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Calcimator

Horizontal Curve Layout Calculator

Calculate horizontal curve elements including radius, arc length, tangent, chord, external distance, and middle ordinate for highway and road design.

Inputs

ft
°
+00

Results

Radius (R)

1,000 ft

≈ 13 tennis courts

Arc Length (L)

523.6 ft

≈ 7 tennis courts

Tangent (T)267.95 ft
Long Chord (C)517.64 ft
External (E)35.28 ft
Middle Ordinate (M)34.07 ft
Degree of Curve5.73°
PC Station732.05 ft
PT Station1,255.65 ft
Sight Distance219.2
How to Use This Calculator
  1. Enter the intersection angle (delta) in degrees, minutes, and seconds.
  2. Input the radius in feet for the horizontal curve.
  3. Set the station of the Point of Curvature (PC).
  4. Review the Tangent Length, Length of Curve, Chord, Middle Ordinate, and Station of PT.
  5. Use the staking interval to calculate stations along the curve for field layout.

How the result changes with Radius

RadiusRadius (R)Arc Length (L)
1,0451,045 ft547.16 ft
3,5333,533 ft1,849.87 ft
6,5186,518 ft3,412.82 ft
9,0059,005 ft4,715.01 ft

What each input means

Input Method
Choose whether to input radius or tangent length with the central angle.
Radius
Curve radius. Minimum depends on design speed and superelevation.
Central Angle (Δ)
Deflection angle (delta) between the two tangent lines, in degrees.
Tangent Length
Length of tangent from PC or PT to PI.
PI Station
Station of the Point of Intersection (PI) in feet.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Input Method = 1, Radius = 1000, Central Angle (Δ) = 30, Tangent Length = 268 = 5 input(s) provided
  2. Calculate Radius
    Radius = R
    1000 = 1000
  3. Calculate Arc Length
    Arc Length = L
    523.6 = 523.6
  4. Calculate Tangent
    Tangent = T
    267.95 = 267.95
  5. Calculate Long Chord
    Long Chord = C
    517.64 = 517.64

Engine last updated . Checked against 4 independently-derived tests — how we verify calculators.

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