This vertical curve calculator handles both sag and crest curves. Enter the two grades and the curve length above to get the mid-curve offset, the rate of grade change, and point elevations.
Formulas
A = |g₂ − g₁| (algebraic grade change, %) Mid-curve offset = A × L ÷ 800 (L in m) Rate of change r = (g₂ − g₁) ÷ L
Example
g₁ = +3%, g₂ = −2%, L = 200 m (a crest): A = 5%, mid-curve offset = 5 × 200 ÷ 800 = 1.25 m.
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Frequently Asked Questions
How do I calculate a vertical curve?
Find the algebraic grade change A, then the mid-curve offset is A times length over 800 (in meters); elevations follow a parabola.
What is the difference between sag and crest curves?
A crest curve goes over a hill (grade decreases); a sag curve goes through a dip (grade increases). The same math applies with the sign of A.
What is the rate of grade change?
It is the grade difference divided by the curve length, which controls rider comfort and sight distance.