One Sheet Manual Calculation

Not going to happen.

You can set calculation to Manual before opening the workbook, and then selectively calculate whatever you want (a sheet, a range, a cell). See Help for the Calculate method.

Hi SHG, I was thinking to do something like you proposed. but I do not know how to call the secod sub when any change happen in the workbook.
any hint in that sense will be great

'First part when the workbook is opened
Private Sub Workbook_Open()
    'To disable Excel Automatic Calculation then all sheet are frozen
    With Application
        .Calculation = xlManual
        .CalculateBeforeSave = False
    End With
    'making sure that check box is false
    Sheet1.CheckBox1.Value = False
    Sheet1.Range("M2") = "FALSE"
    
    'to calculate only the sheets with the true condition when the workbook is open
    'sheet3 and 4 to update results
    Sheet3.Calculate
    Sheet4.calcualate
    'sheet 1 to update results
    Sheet1.Calculate
End Sub


'second part
'This is the bit that I do not know how to do it
'When any change happen in the workbook any of the sheets even shhet 2
    'calculate only the sheets with the true condition stated in sheet1(eg. sheet3 and 4 first to update results)
    'Sheet3.Calculate
    'Sheet4.calcualate
    
    'check if sheet2 has to be calculated (if the user tick the check box
    'If Sheet1.Range("M2") = "TRUE" Then
    '    Sheet2.Calculate
    'Else
    'End If
    
    'sheet 1 to update all results from sheet2,3,4
    'Sheet1.Calculate

'End

oOarthurOo, time to get reacquainted with the forum rules, and then start your own thread,

At the time of posting, I was aware of rule 2:

Don't post a question in the thread of another member -- start your own thread. If you feel it's particularly relevant, provide a link to the other thread.

I decided it was likely appropriate to post in the thread since I have a suggested solution. Granted, not certain if the idea will work, thus phrased it as a question. But this is what I had in mind:

Private Sub Worksheet_Activate()
Application.Calculation = xlCalculationManual
End Sub

Private Sub Worksheet_Deactivate()
Application.Calculation = xlAutomatic
End Sub

Of course, I will defer to your (or other mods) judgement on whether this comment requires a new thread.

You can always post recommended solutions in a thread, but it's unlikely the OP is stopping back 15 months later (to the day, as it turns out) to check.

The correct constant is xlCalculationAutomatic, not xlAutomatic.