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Crest Vertical Curve Length Calculator

This calculator estimates the minimum required length of a crest vertical curve on roads to ensure sufficient sight distance for safe vehicle operation. It helps highway designers evaluate visibility constraints and alignments based on grades, stopping sight distance, and driver eye/obstruction height.

Vertical Curve Length Estimator

Input Fields
S
m
g₁
%
g₂
%
h₁
m
h₂
m
If enabled, the result will update automatically when you change any value.

Crest Vertical Curve Length Formula

Formula
\[\text{If } S < L_m: \quad L_m = \frac{A \cdot S^2}{200 \cdot (\sqrt{h_1} + \sqrt{h_2})^2}\]\[\text{If } S > L_m: \quad L_m = 2S – \frac{200 \cdot (\sqrt{h_1} + \sqrt{h_2})^2}{A}\]

Where:

  • $$L_m$$ = minimum length of crest curve (m)
  • $$A$$ = absolute grade difference (%), $$|g1 – g2|$$
  • $$S$$ = stopping sight distance (m)
  • $$h_1$$ = driver’s eye height (m)
  • $$h_2$$ = object height (m)


Crest vertical curves are used in road design where two opposing gradients meet. These curves must be long enough to provide clear visibility for drivers. The equations differ depending on whether the stopping sight distance S is less than or greater than the curve length $$L_m$$. This calculator supports quick estimation for engineers, enhancing road safety and compliance with geometric design standards.

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