How to determine the arc length in Excel?

G

Guest

In a 60 degree right triangle, x-axis = 1 and y-axis = Sqrt(3).
In degree mode, Tan(60) = Sqrt(3).
In radian mode, Tan(60 x Pi / 180) = Sqrt(3)
60 x Pi / 180 is the arc length between 60 degree angle.
Therefore, there is a direct relationship between arc length and x & y
length for each triangle.
Given with any x and y lengths for a right triangle, I would like to
determine the arc length based on this relationship.
Does anyone have any suggestions on how to determine the formula to
calculate the arc length?
In this example, x =1 in cell A1 and y = Sqrt(3) in cell B1, I would like to
determine the arc length = Pi / 3 in cell C1.
Does anyone have any suggestions?
Thanks in advance for any suggestions
Eric
 
G

Guest

First, your geometry is a little off. A true arc length both points should
lie on the circle which means X & Y should both be the same length. With a
right triangle If X if on the circle, Y will extend out past the circle. If
Y is on the circle, X will be inside the circle and you would have to extend
X to intersect the circle.

Arc length is the circumference times (angle of arc/360)
circumference = 2 *pi*radius

Your case where X is on the circle
Radius is X
circumference = 2 * pi * X
angle of arc (radians) = tan(Y/X)
angle of arc (degrees) = (pi/180) * tan(Y/X)

Arc Length = (2 * pi * X) * (pi/180) * tan(Y/X)

The answer could also be if Y is on the circle

Arc Length = (2 * pi * Y) * (pi/180) * tan(Y/X)
 
M

MartinW

This should work although I am sure there is a way to simplify it.

=DEGREES(ATAN(B1/A1)*SQRT(A1^2+B1^2)*(PI()/180))

HTH
Martin
 
G

Guest

My last posting I had Tan instead of ATan

First, your geometry is a little off. A true arc length both points should
lie on the circle which means X & Y should both be the same length. With a
right triangle If X if on the circle, Y will extend out past the circle. If
Y is on the circle, X will be inside the circle and you would have to extend
X to intersect the circle.

Arc length is the circumference times (angle of arc -degrees/360)
or
Arc length is the circumference times (angle of arc-radians/2 * pi)
circumference = 2 *pi*radius

Your case where X is on the circle
Radius is X
circumference = 2 * pi * X
angle of arc (radians) = arctan(Y/X)

Arc Length = (2 * pi * X) * (Atan(Y/X)/ (2 * pi)
Arc Length = X * Atan(Y/X)

The answer could also be if Y is on the circle

Arc Length = Y * Atan(Y/X)

Martin solution doesn't make sense
=DEGREES(ATAN(B1/A1)*SQRT(A1^2+B1^2)*(PI()/180))

A and B would be the legs of the triangle. You have one leg and the
hypotenuse
it should of been
 
M

MartinW

If the X and Y values are a co-ordinate then the circle through
that point has a radius of the hypotenuese of that triangle.
My formula calculates the arc length of that circle
back to the baseline.

I have no idea what the OP is trying to achieve but it
seems from his post that is the value that he requires.

Regards
Martin
 
G

Guest

Thank eveyone for suggestions
Eric

MartinW said:
This should work although I am sure there is a way to simplify it.

=DEGREES(ATAN(B1/A1)*SQRT(A1^2+B1^2)*(PI()/180))

HTH
Martin
 

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