price calculation trouble, precision

gaucho

Hello all,
I need to do some price calculations. The function I wrote works perfect in respect of mathematical correctness, but sometimes seems not to work in respect of price calculation. Well, I had no calculation errors for months, but today I had to calculate some prices and I run into an calculation error (1 cent in total sum) which seems to be a kind of exception.

net price 13.78, VAT 7% = gross 14.75 (this is the fact)

Now calculation (with PHP and calculator)
calculate gross: 13.78 * 1.07 = 14.7446000000000001506351 rounded = 14.74
calculate net: 14.75 / 1.07 = 13.7850467289719613717125 rounded = 13.79

I mean, depending on the direction you get different results.
This causes an error when adding prices, at least of 1 cent.

Does anybody know how I could solve this dilemma?

Thanks in advance

Ralf

laserlight

I think that is unavoidable. You may consider storing a fraction of a cent, e.g., to three decimal places.

gaucho

Hello laserlight,
thanks for your reply.
I'm already storing 7 decimals. And this has worked correctly for months, but I never had to calculate the mentioned price-VAT combination before.

Best regards

Ralf

laserlight

If you are "storing 7 decimals", then why do you use 14.75 as the gross price? It should be 14.7446, or at least 14.745. Once you use the version that is rounded to two decimal places, do not expect results accurate to the second decimal place where multiplication or division is involved.

gaucho

Well, input price from form has only 2 decimals, thats why.
OK, what I have found out till now is that it seems to be a rounding problem.
As far as I can see right now it seems that I I used the wrong precision in my calculations, I thought that the more decimals I use, the more accurate the results, but dealing with money seems to follow different rules. I found out that whenever officials do price calculations they just use four decimals at most, rounding to 2 decimals after each operation.

Maybe this is the solution, but I'm not really sure.
Is there anybody out there coming from Germany who might be better informed about this matter (Calculation of prices, rounding).

Best regards

Ralf