# Circle Sector

#### Michael M

##### Well-known Member
Hi All
I am trying to calculate the segment area of a circle, but my unknown is the central angle.
As an example
A 500mm Dia circle with the bottom 30mm cut off....I need the area of the bottom 30mm, but, as I said , I don't have the central angle

I'd really appreciate anyones Geometry assistance, all I can find on the Net requires that central angle,

### Excel Facts

Copy formula down without changing references
If you have =SUM(F2:F49) in F50; type Alt+' in F51 to copy =SUM(F2:F49) to F51, leaving the formula in edit mode. Change SUM to COUNT.

#### Fazza

##### MrExcel MVP
diameter 500

looking at a cut-off point, radius 250, horizontal distance to centre is 220

so angle from 'vertical' to cut off point has side 220 & hypotenuse 250

or cosine angle = 220/250

OK?

#### Michael M

##### Well-known Member
Hi Fazza
Did I mention my complete and utter inability to understand geometry....LOL !!

So, the answer you gave me was the Cosine of the central angle ??

#### Fazza

##### MrExcel MVP
actually half of the subtended angle

a little sketch will show it. remember that the radius is 250 and the cut off of 30 gives the 220...

#### Michael M

##### Well-known Member
Thanks Fazza
I have a sketch...I'll try and make some sense of the maths
I have been looking at another way by calculating the chord length and then the area of the 2 triangles, which apparently is accurate to within 0.3%, which is more than adequate.

#### sulakvea

##### Well-known Member
sry - will get back shortly

Last edited:

#### Michael M

##### Well-known Member
Fazza, yep been there....but i think I'll run with the Chord length method.
Really appreciate the input though....out here in the bush, we just clap hands to find the central angle....LOL !!

Sulakvea
Thanks for the input....but I don't have the central angle...as I said, I'll go with the chord method for a suitable degree of accuracy

#### sulakvea

##### Well-known Member
hi Michael, sorry for the previous post - made a mistake in calculations and knew wouldnt let me edit by the time i fixed it. here it is:

the formula is (R^2) /2 * (Angle - Sin (Angle))

just like Fazza suggested - cos() of the half angle would be 220/250. sin() of the same half angle would be 1-cos() = 1-22/25 = 3/25 = 0.12

you need the angle (i.e. Arcsin).

Arcsin(X) = Atn(X / Sqr(-X * X + 1)) (from VBA help), plug in 0.12 and you get 0.120289882394788. times 2 = 0.240579765.

plug in the numbers. you get (250^2)*2 / (0.240579765-0.12)

HTH

#### Michael M

##### Well-known Member
Thanks again
I am going to try the formulae and see how much difference there really is between the 2.
But if I can get within 0.5%, I will be more than happy

1,105,970
Messages
5,508,467
Members
408,686
Latest member
celobacara

### This Week's Hot Topics

• Turn fraction around
Hello I need to turn a fraction around, for example I have 1/3 but I need to present as 3/1
• TIme Clock record reformatting to ???
Hello All, I'd like some help formatting this (Tbl-A)(Loaded via Power Query) [ATTACH type="full" width="511px" alt="PQdata.png"]22252[/ATTACH]...
• TextBox Match
hi, I am having a few issues with my code below, what I need it to do is when they enter a value in textbox8 (QTY) either 1,2 or 3 the 3 textboxes...
• Using Large function based on Multiple Criteria
Hello, I can't seem to get a Large formula to work based on two criteria's. I can easily get a oldest value based one value, but I'm struggling...
• Can you check my code please
Hi, Im going round in circles with a Compil Error End With Without With Here is the code [CODE=rich] Private Sub...
• Combining 2 pivot tables into 1 chart
Hello everyone, My question sounds simple but I do not know the answer. I have 2 pivot tables and 2 charts that go with this. However I want to...