What is the R-Value of plastic over a window?
A 0.0025 inch thick sheet of any solid has negligible R-value in-and-of-itself (for purposes of home insulation).

The (relatively) calm air next to it does have some R-value, on the order of R 0.7.

Heat flow is calculated using conductivity (U-value).  U-value is the inverse of R-value.  R-value has units of (square foot)(hour)(Fahrenheit degree)/(British Thermal Unit).  A British Thermal Unit is enough heat to raise the temperature of one pound of water by one Fahrenheit degree, or about 1055 Joules.  1 BTU/hour is about 1055 Joules / 3600 seconds, or about 0.3 Watts.

If you have pulled your sheet of plastic tight against the window, then you have not trapped any air between the plastic and the window.  Thus, you have not improved the R-value of the window.

If you have pulled your sheet of plastic taut, but with a layer of still air between the plastic and the window, then you have replaced an air-pane assembly (with a total R-value of about 1.2) with an air-pane-air-plastic assembly with a slightly higher R-value (perhaps 1.9).  If the effective R-value of the original assembly was higher, your savings would be less.

Here are the ΔU-value calculations for going from an R-value of 1.2 to 1.9, and from an R-value of 2.2 to 2.9:


1/1.2 - 1/1.9 = U 0.83 - U 0.53 = ΔU 0.30
1/2.2 - 1/2.9 = U 0.45 - U 0.35 = ΔU 0.10


Suppose you reduced the heat conduction by 0.10 - 0.30 BTU/sf/hr/F°.  For 140 square feet, with a temperature difference of 58 F°, this is a savings of 800 - 2400 BTU/hour, or 250 - 750 Watts.

Citation (for materials available in 1950):  http://wps.prenhall.com/wps/media/objects/2513/2574258/pdfs/E09.4.pdf