Vertical Curve Calculator — Road Design Parabolic Curve
Enter the entry grade G1, exit grade G2, curve length L and BVC elevation to compute the K-value, curve type (sag or crest), EVC elevation, and the location and elevation of the high or low point, with a profile plot of the full curve.
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%
m
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K = L / |A| — compare to applicable design standard for the design speed
- 1
Grade difference
A = 2 − (-3) = 5 - 2
Rate of vertical curvature
K = 150 ÷ |5| = 30Larger K means a longer, gentler curve — compare to the design standard for your design speed.
How does this calculator work?
A parabolic vertical curve joins two road grades G1 and G2 over length L. K = L/|A| (where A = G2−G1) is the key design parameter. Elevations follow Y(x) = Y_BVC + G1x/100 + Ax²/(200L). A high or low point occurs at x = −G1L/A when it falls within the curve length.
Formula
How this is calculated
A parabolic vertical curve smoothly transitions between two tangent grades G1 (entry, %) and G2 (exit, %) over a horizontal length L. The algebraic grade difference A = G2 − G1 (in %) determines the sharpness of the transition; the rate of vertical curvature K = L / |A| (m/%) is the key design parameter — a higher K means a longer, gentler curve. Design standards (AASHTO Green Book, country-specific manuals) specify minimum K values for each design speed and curve type to satisfy stopping-sight-distance (SSD) and other criteria.
Elevations along the curve follow the parabolic formula Y(x) = Y_BVC + (G1/100)x + (A/(200L))x², where x is the horizontal distance from the beginning of the vertical curve (BVC). The ending elevation at EVC is Y_BVC + (G1 + G2)L/200. Setting the derivative to zero gives the high-point (crest) or low-point (sag) location: x_HL = −G1·L / A. This point exists on the curve only when 0 < x_HL < L.
A sag curve (A > 0, concave up) occurs when the grade increases from G1 to G2; a crest curve (A < 0, concave down) occurs when it decreases. The incoming and outgoing tangent lines are shown dashed in the profile plot. All computations assume an equal-tangent parabolic curve; unequal-tangent designs require separate analysis of each half.
Frequently asked questions
K = L / |A| is the length of vertical curve per 1 % change in grade. A larger K means a gentler, longer curve. Design standards specify minimum K values for each design speed and curve type (sag or crest) to ensure drivers have adequate stopping sight distance.
A high point exists on a crest curve and a low point on a sag curve when the two tangent grades straddle zero — i.e., G1 and G2 have opposite signs. The location is x = −G1·L / A from the BVC. If G1 and G2 have the same sign, the grade never reverses direction and no extreme point exists within the curve.
Grades are in percent (%), curve length and elevations are in metres. The K-value is in m/%. For foot-based calculations enter the length in feet and the elevations in feet — the formulas are identical; K will then be in ft/%. Make sure all length inputs use the same unit.
Also known as
TG we-Calculate Editorial Team. (2026). Vertical Curve Calculator — Road Design Parabolic Curve [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/vertical-curve-calculator
TG we-Calculate Editorial Team. "Vertical Curve Calculator — Road Design Parabolic Curve." TG we-Calculate. 2026. https://we-calculate.com/calculator/vertical-curve-calculator.
TG we-Calculate Editorial Team, "Vertical Curve Calculator — Road Design Parabolic Curve," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/vertical-curve-calculator
@misc{wecalculate_vertical_curve_calculator, title = {Vertical Curve Calculator — Road Design Parabolic Curve}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/vertical-curve-calculator}}, year = {2026}, note = {TG we-Calculate} }
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