How to calculate arc length

Question

I forgot my secondary school maths, so I need to ask to confirm.

Arc Length = Radius*(Angle In Radian)

Is it correct?

This might be enlightening: http://www.mathwarehouse.com/trigonometry/radians/s=r-theta-formula-equation.php — Brendan W. Sullivan, Sep 26 '12 at 08:02

score 3 · Accepted Answer · answered Sep 26 '12 at 08:00

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Yes. This works because $C = 2\pi R$ and, coincidentally, there are $2\pi$ radians in one full rotation. Clearly, a fraction of a full rotation produces a fraction of circumference.

To be fair, your equation is in fact the definition of radian.

answered Sep 26 '12 at 08:00

Karolis Juodelė

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mak · Answer 2 · 2012-09-26T08:02:50.163

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It's approximately correct only because you assume that the arc is the base of a triangle... It only works where you can say that sin(θ) is approximately θ. For small angles only. General solution using $sin^{-1}$ is also an approximation tho because of the curvature. If it was me, I would calculate the perimeter with the given Radius and calculate the ratio corresponding to the ratio $\frac{360}{\theta}$.

edited Sep 26 '12 at 08:02

answered Sep 26 '12 at 07:57

mak

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1 radian is the arclength equivalent to the radius of the circle, by definition. – Daryl Sep 26 '12 at 08:00
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http://en.wikipedia.org/wiki/Radian – Karolis Juodelė Sep 26 '12 at 08:00
Oh... My bad... – mak Sep 26 '12 at 08:03

How to calculate arc length

2 Answers2