For watershed area you need topographic map, and from your point of interest on map, move from sample point up to ridge without crossing streams. Just follow the ridge crenulations up ... Some call it the fall line. When on the ridge, follow it around to the other side top of ridge that connects to the other line from your sample point to the ridge. There is no way to calculate runoff from rainfall only. If you have other stream gauges in area who received similar storm, you might use the same percentage. To calculate runoff, you need streamflow measurements with a cross section that use a current meter typically at 0.6 depth, at 10 plus locations for major shifts in stream stage. Basically mean velocity times cross section equals discharge rate. If there was enough interest in the college, a flume or weir could be installed in the challel to help gauge flow, and install a transducer to record stream stage with time. The discharge or flow rate changes with stream stage (elevation), and it is the sum of all these stream discharges over time that results in runoff volume. I think I may have a example to send when I get into my computer.
There is a few more steps. I did not tell you how to proceed. From the west fork excel file, the individual times are at 5 minute intervals or 96 readings per day. The readings are in cubic feet per second, which is from the stream gage elevation and flow rating curve shown. So for any date, the average flow rate is the sum of all the 96 measurements and divide by 96. So for one day 3/16, the sum was 9555.9/96 = 99,54 cubic feet per second. I know you probably use cubic meters per second, so convert if you want. There is 86,400 seconds in a day, so 99.54 times 86400 = 8,600,256 cubic feet of flow in the one day. You can convert cubic feet in one day to other units such as liters per day, etc. by using conversion factors. I find that that is 197.4 acre feet of water. The area of the watershed .is say 30,000 acres, I don't remember. So 197.4 acres divided by 30000 acres is 0,00658 feet of water or 0,078 inches of water from that day. I know, the English units may be confusing to you, but that is a quick example I can do without doing a lot of conversions my self. So the runoff from the storm may last several days, so you add up the amounts. If you want to separate out the stormflow from the baseflow, that is more complicated. But I think you may get the idea that getting streamflow data is a lot of measurements and calculations. With computers and transducers, the whole process today is so much easier than it used to be. This type information and examples is common in hydrology courses, and with some more data, you can actually determine how much of the rain actually was actually converted to runoff. ..
The USDA Natural Resources Conservation Service (formerly Soil Conservation Service) has a number of references available online that may help. Probably the simplest method is found in the Engineering Field Handbook, Chapter 2, Estimating Runoff. http://directives.sc.egov.usda.gov/OpenNonWebContent.aspx?content=17541.wba
The complete Engineering Field Handbook can be found at: http://directives.sc.egov.usda.gov/viewerFS.aspx?hid=21429
@ Oluwaseun Franklin Olabode you can use L-THIA model it is open software also is special for runoff calculation when thers are data series over 30 years like your case