Radius of Curve using External Distance Calculator

✖External distance can be described as distance from point of intersection of tangents to midpoint of curve.ⓘ External Distance [E]			+10% -10%
✖Central angle of curve can be described as the deflection angle between tangents at point of intersection of tangents.ⓘ Central Angle of Curve [I]			+10% -10%

✖Radius of Circular Curve is the radius of a circle whose part, say, arc is taken for consideration.ⓘ Radius of Curve using External Distance [R_c]

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Formula

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Radius of Curve using External Distance

Formula

`"R"_{"c"} = "E"/((sec(1/2)*("I"*(180/pi)))-1)`

Example

`"129.9917m"="5795m"/((sec(1/2)*("40°"*(180/pi)))-1)`

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Download Circular Curves on Highways and Roads Formulas PDF

Radius of Curve using External Distance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Circular Curve = External Distance/((sec(1/2)*(Central Angle of Curve*(180/pi)))-1)
R_c = E/((sec(1/2)*(I*(180/pi)))-1)
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sec - Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine., sec(Angle)

Variables Used

Radius of Circular Curve - (Measured in Meter) - Radius of Circular Curve is the radius of a circle whose part, say, arc is taken for consideration.
External Distance - (Measured in Meter) - External distance can be described as distance from point of intersection of tangents to midpoint of curve.
Central Angle of Curve - (Measured in Radian) - Central angle of curve can be described as the deflection angle between tangents at point of intersection of tangents.

STEP 1: Convert Input(s) to Base Unit

External Distance: 5795 Meter --> 5795 Meter No Conversion Required
Central Angle of Curve: 40 Degree --> 0.698131700797601 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_c = E/((sec(1/2)*(I*(180/pi)))-1) --> 5795/((sec(1/2)*(0.698131700797601*(180/pi)))-1)

Evaluating ... ...

R_c = 129.991735664109

STEP 3: Convert Result to Output's Unit

129.991735664109 Meter --> No Conversion Required

FINAL ANSWER

129.991735664109 ≈ 129.9917 Meter <-- Radius of Circular Curve

(Calculation completed in 00.004 seconds)

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National Institute of Technology (NIT), Warangal

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< 25 Circular Curves on Highways and Roads Calculators

Radius of Curve using External Distance

Go Radius of Circular Curve = External Distance/((sec(1/2)*(Central Angle of Curve*(180/pi)))-1)

External Distance

Go External Distance = Radius of Circular Curve*((sec(1/2)*Central Angle of Curve*(180/pi))-1)

Central Angle of Curve for given Length of Long Chord

Go Central Angle of Curve = (Length of long Chord/(2*Radius of Circular Curve*sin(1/2)))

Radius of Curve given Length of Long Chord

Go Radius of Circular Curve = Length of long Chord/(2*sin(1/2)*(Central Angle of Curve))

Length of Long Chord

Go Length of long Chord = 2*Radius of Circular Curve*sin((1/2)*(Central Angle of Curve))

Central Angle of Curve for given Tangent Distance

Go Central Angle of Curve = (Tangent Distance/(sin(1/2)*Radius of Circular Curve))

Radius of Curve using Tangent Distance

Go Radius of Circular Curve = Tangent Distance/(sin(1/2)*(Central Angle of Curve))

Radius of Curve using Midordinate

Go Radius of Circular Curve = Midordinate/(1-(cos(1/2)*(Central Angle of Curve)))

Exact Tangent Distance

Go Tangent Distance = Radius of Circular Curve*tan(1/2)*Central Angle of Curve

Length of Curve or Chord by Central Angle given Tangent Offset for Chord of Length

Go Length of Curve = sqrt(Tangent Offset*2*Radius of Circular Curve)

Length of Curve or Chord determined by Central Angle given Chord Offset for Chord of Length

Go Length of Curve = sqrt(Chord Offset*Radius of Circular Curve)

Length of Curve or Chord by Central Angle given Central Angle for Portion of Curve

Go Length of Curve = (100*Central Angle for Portion of Curve)/Degree of Curve

Central angle for Portion of Curve Approximate for Chord definition

Go Central Angle for Portion of Curve = (Degree of Curve*Length of Curve)/100

Central Angle for Portion of Curve Exact for Arc definition

Go Central Angle for Portion of Curve = (Degree of Curve*Length of Curve)/100

Length of Curve given Central Angle for portion of Curve

Go Length of Curve = (Central Angle for Portion of Curve*100)/Degree of Curve

Degree of Curve when Central Angle for Portion of Curve

Go Degree of Curve = (100*Central Angle for Portion of Curve)/Length of Curve

Degree of Curve for given Radius of Curve

Go Degree of Curve = (5729.578/Radius of Circular Curve)*(pi/180)

Radius of Curve

Go Radius of Circular Curve = 5729.578/(Degree of Curve*(180/pi))

Tangent Offset for Chord of Length

Go Tangent Offset = Length of Curve^2/(2*Radius of Circular Curve)

Central Angle of Curve for given Length of Curve

Go Central Angle of Curve = (Length of Curve*Degree of Curve)/100

Degree of Curve for given Length of Curve

Go Degree of Curve = (100*Central Angle of Curve)/Length of Curve

Exact Length of Curve

Go Length of Curve = (100*Central Angle of Curve)/Degree of Curve

Radius of Curve using Degree of Curve

Go Radius of Circular Curve = 50/(sin(1/2)*(Degree of Curve))

Radius of Curve Exact for Chord

Go Radius of Circular Curve = 50/(sin(1/2)*(Degree of Curve))

Approximate Chord Offset for Chord of Length

Go Chord Offset = Length of Curve^2/Radius of Circular Curve

Radius of Curve using External Distance Formula

Radius of Circular Curve = External Distance/((sec(1/2)*(Central Angle of Curve*(180/pi)))-1)
R_c = E/((sec(1/2)*(I*(180/pi)))-1)

What is external distance?

External distance is defined as the distance from point of intersection of tangents to midpoint of curve

How to Calculate Radius of Curve using External Distance?

Radius of Curve using External Distance calculator uses Radius of Circular Curve = External Distance/((sec(1/2)*(Central Angle of Curve*(180/pi)))-1) to calculate the Radius of Circular Curve, The Radius of Curve using External Distance can be defined as the absolute value of the reciprocal of the curvature at a point on a curve. Radius of Circular Curve is denoted by R_c symbol.

How to calculate Radius of Curve using External Distance using this online calculator? To use this online calculator for Radius of Curve using External Distance, enter External Distance (E) & Central Angle of Curve (I) and hit the calculate button. Here is how the Radius of Curve using External Distance calculation can be explained with given input values -> 129.9917 = 5795/((sec(1/2)*(0.698131700797601*(180/pi)))-1).

FAQ

What is Radius of Curve using External Distance?

The Radius of Curve using External Distance can be defined as the absolute value of the reciprocal of the curvature at a point on a curve and is represented as R_c = E/((sec(1/2)*(I*(180/pi)))-1) or Radius of Circular Curve = External Distance/((sec(1/2)*(Central Angle of Curve*(180/pi)))-1). External distance can be described as distance from point of intersection of tangents to midpoint of curve & Central angle of curve can be described as the deflection angle between tangents at point of intersection of tangents.

How to calculate Radius of Curve using External Distance?

The Radius of Curve using External Distance can be defined as the absolute value of the reciprocal of the curvature at a point on a curve is calculated using Radius of Circular Curve = External Distance/((sec(1/2)*(Central Angle of Curve*(180/pi)))-1). To calculate Radius of Curve using External Distance, you need External Distance (E) & Central Angle of Curve (I). With our tool, you need to enter the respective value for External Distance & Central Angle of Curve and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Radius of Circular Curve?

In this formula, Radius of Circular Curve uses External Distance & Central Angle of Curve. We can use 8 other way(s) to calculate the same, which is/are as follows -

Radius of Circular Curve = 50/(sin(1/2)*(Degree of Curve))
Radius of Circular Curve = 5729.578/(Degree of Curve*(180/pi))
Radius of Circular Curve = 50/(sin(1/2)*(Degree of Curve))
Radius of Circular Curve = Tangent Distance/(sin(1/2)*(Central Angle of Curve))
Radius of Circular Curve = Midordinate/(1-(cos(1/2)*(Central Angle of Curve)))
Radius of Circular Curve = Length of long Chord/(2*sin(1/2)*(Central Angle of Curve))
Radius of Circular Curve = Length of Curve^2/(2*Tangent Offset)
Radius of Circular Curve = Length of Curve^2/Chord Offset

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