Why A directional wattmeter (or directional coupler) separates the power traveling toward the antenna from the power reflected back down the line. Knowing forward and reflected power gives you the reflection coefficient, rho = sqrt(Pref/Pfwd), and SWR = (1 + rho) / (1 - rho). That is exactly how an inline SWR/power meter works, so standing wave ratio falls right out of the two readings.
Watch out Front-to-back ratio compares radiation off the front and back of an antenna, which requires a field strength meter and a distant signal source, not a meter inserted in the feedline.
Forward minus reflected: two power readings in the feedline equal SWR.