Height over bore or sight height, is usually a measurement asked for by ballistic calculators to help calculate your "dope" for your specific rifle/set up.
There are a few procedures that are commonly used to find sight height. A very basic way is to measure from the center of the barrel to center of the scope or scope rings. While not super accurate a pretty easy and quick way to get a measurement.
Another simple method is to remove the bolt of the rifle and run a cleaning rod from the muzzle through the action to help give you a center line. Using a bore guide will help to be more precise. Measure from the center of the scope to the center of the bore guide/cleaning rod.
Below is a formula to help you be a little more precise when determining sight height.
1.) Measure the bolt diameter and divide it in half.
2.) Measure the scope tube diameter and divide it in half. 1.000” / 2 = 0.500” (for 30mm tubes use 1.181”)
3.) Measure the distance from the top of the bolt in the rifle to the bottom of the scope on the rifle.
4.) Add the numbers found in the steps 1-3.
Example: Remington 700 .308 with a Leupold Mark 4 M1 Extended Range Tactical Riflescope, 6.5x20x50mm
1) Bolt diameter .696". .696"/2= .348"
2) Scope tube diameter 30mm 1.181/2= .591"
3) Distance from top of bolt to bottom of scope = .75"
Sight Height = .348" + .591" + .75" = 1.68"
The most common sight heights run from about 1.5 to 1.8 inches above center of bore.