How to Find the Midpoint on a Topographic Map
- 1). Check the map's scale. This information will be listed at the bottom of the map. Most topographical maps use a 1:24,000 scale. That means every inch on the map represents 24,000 inches, or 2,000 feet, over land. The scale for the contour lines will be given as well. Usually there is a 20-foot vertical difference between contour lines.
- 2). Use the map's legend to find the route you're interested in following. Trails and roads---the usual routes of travel---rarely follow a straight line. It may be useful to lay a string over the route in order to account for its curves. Put one end of the string at the start point and hold it there. Overlay the string with the road or trail, following its curves, until you reach your planned destination on the map. Mark that point on the string.
- 3). Stretch the string out and measure the distance from the end to the mark with a ruler or yardstick. Multiply the number of inches you get by the map's scale. If your string is 8 inches and your map uses a 1:24,000 scale, then the distance of your route is 16,000 feet or about three miles. That distance is accurate as long as the land is flat. Rises and falls in the landscape add distance to your route.
- 4). Count the number of contour lines your route crosses. Multiply the number of contour lines by the contour scale. If your route crosses 20 contour lines at 20 feet per line, that would be 400 feet.
- 5). Use the Pythagorean theorem to calculate the total distance you'll travel. This states that the flat distance times itself plus the vertical distance times itself will equal the square of the total distance traveled. In other words (X x X)+(Y x Y)=(Z x Z). Z is the total distance of the route. Using the numbers we have above, you would get (16,000 x 16,000) + (400 x 400)= (Z x Z). Solving for Z would yield 16,004 feet.
- 6). Divide that number in half to determine the midpoint of the route. Unless you gain or lose a lot of elevation on your route, elevation changes add only a small amount to the distance traveled. You can estimate the midpoint fairly accurately by taking half the length of the string and converting it to feet using the map scale. You can also use the string with the map to see roughly where the midpoint falls on the map. The above calculation will find the exact midpoint in feet for any route you measure out.
