Radius of Curve given Tangent Calculator

✖Tangent Length is equal to the length of a line segment with endpoints as the external point and the point of contact.ⓘ Tangent Length [T]			+10% -10%
✖Deflection Angle is the angle between the first sub chord of curve and the deflected line with equal measurement of first sub chord from tangent point.ⓘ Deflection Angle [Δ]			+10% -10%

✖Curve Radius is the radius of a circle whose part, say, arc is taken for consideration.ⓘ Radius of Curve given Tangent [R_Curve]

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Formula

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Radius of Curve given Tangent

Formula

`"R"_{"Curve"} = "T"/tan("Δ"/2)`

Example

`"199.9779m"="127.4m"/tan("65°"/2)`

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Radius of Curve given Tangent Solution

STEP 0: Pre-Calculation Summary

Formula Used

Curve Radius = Tangent Length/tan(Deflection Angle/2)
R_Curve = T/tan(Δ/2)
This formula uses 1 Functions, 3 Variables

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)

Variables Used

Curve Radius - (Measured in Meter) - Curve Radius is the radius of a circle whose part, say, arc is taken for consideration.
Tangent Length - (Measured in Meter) - Tangent Length is equal to the length of a line segment with endpoints as the external point and the point of contact.
Deflection Angle - (Measured in Radian) - Deflection Angle is the angle between the first sub chord of curve and the deflected line with equal measurement of first sub chord from tangent point.

STEP 1: Convert Input(s) to Base Unit

Tangent Length: 127.4 Meter --> 127.4 Meter No Conversion Required
Deflection Angle: 65 Degree --> 1.1344640137961 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_Curve = T/tan(Δ/2) --> 127.4/tan(1.1344640137961/2)

Evaluating ... ...

R_Curve = 199.977942524816

STEP 3: Convert Result to Output's Unit

199.977942524816 Meter --> No Conversion Required

FINAL ANSWER

199.977942524816 ≈ 199.9779 Meter <-- Curve Radius

(Calculation completed in 00.004 seconds)

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NSS College of Engineering (NSSCE), Palakkad

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National Institute of Technology (NIT), Warangal

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< 11 Simple Circular Curve Calculators

Radius of Curve given Long Chord

Go Curve Radius = Length of Long Chord/(2*sin(Deflection Angle/2))

Length of Curve if 30m Chord Definition

Go Length of Curve = 30*Deflection Angle/Angle for Arc*(180/pi)

Length of Curve if 20m Chord Definition

Go Length of Curve = 20*Deflection Angle/Angle for Arc*(180/pi)

Radius given Apex Distance

Go Curve Radius = Apex Distance/(sec(Deflection Angle/2)-1)

Apex Distance

Go Apex Distance = Curve Radius*(sec(Deflection Angle/2)-1)

Mid Ordinate

Go Mid Ordinate = Curve Radius*(1-cos(Deflection Angle/2))

Radius of Curve given Tangent

Go Curve Radius = Tangent Length/tan(Deflection Angle/2)

Tangent Length

Go Tangent Length = Curve Radius*tan(Deflection Angle/2)

Deflection Angle given Length of Curve

Go Deflection Angle = Length of Curve/Curve Radius

Radius of Curve given Length

Go Curve Radius = Length of Curve/Deflection Angle

Length of Curve

Go Length of Curve = Curve Radius*Deflection Angle

Radius of Curve given Tangent Formula

Curve Radius = Tangent Length/tan(Deflection Angle/2)
R_Curve = T/tan(Δ/2)

What are the types of Curves?

(i) Simple: A simple curve consists of a single arc of a circle connecting two straights.
(ii) Compound: A compound curve consists of two or more simple curves having different radii bending in the same direction and lying on the same side of the common tangent.
(iii) Reverse: A reverse or serpentine curve is made up of two arcs having equal or different radii bending in opposite directions with a common tangent at their junction.
(iv) Deviation: A deviation curve is simply a combination of two reverse curves.

How to Calculate Radius of Curve given Tangent?

Radius of Curve given Tangent calculator uses Curve Radius = Tangent Length/tan(Deflection Angle/2) to calculate the Curve Radius, The Radius of Curve given Tangent formula is defined as a radius of an arc or curve created by part of a circle that can be made from the same radius. Curve Radius is denoted by R_Curve symbol.

How to calculate Radius of Curve given Tangent using this online calculator? To use this online calculator for Radius of Curve given Tangent, enter Tangent Length (T) & Deflection Angle (Δ) and hit the calculate button. Here is how the Radius of Curve given Tangent calculation can be explained with given input values -> 199.9779 = 127.4/tan(1.1344640137961/2).

FAQ

What is Radius of Curve given Tangent?

The Radius of Curve given Tangent formula is defined as a radius of an arc or curve created by part of a circle that can be made from the same radius and is represented as R_Curve = T/tan(Δ/2) or Curve Radius = Tangent Length/tan(Deflection Angle/2). Tangent Length is equal to the length of a line segment with endpoints as the external point and the point of contact & Deflection Angle is the angle between the first sub chord of curve and the deflected line with equal measurement of first sub chord from tangent point.

How to calculate Radius of Curve given Tangent?

The Radius of Curve given Tangent formula is defined as a radius of an arc or curve created by part of a circle that can be made from the same radius is calculated using Curve Radius = Tangent Length/tan(Deflection Angle/2). To calculate Radius of Curve given Tangent, you need Tangent Length (T) & Deflection Angle (Δ). With our tool, you need to enter the respective value for Tangent Length & Deflection Angle 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 Curve Radius?

In this formula, Curve Radius uses Tangent Length & Deflection Angle. We can use 3 other way(s) to calculate the same, which is/are as follows -

Curve Radius = Length of Curve/Deflection Angle
Curve Radius = Length of Long Chord/(2*sin(Deflection Angle/2))
Curve Radius = Apex Distance/(sec(Deflection Angle/2)-1)

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