Vertical Curve Elevation Calculator

Work out vertical curve elevation instantly with clear inputs, formula shown and shareable results.

About Vertical Curve Elevation Calculator

A parabolic vertical curve changes grade at a constant rate, so elevation relative to the curve start is g1 x + (g2 - g1) x² / (2L). The offset term is the departure from the incoming tangent. The high or low point occurs where the grade reaches zero, at -g1 L / (g2 - g1) from the start, and the K value, length per percent of grade change, is how curves are specified in design standards.

Formulas

Parabolic curve

Elevation change = g1 x + (g2 - g1) x² / (2 L)

Turning point

x = -g1 L / (g2 - g1); K = L / |algebraic grade difference|

Worked example

With the default values below, Vertical Curve Elevation Calculator returns Elevation change from the curve start of 1.1875. Change any input above and every figure here is recalculated in your browser.

Inputs used

Incoming gradeaccepts -20–20 %: 3 %
Outgoing gradeaccepts -20–20 %: -2 %
Curve lengthminimum 1 m: 200 m
Distance from the start of the curveminimum 0 m: 50 m

Results

Elevation change from the curve start: 1.1875 m
Offset from the tangent: -0.3125 m
Distance to the high or low point: 120.00 m
K value of the curve: 40.000 m per %

Step by step

1Values used
2Parabolic curve
3Turning point
4Elevation change from the curve start= 1.1875 m
5Offset from the tangent= -0.3125 m
6Distance to the high or low point= 120.00 m
7K value of the curve= 40.000 m per %

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
Preliminary estimate only. Vertical alignment design must satisfy the sight distance, comfort and drainage criteria of the applicable highway design standard.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Preliminary estimate only. Vertical alignment design must satisfy the sight distance, comfort and drainage criteria of the applicable highway design standard.

Frequently Asked Questions

How is the Vertical Curve Elevation figure worked out?

Elevation change = g1 x + (g2 - g1) x² / (2 L). A parabolic vertical curve changes grade at a constant rate, so elevation relative to the curve start is g1 x + (g2 - g1) x² / (2L).

Why is the curve parabolic rather than circular?

A parabola gives a constant rate of grade change, which produces constant vertical acceleration and is far easier to set out by offsets from the tangent.

What values do I need to enter?

This calculator takes 4 inputs: Incoming grade, Outgoing grade, Curve length, Distance from the start of the curve. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.