Calculating the length of an arc

sponge_designs

New Member
Joined
Aug 25, 2015
Messages
8
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


 

Excel Facts

Lock one reference in a formula
Need 1 part of a formula to always point to the same range? use $ signs: $V$2:$Z$99 will always point to V2:Z99, even after copying
I feel angle not required in degrees
For angle in radians
Code:
[COLOR=#666666][FONT=Arial]C = 2 *Atan[/FONT][/COLOR][COLOR=#666666][FONT=Arial](w/(2*(r-h)))[/FONT][/COLOR]

For arc length
Code:
L=r*C[/FONT][/COLOR]
 
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