Horizontal Curve Parameters
°
Angle between the two tangents
m
Radius of the circular curve
m
Point of Intersection stationing
°
Central angle subtended by 100' arc
m/m
Cross slope of the roadway
Horizontal Curve Diagram
Vertical Curve Parameters
%
Approaching grade
%
Departing grade
m
Length of vertical curve
m
Point of Vertical Intersection
m
Elevation at PVI
Vertical Curve Diagram
Elevation at Point
m
m
Sight Distance Calculation
km/h
sec
Standard: 2.5 sec (AASHTO)
m/s²
Standard: 3.4 m/s² (AASHTO)
Minimum Radius Calculation
km/h
m/m
Standard: 0.08-0.12 (AASHTO)
unitless
Standard: 0.12-0.18 (AASHTO)
About the Curve Calculator
Horizontal and Vertical Curve Calculator

This web-based tool is designed for civil engineers, transportation designers, and surveyors to calculate key parameters of horizontal and vertical curves used in roadways, highways, and railways.

The tool supports both horizontal curves (plan view) and vertical curves (profile view), ensuring alignment and grading transitions are safe, smooth, and standard-compliant.

Features
  • Calculate horizontal curve parameters (radius, tangent length, curve length, etc.)
  • Design vertical curves (crest and sag) with elevation calculations
  • Determine sight distance requirements (stopping and passing)
  • Calculate minimum radius based on design speed and superelevation
  • Supports AASHTO and IRC design standards
  • Toggle between metric and imperial units
  • Visual diagrams of curves
  • Export results as PDF reports
User Guide and Formulas
Horizontal Curves

Horizontal curves are circular arcs that provide a transition between two straight sections (tangents) of a roadway.

Key Formulas
  • Tangent Length (T): T = R × tan(Δ/2)
  • Curve Length (L): L = R × Δ (in radians)
  • External Distance (E): E = R × (sec(Δ/2) - 1)
  • Middle Ordinate (M): M = R × (1 - cos(Δ/2))
  • Degree of Curve (D): D = 5729.578 / R (for 100' arc definition)
Design Considerations
  • Minimum radius based on design speed and superelevation
  • Sight distance requirements
  • Superelevation runoff and transition lengths
  • Spiral transitions (not included in this calculator)
Vertical Curves

Vertical curves are parabolic curves that provide a gradual change between two grades in the elevation profile of a roadway.

Key Formulas
  • K-Value: K = L / |G1 - G2|
  • Elevation at point x: y = y₀ + G1×x + (G2-G1)×x²/(2L)
  • High/Low Point: x = L×G1/(G1-G2)
Design Considerations
  • Crest curves require stopping sight distance
  • Sag curves require headlight sight distance
  • Minimum K-values based on design speed
  • Drainage considerations on sag curves
Sight Distance

Sight distance is the length of roadway ahead visible to the driver, critical for safe stopping and passing maneuvers.

Stopping Sight Distance (SSD)

SSD = 0.278×V×t + V²/(254×(f ± G))

Where:
V = speed (km/h)
t = reaction time (sec)
f = friction factor
G = grade (decimal)

Passing Sight Distance (PSD)

PSD depends on:

  • Initial maneuver distance
  • Distance while passing
  • Clearance distance
  • Opposing vehicle distance