What this calculator does
Vertical exaggeration is how much taller a cross-section or topographic profile has made the landscape look, compared with how it would appear if height and distance were drawn at the same scale. A profile drawn with no exaggeration at all, at typical map scales, looks almost flat, since real relief is tiny compared with real horizontal distance. Exaggerating the vertical scale is what makes hills, valleys and slopes visible and interpretable on the page.
The number itself is a simple ratio between two scales, both written as 1:x. A horizontal scale of 1:24,000 alongside a vertical scale of 1:2,400 produces a vertical exaggeration of 10, meaning vertical relief has been stretched to ten times its true proportion relative to the horizontal distance.
The formula
Divide the horizontal scale denominator by the vertical scale denominator. Both scales need to be expressed the same way, as 1:x, using the same real-world unit on both axes (for example, 1 inch representing so many feet on each). The result greater than 1 means the vertical axis is stretched relative to the horizontal; a result of exactly 1 means there is no exaggeration at all.
| Term | Meaning |
|---|---|
| Vertical exaggeration (VE) | How many times taller relief appears than it would at true, unexaggerated scale: horizontal denominator ÷ vertical denominator. |
| Horizontal scale | The map or profile scale along the horizontal axis, written as 1:x. |
| Vertical scale | The scale used for height or elevation on the same profile, written as 1:x. |
The inputs explained
| Field | What to enter |
|---|---|
| Horizontal scale denominator (the x in 1:x) | The denominator of the horizontal scale, the x in 1:x. A larger number means a smaller, more zoomed-out scale. |
| Vertical scale denominator (the x in 1:x) | The denominator of the vertical scale, the x in 1:x. This is usually smaller than the horizontal denominator, which is what stretches the relief. |
When to use it
Drawing a geological or topographic cross-section
A profile drawn at true scale usually looks like a flat line, since real elevation change is small next to real horizontal distance. Working out the vertical exaggeration in use tells you, and your reader, exactly how much the relief has been stretched to make it legible.
Comparing two published cross-sections
Two profiles of the same landscape can look completely different in steepness purely because one used a higher vertical exaggeration than the other. Calculating both figures puts the comparison on equal footing.
Choosing a vertical scale for a new profile
Picking a target exaggeration factor first, then working backwards to the vertical scale denominator needed for a given horizontal scale, is a quicker way to set up a legible cross-section than guessing and redrawing.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How vertical exaggeration changes with the horizontal scale
A fixed vertical scale of 1:2,400, against a range of horizontal scale denominators.
| Horizontal scale | Vertical exaggeration | Reading |
|---|---|---|
| 1:2,400 | 1.00× | No exaggeration: both scales match |
| 1:4,800 | 2.00× | Vertical relief is stretched, making slopes look steeper than they really are |
| 1:12,000 | 5.00× | Vertical relief is stretched, making slopes look steeper than they really are |
| 1:24,000 | 10.00× | Vertical relief is stretched, making slopes look steeper than they really are |
| 1:48,000 | 20.00× | Vertical relief is stretched, making slopes look steeper than they really are |
| 1:62,500 | 26.04× | Vertical relief is stretched, making slopes look steeper than they really are |
How vertical exaggeration changes with the vertical scale
A fixed horizontal scale of 1:24,000, against a range of vertical scale denominators.
| Vertical scale | Vertical exaggeration | Reading |
|---|---|---|
| 1:1,200 | 20.00× | Vertical relief is stretched, making slopes look steeper than they really are |
| 1:2,400 | 10.00× | Vertical relief is stretched, making slopes look steeper than they really are |
| 1:4,800 | 5.00× | Vertical relief is stretched, making slopes look steeper than they really are |
| 1:6,000 | 4.00× | Vertical relief is stretched, making slopes look steeper than they really are |
| 1:12,000 | 2.00× | Vertical relief is stretched, making slopes look steeper than they really are |
| 1:24,000 | 1.00× | No exaggeration: both scales match |
Questions
What counts as a normal amount of vertical exaggeration?
It depends entirely on the terrain and the purpose of the profile. Gently rolling landscapes are often exaggerated by a factor of 5 to 20 just to make the relief visible at all, while already-steep terrain may need little or no exaggeration to read clearly.
Why not just draw every profile at true scale?
At true scale, most real landscapes produce a profile that looks close to a flat line, because horizontal distances are so much larger than vertical relief. Exaggeration trades geometric accuracy for legibility, which is usually the more useful trade-off for a cross-section.
Does vertical exaggeration change the slope angles shown on the profile?
Yes, substantially. A gentle real-world slope can look alarmingly steep once vertically exaggerated, so slope angles measured directly off an exaggerated profile do not represent the true angle on the ground.
Can vertical exaggeration be less than 1?
Yes, if the vertical scale denominator is larger than the horizontal one, which compresses relief rather than stretching it. This is unusual in practice, since the whole point of exaggeration is normally to make relief more visible, not less.
For the closely related idea of a slope expressed as a rise:run ratio and angle, see the pitch calculator. For converting a general real-world measurement to a scale drawing size, see the scale calculator.