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Vertical Curve Length from K Value

L=K AL = K\,A

Worked example: 300 m curve for a 6 % grade change → K = 50 m/% — press Try an example to run it live, then adjust anything.

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Vertical Curve Length from K Value explained

AKL

K is the length of vertical curve required per one percent of grade change, and it is the single number that carries a design speed into a profile. AASHTO's Green Book tabulates it directly: a crest curve at 50 mph needs K = 84, at 70 mph K = 247, because sight distance grows roughly with the square of speed while curve length grows linearly with K. Sag curves get their own, smaller table driven by headlight throw and rider comfort rather than sight distance. Since A is in percent and L in length, K carries the awkward units of length per percent — feet per percent in the imperial tables, metres per percent in the metric ones — which is why the tables are never interchangeable.

A worked example: a road drops at −2 % and rises at +3 %, so A = 5 %. At a design speed calling for K = 50 ft/%, the crest needs L = 50 × 5 = 250 ft of vertical curve. Halve the grade change and you halve the curve. The trap is the sign: A is the algebraic difference g₂ − g₁, so a −2 % to +3 % sag is a 5 % change, not 1 %, and getting that wrong shortens the curve by a factor of five.

Vertical Curve Length from K Value formula

L=K AL = K\,A
Where
  • LL= Curve length (m)
  • KK= K value (length per percent) (m)
  • AA= Algebraic grade change (%)

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