Vertical curve elevation calculator

Enter the starting elevation, the signed entry and exit grades as percentages, the horizontal curve length, and the station distance. The result includes the calculated elevation, elevation change from the start, and instantaneous grade at that station. It is suitable for preliminary road, railway, path, drainage, and site-profile checks where a standard constant-rate grade transition is assumed.

Set up the curve and station consistently

Begin with the elevation at the point where the vertical curve starts, often called the PVC or beginning of vertical curve. Enter both tangent grades as signed percentages: a rising grade is positive and a falling grade is negative. For example, a grade of two percent means the profile rises two linear units for every one hundred horizontal units. Curve length and station from start must use the same horizontal unit, while the starting elevation uses the corresponding vertical unit. Feet may be used throughout, or metres may be used throughout; the equation is unit-consistent and does not convert between systems. The requested station must lie from zero through the full curve length. A station of zero returns the starting elevation and entry grade, while a station equal to the length returns the curve-end elevation and exit grade. Use station distance from the curve start, not a project-wide chainage, unless you first subtract the curve-start chainage. This distinction prevents a common and potentially large calculation error.

Understand the parabolic elevation calculation

The calculator uses the standard symmetric parabolic vertical-curve model in which grade changes at a constant rate over horizontal distance. First, the entry and exit percentages are divided by one hundred to obtain decimal slopes. At a distance x from the start, the elevation equals the starting elevation plus the entry-grade tangent rise, then plus a quadratic correction based on the grade difference and curve length. In compact form, that is start elevation plus g1 times x plus the quantity (g2 minus g1) times x squared divided by twice the curve length. The formula works for crest curves, sag curves, and transitions whose two grades have the same sign. The instantaneous grade is interpolated linearly between the entry and exit grades. This tool assumes that stations represent horizontal distance, as is customary in basic vertical alignment calculations. It does not apply arc-length correction, earth curvature, refraction, superelevation, or a nonsymmetric curve model. Keep the original design precision available when carrying the result into later computations.

Check and use the result in design work

Treat the computed elevation as one point on the proposed profile and check it against the surrounding alignment. At minimum, calculate the start and end stations as quick controls: the start should exactly reproduce the supplied starting elevation, and the grades reported at the endpoints should match the supplied entry and exit grades. For a crest curve, the grade generally decreases along the curve; for a sag curve, it generally increases. If the grades have opposite signs, the calculator can also help sample points near the high or low location, although it does not independently report the extremum station. When comparing a design profile with surveyed ground, confirm that both elevations use the same datum and that stationing uses the same origin. The calculation provides geometry, not a compliance decision. Sight distance, drainage, comfort, clearance, and agency-specific minimum K values require separate checks under the governing design standard. For construction setting-out or signed engineering documents, retain appropriate precision, verify independently, and follow the review procedures required for the project.