Calculating the length of an arc

[sponge_designs]

Hey guys, Im putting together a spreadsheet for work, and finding the length of an arc is something we often need to calculate. Theres plenty of webpages that I can just punch the numbers in, but Id like to have it in a spreadsheet, as there are factors prior to this that have already been calculated.

I can do Step 1 no worries, but how do I do the formulas for steps 2 and 3?

Cheers,
Matt


If the height of the arc is 1 m and width is 2 m.
[h=4]Step 1 : Find the Radius[/h]r = (h/2) + (w²/(8h))r = (1/2) + (2²/(8x1))
= 0.5 + (4/8)
= 0.5 + 0.5
= 1
The radius is 1 m



[h=4]Step 2 : Find the Center Angle of Arc[/h]C = 2 tan^-1(w/(2×(r-h)))
if(C<0)
C = 360 + C C = 2 tan^-1(2/(2 × (1-1)))
= 2 tan^-1(2/(2 × 0))
= 2 tan^-1(2/0)
= 2 tan^-1(∞)
= 2 × 90
C = 180
Round the result, center angle is 180°



[h=4]Step 3 : Find Length of Arc[/h]l = C × 2 Π r / 360 l = 180 × 2 Π * 1 / 360
= 3.14159
Arc Length is 3.14159 m

 

[MARK858]

See the link attached where the formula in post 8 which works out (cell F1) with your example to

Excel Workbook
	A	B	C	D	E	F	G	H	I
1	2	1	1.570796	3.67321E-06	1	3.141593			3.141593
Sheet2

Cell I1 is the formula from post #10

 

[kvsrinivasamurthy]

I feel angle not required in degrees
For angle in radians

[COLOR=#666666][FONT=Arial]C = 2 *Atan[/FONT][/COLOR][COLOR=#666666][FONT=Arial](w/(2*(r-h)))[/FONT][/COLOR]

For arc length

L=r*C[/FONT][/COLOR]

 

[sponge_designs]

Thats brilliant! Thank you

 

[kvsrinivasamurthy]

welcome.Thanks for the compliment.