###### Asked in Length and DistanceMath and ArithmeticTrigonometry

Length and Distance

Math and Arithmetic

Trigonometry

# What is the Formula for calculating chord length?

## Answer

###### Wiki User

###### June 18, 2008 9:19PM

Assume you mean the chord of a circle? If the angle between the two radii from the ends of the chord is A, and the radius of the circle is R, the chord length L will be

L = 2RsinA/2. You can prove this easily by joining the point bisecting the chord to the centre, you then have two rightangled triangles, with an included angle of A/2, and an opposite side of L/2. So sinA/2 = L/2R.

## Related Questions

###### Asked in Math and Arithmetic, Algebra, Geometry

### How do you find the radius given the chord length?

If you are given a chord length of a circle, unless you are
given more information about the chord, you can not determine what
the radius of the circle will be.
This is because the chord length in a circle can vary from a
length of (essentially) 0, up to a length of double the radius (the
diameter).
The best you can say about the radius if given the chord length,
is that the length of the radius is at least as long has half half
the chord length.

###### Asked in Units of Measure, Geometry, DIY Projects

### How do you find the radius of a circle if you know the length of a chord and the shortest distance from the center of the chord to the circle?

Imagine if you will a circle with a chord drawn through it and a
line running from the center of that chord to the center of the
circle. That line is necessarily perpendicular to the chord. This
means you have a right triangle whose hypotenuse is the radius of
the circle. The radius is thus given by: r = sqrt{(1/2 chord
length)^2 + (length of perpendicular line)^2} The actual formula to
find the radius is as follows: r= C squared/8a + a/2, where C is
the chord length, and a is the distance from center point of the
chord to the circle , and a and C form an angle of 90 degrees. the
entire formula before simplification is r = sqrt {(1/2 C)^2 +
(r-a)^2}

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