Vertical Exaggeration Calculator (topographic profile VE from map scales)

Understanding the vertical exaggeration calculator — concept and principle

When you draw a topographic profile, heights are usually stretched compared with horizontal distances, otherwise most hills would look almost flat. This calculator finds the vertical exaggeration (VE) from the map's horizontal scale and the profile's vertical scale, and shows how steep a real slope will look on the stretched profile. Geography and geology students use it constantly.

Stretching height ten times turns a gentle 10° slope into a steep-looking 60.4°.

How it is calculated

VE = H ÷ V

Apparent slope = atan(VE × tan(true slope))

H is the horizontal scale denominator (1 : H) and V the vertical scale denominator (1 : V).
A vertical scale written as "1 cm = X m" is 1 : 100X; "1 inch = X ft" is 1 : 12X.
The calculator also shows how many metres 1 cm on the profile represents vertically and horizontally.

The principle

A scale's denominator says how many real units one drawing unit represents. A smaller denominator means the drawing is enlarged more. If the vertical scale has a denominator ten times smaller than the horizontal one, each metre of height is drawn ten times larger than each metre of distance, so VE = H ÷ V = 10. Stretching only the vertical direction multiplies the rise of every slope while the run stays the same, so the tangent of each slope angle is multiplied by VE. The steepness you see therefore grows, but not in proportion, because angles approach 90° without reaching it.

Worked example

Default inputs: horizontal scale 1 : 24,000, vertical scale 1 : 2,400, true slope 10°.

VE = 24,000 ÷ 2,400 = 10×.
Vertical scale denominator = 2,400.
tan 10° = 0.1763; × 10 = 1.763; atan(1.763) = 60.4° apparent slope.
1 cm on the profile = 2,400 ÷ 100 = 24 m of height.
1 cm horizontally = 24,000 ÷ 100 = 240 m of distance.

Each point is the calculator re-run with only “Vertical scale value” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Vertical scale value	Vertical exaggeration
600	40×
1,200	20×
1,800	13.33×
2,400	10×
3,000	8×
3,600	6.67×
4,800	5×

How to read the result

VE = 1 shows the landscape true to shape. Values of 2–10× are common for hilly areas, and much larger values are used for gentle terrain such as plains or the sea floor. Always state the VE on the profile, because readers easily misjudge slopes otherwise: a gentle 10° hillside looks like a 60° cliff at 10×. When comparing profiles, use the same VE.

Common mistakes

Dividing V by H instead of H by V.
Forgetting to convert "1 cm = X m" to a ratio (multiply X by 100).
Measuring slopes directly off an exaggerated profile as if they were true angles.

Keep in mind: Apparent slopes on an exaggerated profile are not real slopes. Use VE = 1 or the true-slope value for any engineering or safety judgement.

Frequently asked questions

Why exaggerate the vertical scale at all?

Relief is usually small compared with horizontal distances, so without exaggeration most profiles would look nearly flat.

What does 10× mean?

Heights are drawn ten times larger than distances at the same scale.

How do I find the true slope from the profile?

true slope = atan(tan(apparent slope) ÷ VE).

Can VE be less than 1?

Mathematically yes, but that flattens relief and is rarely used.

Sources: Standard map-reading formulas: VE = horizontal scale ÷ vertical scale (as representative fractions); apparent slope tan θ′ = VE × tan θ

Checked 9 Nov 2026. Vertical exaggeration VE = horizontal scale ÷ vertical scale (as representative fractions) for topographic profiles; apparent slope tan θ′ = VE·tan θ (standard map-reading formulas).

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