If you are lucky, the point you want to measure will be close to a spot height value or along a contour line. In this case, you can directly read its elevation. In most cases however, you will have to interpolate the elevation of a point from neighbouring known points. The principle of height interpolation is that the terrain slope will be linear between two successive contours (or between a contour and a spot height).
Draw the shortest line between the nearest higher contour and lower contour passing on the point. If the point is located at 1/3 of the total length of the line, the difference of elevation will be 1/3 of the contour interval. In this example, the (estimated) elevation of the point will be 633 m (650 – 50/3).
Slope is given by the ratio between the difference of elevation of two points and the horizontal distance between these points. It is usually given in %.
If you climb 100m when you travel 1000m, the slope is 10% (100% slope corresponds to a 45° angle).
To measure a slope on a map, you have to first measure the distance on the map, to translate it to ground distance, and to determine the elevation of the upper and lower points defining the slope. In the previous example, if the distance along the dashed line is 1000m, then the average slope on the “?” point is 50m/1000m = 5%.
You can of course also measure average slope along a broken line such as a road, a river, etc. It is then possible to draw longitudinal profiles along or across a valley, etc.
A quicker way to estimate terrain slope is to evaluate the density of contour lines.
On a 1:250'000 map with contour interval of 50 m, 1 contour / cm = 50m / 2500 m = 2% slope. When you know this, two contours per cm corresponds to 4%, etc. If you use this method, be sure you count contours located on the same slope.