How this calculator works
A map scale of 1:50000 means one unit on the paper represents fifty thousand of the same units on the ground. If the same map uses a different vertical scale, the drawing is stretched or squashed in the height direction. Vertical exaggeration is the ratio of the two scale denominators, horizontal divided by vertical, so a 1:50000 horizontal scale with a 1:5000 vertical scale exaggerates heights ten times. A cross section with an exaggeration of 1 is true scale and shows slopes at their real angles. Anything above about two makes slopes look steeper than they are, which is useful for showing subtle relief but misleading for measuring gradients.
Formula
vertical exaggeration = horizontal scale denominator / vertical scale denominator. From measured heights it is drawn height / real height. A true scale section has an exaggeration of 1.
Worked example
A geological section is drawn with a horizontal scale of 1:50000 and a vertical scale of 1:5000. The vertical exaggeration is 50000 / 5000 = 10, so every hill is drawn ten times taller than its length suggests, and real slopes look much steeper. If a 20 metre hill is drawn 200 metres tall, the exaggeration is 200 / 20 = 10 as well. A true scale section would use 1:50000 in both directions.
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Frequently asked questions
Why do maps exaggerate height?
At true scale, terrain relief is tiny compared with the distances covered. A range of hills a few hundred metres high would be invisible on a country-scale map, so vertical exaggeration makes the shape readable.
Does vertical exaggeration change distances?
Only vertical distances and slopes. Horizontal distances and map positions stay true, so measure them on the horizontal scale. Gradients measured on an exaggerated section are too steep by the exaggeration factor.
How do I remove the exaggeration from a section?
Divide vertical measurements by the exaggeration to recover real heights, or redraw with the two scales equal. Most geology software can rescale an existing section once you know the factor.
What exaggeration do geological sections usually use?
Common values run from 2 to 10, chosen to show the structure without making it look absurd. Regional cross sections may use more, while detailed local studies often use 1 or 2.