To determine gradient, simply divide the change in elevation between the two points found on your topographic map by their horizontal distance.
That's it Gradient is commonly also expressed as the ratio of two different units of measurement, such as feet/mile.
Topographic Map Example
The more closely spaced the contour lines, the steeper the slope.
You can find out exactly how steep the slope of the area you are interested in by subtracting the lowest elevation from the highest, and dividing the result by the horizontal distance.
Answer and Explanation:
For the sake of this explanation, I'll assume the area is rectangular, which is calculated as length x width.
The method is the same for any shape area, just use the appropriate formula and measurements for the shape (1/2 x base x height for a triangle; pi x radius squared for a circle).