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TOPOGRAPHIC GRADIENTS

A gradient is the ratio of vertical change in elevation to horizontal change
in distance. Gradient can be thought of as ‘steepness’ and it answers the
question “for every unit of horizontal distance I travel, how far vertically do I go

up or down?”
A simple way to remember gradient is the think rise over run. A gradient
can be expressed in whatever units are of interest. Typically, Americans
express gradient in feet per mile. If the units of vertical and horizontal distance

are the same, then gradient becomes a percent ratio.
For example:
The maximum steepness of a railroad track bed over any length of track is
traditionally given as 2.5%, called ‘railroad grade’. This means that, for every

mile of track, the elevation change in the rail bed can be no more that 2.5% of a
mile. 2.5% = .025 X 5280 ft/mile = 132 feet. Thus, a gradient of 132 feet per
mile (=2.5%) is the maximum gradient used for railroad lines.

ESTIMATING A GRADIENT FROM A MAP

To estimate a gradient from a map, you must measure two quantities

between two points on a map.
1. You must use the map scale to measure the horizontal distance (usually
in miles or kilometers) between the two points.
2. You must use the contour lines to calculate the change in elevation
(usually in feet or meters) from the first point to the last point.

3. Dividing change in elevation (rise) by horizontal distance (run) will give
the gradient between the two points. If the horizontal distance- and
elevation units are different they must be included in the gradient (as in

feet per mile or meters per kilometer). If the units are the same they can
be reported as a percent.

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