R-C Snubber: How to Calculate Values

To damp the ringing in an inductor such such as a relay or solenoid, a series R-C circuit or a diode may be added. 

R-C Snubber

(Image from Mercury Relays)

  

Diode and Zener+Diode Damping

Generally, a silicon diode across the coil opposite to direction of current flow is sufficient (shown in 1st example).

To minimize the off-switching time for a DC solenoid or relay, use a zener instead, which allows a larger voltage to exist across the coil in reverse. Adding the additional diode (as shown in the 3rd example) puts its relatively low capacitance in series with the much larger zener capacitance, thereby reducing the net value to just the C of the diode.

Experimentally I've found the optimum Vz to fall between 1x and 2x of the supply voltage. Further explanation is here on Electronics Stack Exchange, where 2x is recommended.

For power switching circuits

To reduce ringing at a node in a pulsed or switching circuit, a snubber can also be used across the switching element. A procedure to calculate values for R and C is described in this TI article by John Betten. Further discussion in this Maxim article.

The graph shows the trade-off between amount of damping and amount of power loss.

Note: To insert a formatted equation, see this LaTeX online equation editor.