Vertical Exaggeration Calculator
Enter the horizontal and vertical map scales as representative fractions (the denominators of 1:n ratios) to calculate the vertical exaggeration of a topographic profile or geologic cross-section. Switch the solve mode to find the vertical scale from a target VE, or find the horizontal scale. Results update instantly as you type.
What is vertical exaggeration?
Vertical exaggeration (VE) is the ratio of the horizontal map scale to the vertical profile scale. When you draw a topographic profile or geologic cross-section, you often need to compress a long horizontal distance (tens or hundreds of kilometres) onto a page while keeping elevation differences readable. To do that, you use a larger scale on the vertical axis than on the horizontal axis, making the terrain look taller and steeper than it really is. A VE of 10x means that one centimetre of vertical distance on the paper represents ten times fewer real-world metres than one centimetre of horizontal distance. The formula is: VE = horizontal scale denominator / vertical scale denominator. For a map at 1:50,000 drawn with a vertical scale of 1:5,000, VE = 50,000 / 5,000 = 10.
How to use this calculator
Choose what you want to solve for using the "Solve for" selector. To find VE from two known scales, leave the default mode and enter the horizontal and vertical scale denominators. To find the vertical scale you need to achieve a target VE, choose "Vertical scale denominator" and enter the horizontal denominator and the desired VE. To find the horizontal scale, choose "Horizontal scale denominator" and enter the vertical denominator and the desired VE. The results include the VE value, both scale denominators, a plain-English interpretation, and a slope angle multiplier showing how slope angles are distorted at that VE. The "Show your work" panel traces every arithmetic step, and the chart shows how slope angles on the profile compare to true slope angles for the computed VE.
Why slope angles matter
One important consequence of vertical exaggeration is that slope angles on the profile are not the same as slope angles in the real landscape. A 10-degree hillslope drawn at VE 10x appears to have a slope of roughly 60 degrees on the page. The apparent angle is arctan(tan(true angle) times VE). This means that geologists and cartographers must label all cross-sections with the VE value so that readers know not to interpret the drawn angle as the real-world gradient. The slope angle multiplier output in this calculator equals the VE itself, because the tangent of the apparent angle equals the tangent of the true angle multiplied by VE. At VE = 1 the multiplier is 1 and slopes match reality; at VE = 20, gentle 3-degree plains appear as steep 30-degree inclines.
Choosing the right vertical exaggeration
The appropriate VE depends on the relief of the study area and the purpose of the figure. In flat terrain such as coastal plains, continental shelves, or sedimentary basins, relief is so subtle that a VE of 10 to 20x or even higher is often needed to make features visible at all. In mountainous terrain, a VE of 2 to 5x may be enough to make the profile legible without severe distortion. For a final published figure intended to show true geological structure quantitatively, the ideal VE is 1 - no exaggeration - but that is rarely practical for regional maps. The reference table below gives common ranges by application. Whatever VE you choose, state it clearly on the figure, for example "Vertical exaggeration x10".
Typical vertical exaggeration values by application
| VE range | Common use case | Effect on slope angles |
|---|---|---|
| < 1 | Vertical compression, rarely used | Slopes appear gentler than true |
| 1 | True scale cross-section | Slopes match reality exactly |
| 2 to 5 | Hilly terrain, river valleys, gentle relief | Modest steepening, generally acceptable |
| 5 to 10 | Coastal plains, basins, geologic cross-sections | Noticeable steepening, label VE |
| 10 to 20 | Flat plains, continental-scale geology, ocean floors | Strong distortion, always label VE |
| > 20 | Sea-floor profiles, atmospheric cross-sections | Extreme distortion, quantitative use only |
Commonly used VE ranges across disciplines. The correct VE depends on the relief of the study area and the purpose of the figure.
Frequently asked questions
What does a vertical exaggeration of 1 mean?
A VE of exactly 1 means the horizontal and vertical scales are the same. Every feature on the profile has its true proportions: a slope of 20 degrees in reality appears as 20 degrees on the page. This is called a true-scale cross-section. It is ideal for quantitative accuracy but is rarely used for regional maps because low-relief terrain would look almost flat.
Can vertical exaggeration be less than 1?
Yes. If the vertical scale denominator is larger than the horizontal denominator, VE is less than 1 and the terrain appears compressed vertically. This is called horizontal exaggeration. It is uncommon in practice but can occur if a profile is drawn for a narrow, steep terrain where you want to stretch the horizontal axis for readability.
How does vertical exaggeration affect slope angles?
The apparent slope angle on a profile is arctan(VE times tan(true angle)). At VE 10x, a 10-degree slope appears as about 61 degrees, and a 30-degree slope already looks nearly vertical. For any quantitative interpretation of slope, always note the VE so readers can apply the inverse formula to recover true angles.
What vertical exaggeration do geologic cross-sections use?
It varies with the scale of the study. Local cross-sections through steep mountains may use VE 2 to 5x. Regional basin cross-sections commonly use VE 5 to 15x. Continental-scale and ocean-floor profiles sometimes reach VE 50 to 100x because the vertical relief is tiny compared with horizontal distances. Always check the stated VE before interpreting any published section.
How do I find the vertical scale from a target VE?
Rearrange the formula: vertical scale denominator = horizontal scale denominator / VE. For a 1:100,000 map where you want VE 10x, the vertical scale denominator is 100,000 / 10 = 10,000, so draw the vertical axis at 1:10,000. Use this calculator's "Solve for: vertical scale denominator" mode to get the answer instantly.
What is the formula for vertical exaggeration using representative fractions?
If the horizontal scale is 1:n_h and the vertical scale is 1:n_v, then VE = n_h / n_v. Both denominators must be in the same unit (centimetres, inches, or any consistent unit). You can also express this as VE = (actual horizontal distance per map unit) / (actual vertical distance per map unit).