Vertical curve elevations calculator

Calculate station and parabolic elevation table and interior stationary station with your own figures.

Your numbers

Use the units shown. Results update as you change valid inputs.

Use station and parabolic elevation table and interior stationary station to compare changes to your inputs. The method and limits below explain the scope.

Examples

Examples

Try the starting example

Start elevation (m)
100
Start grade (fraction)
0.02
End grade (fraction)
-0.01
Curve length (m)
100
Stations from curve start (m)
0,25,50,75,100
Station and parabolic elevation table
[[0,100],[25,100.40625],[50,100.625],[75,100.65625],[100,100.5]]
Interior stationary station (m, or none)
66.666667
Interior stationary elevation (m, or none)
100.666667

Try another scenario

Start elevation (m)
110.00000000000001
Start grade (fraction)
0.02
End grade (fraction)
-0.01
Curve length (m)
100
Stations from curve start (m)
0,25,50,75,100
Station and parabolic elevation table
[[0,110],[25,110.40625],[50,110.625],[75,110.65625],[100,110.5]]
Interior stationary station (m, or none)
66.666667
Interior stationary elevation (m, or none)
110.666667
Calculation method

Calculation method

Station and parabolic elevation table

z=z0+g0 x+(g1-g0)x²/(2L); dz/dx=0 at -g0 L/(g1-g0).

Interior stationary station (m, or none)

z=z0+g0 x+(g1-g0)x²/(2L); dz/dx=0 at -g0 L/(g1-g0).

Interior stationary elevation (m, or none)

z=z0+g0 x+(g1-g0)x²/(2L); dz/dx=0 at -g0 L/(g1-g0).

Symbols and units
a
Start elevation (m)
b
Start grade (fraction)
c
End grade (fraction)
d
Curve length (m)
e
Stations from curve start (m)

Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.

Assumptions & limits

Assumptions & limits

  • Calculation uses the entered values and stated mathematical model; quantities must use the labelled units. Supported limits: All required fields must be finite values of the exact declared type and within displayed bounds. Lists contain1–1000 finite numbers. JSON tables are numeric rectangular rows, at most100 rows and30 columns; individual tools have stricter shape/domain constraints. z=z0+g0 x+(g1-g0)x²/(2L); dz/dx=0 at -g0 L/(g1-g0).
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