Calculation of PI() and 3.14159265358979 in excel

[Elakkiya630]

In Excel while Calculating `=SIN(PI())` formula it returns `1.22515E-16`.If the `PI()` `Value(3.14159265358979)` is directly given like =SIN(3.14159265358979), it returns `3.23114E-15`.

Please anyone can share your opinion about how the excel calculates differently, when 'PI' and 3.14159265358979 are passed as parameter.

[MrShorty]

I doubt the calculation is different. I expect that the explanation is in the common and unavoidable properties of floating point arithmetic. I would guess that, deep in the floating point representations, there is a slight difference between the value of the PI() function and the constant 3.14159265358979 (perhaps not visible in the cell display, but only visible when the numbers are stored as/converted to binary). Then there could be how floating point error effects the SIN() function. I am not intimately familiar with the internal workings of computer arithmetic, but I think we have at least one user here who may be able to shed much more light on the details, if that is of interest.

Until then, you might review some of the links I posted here that discuss floating point errors: https://www.excelforum.com/groups/ma...nd-errors.html

[joeu2004]

In Excel while Calculating `=SIN(PI())` formula it returns `1.22515E-16`.If the `PI()` `Value(3.14159265358979)` is directly given like =SIN(3.14159265358979), it returns `3.23114E-15`. Please anyone can share your opinion about how the excel calculates differently, when 'PI' and 3.14159265358979 are passed as parameter.

PI() does not return "exactly" 3.14159265358979. It only appears that way because Excel formats only up to the first 15 significant decimal digits, an arbitrary limitation.

In fact, the difference can be calculated, to wit: =SUM(PI(),-3.14159265358979) formatted as Scientific is about 3.11E-15. More precisely:

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I use period for the decimal point and comma to demarcate the first 15 significant decimal digits.