Reading Height and Spacing on Contour Maps

Reading a Contour Map

A contour map records the heights of a surface by drawing curves of constant height in the horizontal plane. To interpret one, read both kinds of information it contains: the values assigned to the curves and the distances between them. The labels tell you which regions are higher or lower; the spacing helps you compare how quickly height changes across the map.

These are related but different questions. A location can be higher than another even if the contours nearby are widely spaced. Conversely, closely spaced contours indicate a rapid change in height only when the height changes represented by those contours are taken into account.

A contour map may use labels such as 10, 20, and 30 metres. Each label gives the height of its curve, not the height of the entire region between curves. If a point lies between the 20-metre and 30-metre contours, its height is between those values, assuming the surface varies continuously there. The map alone does not generally give its exact height.

Contour Labels Tell You Which Way Is Higher

To compare heights at two locations, find the contour each location lies on, or identify the two labelled contours between which it lies. A point on the 30-metre contour is 10 metres higher than a point on the 20-metre contour. If the labels increase in one direction across a sequence of contours, height increases in that direction; if they decrease, height decreases.

The contour interval is the difference in height between successive contours in a sequence. For example, labels 100, 110, 120, and 130 metres have a constant contour interval of 10 metres. A map can also use a nonconstant interval, so check the labels instead of assuming that every contour represents the same height change.

Spacing Relates Height Change to Distance

Spacing is useful when comparing how quickly height changes across a map. The relevant comparison is the height change divided by the horizontal distance travelled. For a short route crossing a band between two contours, this is an average change over that band, not an instantaneous measurement at each point. No derivatives are needed to make this comparison.

Here is why the comparison works. Suppose a route crosses from one contour to the next, changing height by \(\Delta h\) over horizontal distance \(d\). The average height change per unit distance is \(\Delta h/d\). If two such gaps have the same positive height change, dividing by the smaller distance gives the larger ratio. For example, if both height changes equal 5 metres, then 5 metres over 100 metres is a larger average change per metre than 5 metres over 400 metres.

The first ratio is four times the second. This explains the usual visual rule: with equal contour intervals, closer contours indicate a steeper region, while wider gaps indicate a gentler region. It is a comparison across the measured distances, rather than a claim that the height changes uniformly at every point.

Compare Both the Height Change and the Distance

Contour gaps can be compared directly only when the corresponding height changes are equal. If the height intervals differ, compare the ratios of height change to distance instead. Distances should be measured in the direction of travel across contours; a gap measured at an angle to that direction can give a misleading comparison.

Why Contour Spacing Is Not Enough by Itself

A common mistake is to assume that the closest contours always mark the steepest region. That conclusion ignores their labels. If one gap represents a small change in height and another represents a much larger change, their map spacing alone does not settle the comparison.

What the Map Can—and Cannot—Tell You

Contour labels provide exact heights on their curves. Between two contours, they provide bounds rather than an exact value: a point between the 20-metre and 30-metre contours has a height between those values if the surface is continuous there. Estimating an intermediate height requires additional information or an explicit interpolation assumption; the contours alone do not guarantee that height changes evenly between them.

Likewise, a contour map gives a finite picture of height changes over distances. It supports qualitative comparisons such as “this band changes height more per kilometre on average than that band.” It does not, from spacing alone, specify how the height changes at every point within a band. That distinction keeps a useful visual estimate from becoming a stronger claim than the map justifies.

When reading a map, use a consistent order: identify the labels, calculate the height change between the contours of interest, measure the horizontal gap in the relevant direction, and account for the map scale. Then compare height change per distance. This approach works whether the contours are regularly spaced in height or not.