'special case: if majorAxis=minorAxis, then it's a circle
If majorAxis = minorAxis Then

Oops! Me bad. You talked me into changing it. :(
When b=a, then the equation is just 2*a*Pi anyway.
So, the above is not necessary either.

Sub TestIt()
'// Ellipse Perimeter
Debug.Print Perimeter(10000, 9975)
Debug.Print Perimeter(9975, 10000)
Debug.Print
Debug.Print Perimeter(10000, 10000)
Debug.Print 2 * [Pi()] * 10000
End Sub

Returns:
62753.3378298691
62753.3378298691

62831.8530717959
62831.8530717959

Function Perimeter(a, b)
Dim k As Double
k = 3 * ((a - b) / (a + b)) ^ 2
Perimeter = (a + b) * (1 + k / (10 + Sqr(4 - k))) * [Pi()]
End Function
= = = = = =
Dana DeLouis


Dana DeLouis wrote:
'just to be technical, if minor axis major axis, swap
...
((majorAxis - minorAxis) / (majorAxis + minorAxis)) ^ 2

Hi. Just to mention if interested. If I am not mistaken, one does not
need to swap the variables. This is because (majorAxis - minorAxis)
gets squared. The result in the same positive value either way.
The code below is the same thing just to demonstrate.

Sub TestIt()
'// Ellipse Perimeter
Debug.Print Perimeter(10000, 9975)
Debug.Print Perimeter(9975, 10000)
End Sub

Returns:
62753.3378298691
62753.3378298691

Function Perimeter(a, b)
Dim k As Double
If a = b Then
Perimeter = 2 * [Pi()] * a
Else
k = 3 * ((a - b) / (a + b)) ^ 2
Perimeter = (a + b) * (1 + k / (10 + Sqr(4 - k))) * [Pi()]
End If
End Function
= = = = = =
HTH
Dana DeLouis

JLatham wrote:
With some great guidance from David Biddulph and Dana DeLouis I've
modified the functions to calculate the actual (approximated)
perimeter/circumference of the ellipse, and have left the perimetric
radius as a 'way point" in the process should anyone need that value.
The previous worksheet formula was revised in the comment in these
functions to also calculate the approximated perimeter.

Function Ram2Perimeter(majorAxis As Double, minorAxis As Double) As
Double
'uses Ramanujan's second formula to approximate the
'perimeter of an ellipse
'INPUTS: majorAxis = the major semi-axis value
' minorAxis = the minor semi-axis value
'OUTPUTS: estimated circumference, or
' if major semi-axis is = minor semi-axis,
' returns circumference of circle of 2*semi-axis diameter
' -1 if error encountered
'
'Reference: http://en.wikipedia.org/wiki/Circumference
'Acknowledgment: Thanks to David Biddulph and Dana DeLouis for
' helping me realize the difference between parimetric radius and
circumference
'
'worksheet equivalent formula where
' B1 holds the majorAxis value and
' B2 holds the minorAxis value
'=(0.5*($B$1+A5))*(1+((3*(($B$1-A5)/($B$1+A5))^2)/(10+SQRT((4-(3*(($B$1-A5)/($B$1+A5))^2))))))
* (2 * Pi())
'
Dim swapValue As Double
Dim majorPlusMinor As Double
Dim majorMinusMinor As Double
Dim quotentSquared As Double
On Error GoTo RamanujanCirErr
'no such thing as negative numbers here!
majorAxis = Abs(majorAxis)
minorAxis = Abs(minorAxis)
'just to be technical, if minor axis major axis, swap
If minorAxis majorAxis Then
swapValue = majorAxis
majorAxis = minorAxis
minorAxis = swapValue
End If
'special case: if majorAxis=minorAxis, then it's a circle
If majorAxis = minorAxis Then
Ram2Perimeter = (4 * Atn(1)) * (2 * majorAxis) ' = pi*D
Exit Function
End If
majorPlusMinor = majorAxis + minorAxis
majorMinusMinor = majorAxis - minorAxis
quotentSquared = (majorMinusMinor / majorPlusMinor) ^ 2
'calculate the perimetric radius
Ram2Perimeter = (0.5 * majorPlusMinor) * _
(1 + ((3 * quotentSquared / _
(10 + Sqr((4 - 3 * quotentSquared))))))
'calculate the circumference [ 4 x Atn(1) = Pi ]
Ram2Perimeter = Ram2Perimeter * 2 * (4 * Atn(1))
On Error GoTo 0
Exit Function
RamanujanCirErr:
Err.Clear
Ram2Perimeter = -1
End Function

Function Ram2Perimeter2(majorAxis As Double, minorAxis As Double) As
Double
'uses Ramanujan's second formula to approximate the
'perimeter of an ellipse
'INPUTS: majorAxis = the major semi-axis value
' minorAxis = the minor semi-axis value
'OUTPUTS: estimated circumference, or
' if major semi-axis is = minor semi-axis,
' returns circumference of circle of 2*semi-axis diameter
' -1 if error encountered
'
'Reference: http://en.wikipedia.org/wiki/Circumference
'Acknowledgment: Thanks to David Biddulph and Dana DeLouis for
' helping me realize the difference between parimetric radius and
circumference
'
'worksheet equivalent formula where
' B1 holds the majorAxis value and
' B2 holds the minorAxis value
'=(0.5*($B$1+A5))*(1+((3*(($B$1-A5)/($B$1+A5))^2)/(10+SQRT((4-(3*(($B$1-A5)/($B$1+A5))^2))))))
* (2 * Pi())
'
Dim swapValue As Double
On Error GoTo RamanujanCir2Err
'no such thing as negative numbers here!
majorAxis = Abs(majorAxis)
minorAxis = Abs(minorAxis)
'just to be technical, if minor axis major axis, swap
If minorAxis majorAxis Then
swapValue = majorAxis
majorAxis = minorAxis
minorAxis = swapValue
End If
'special case: if majorAxis=minorAxis, then it's a circle
If majorAxis = minorAxis Then
Ram2Perimeter2 = (4 * Atn(1)) * (2 * majorAxis) ' = pi*D
Exit Function
End If
'calculate the perimetric radius
Ram2Perimeter2 = (0.5 * (majorAxis + minorAxis)) * _
(1 + ((3 * (((majorAxis - minorAxis) / (majorAxis + minorAxis)) ^
2) / _
(10 + Sqr((4 - 3 * (((majorAxis - minorAxis) / (majorAxis +
minorAxis)) ^ 2)))))))
'calculate the circumference [ 4 x Atn(1) = Pi ]
Ram2Perimeter2 = Ram2Perimeter2 * 2 * (4 * Atn(1))
On Error GoTo 0
Exit Function
RamanujanCir2Err:
Err.Clear
Ram2Perimeter2 = -1
End Function


"M" wrote:

Is there a formula to Calculate the Circumference of an ellipse in
excel?