Exactly how to calculate a halfway distance depends on your goals and the tools you have available. If you want to meet a friend halfway between two starting points, use an Internet travel website and a pencil. If you're assembling base camp on a multi-day adventure hike, you'll need a map and some string. Regardless of the details, the process remains essentially the same. You need to calculate overall distance, calculate the halfway distance and finally adjust for topographical reality.
Locate your two points on the map. If you're measuring the halfway point for a trip, this will be your start and finish points. For meeting somebody, it will be the starting points for each person.
Measure the full distance between the two points, using a ruler or other measuring tool. Most online resources include an easy tool for doing this. In many cases, this distance won't be a straight line, but will rather follow roads or trails.
Use the map scale to determine actual distance, if necessary. Most computer map utilities will do this automatically.
Divide the full distance by two.
Measure that distance from one of your two starting points and mark in on your map.
Check your work by doing the same from the other starting point.
Check your map to make certain the halfway point is realistic for your needs. If you plan to camp at the halfway point, you can't do it in the middle of a lake. If you plan to meet at a halfway point, you can't do it on the side of an empty highway.
Get information about the general region for the halfway point. Sample resources might include online map databases, travel clubs, guidebooks, frequent visitors to the area or locals.
Adjust your plans, moving the mathematical halfway point to a utilitarian spot somewhere nearby.
The pure math version of this is simple. If the distance from point a to point b = z, then the halfway point is z/2.