Are you sure you have the correct plug; this laptop is designed for a headset, which has both headphone and mic components (similar to a phone). These use a TRRS plug which is not the same as a headphone-only TRS plug. You can google these to see pictures that show what each plug looks like. If you do not have the correct plug you will need to buy an adapter.
As much as I agree with all above, basically you have a plug and a hole, that you want to know the dimentions of. The tool to use is a caliper. If you never heard of that, google it and look at pictures. If you don't know how to use one, there are several Youtubes that shows how to.