68° WBT, & 10 ft sea level.

Method-1:

Saturation pressure @ given temperature

$\ln(p_{t}) = \dfrac{C_{8}}{t} + C_{9}$
$\quad\quad+$ $C_{10}*t + C_{11}*t^2 + C_{12}*t^3$
$\quad\quad+$ $C_{13}*\ln(t)$
Saturation pressure @ DBT = Saturation pressure
$p_{s} = p_{dbt}$
$\ln(p_{dbt}) = \dfrac{-10440.397}{534.67} + -11.29465$
$\quad+$ $-0.027022355*534.67 + 1.28904E-05*534.67^2$
$\quad+$ $-2.47807E-09*534.67^3$
$\quad+$ $6.5459673*\ln(534.67)$

$p_{s} = p_{dbt} = 0.43 psia$

Humidity ratio at Saturation

$W_{s} = \dfrac{0.621945 * p_{s}} {p-p_{s}}$
Here $p_{s}$ represents the saturation pressure of water vapor in the absence of air at the given temperature and it differs slightly from the vapor pressure of water in saturated moist air.

Humidity ratio @ DBT = Humidity ratio at Saturation
$W_{dbt} = W_{s}$
$W_{dbt} = \dfrac{0.621945 * 0.43} {14.691-0.43}$
$W_{s} = W_{dbt} = 0.0188$

Relative Humidity (RH)

$\Phi = \dfrac{W}{W_{s}}$

$=\dfrac{0.0131}{0.0188} = 0.697 = 69.7$ %

Method-2:

Partial pressure of Water vapour

$p_{w} = \dfrac{p * W} {0.621945 + W}$

Where,
$p_{w}$ - Partial pressure of water vapour (VP) in psia
$W$ - Humidity ratio in lb/lb
$p$ - Standard atmospheric pressure at given altitude(sea-level) in psia (Refer Humidity Ratio calculation for details)

$p_{w} = \dfrac{14.691 * 0.0131} {0.621945 + 0.0131} = 0.303 \, psia$

Relative Humidity (RH)

$\Phi = \dfrac{p_{w}}{p_{s}}$

$=\dfrac{0.303}{0.43} = 0.705 = 70.5$ %