Why does Math.cos(90 * Math.PI/180) yield 6.123031

Question

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• Is floating point math broken? 28 answers

I convert degrees to radians (degrees * Math.PI/180) but why does the following:

Math.cos(90 * Math.PI/180)

yield 6.123031769111... and not zero?

I'm trying to perform 2D rotations uses matrixes and the results are completely out of whack.

Answer 1

6.123233995736766e-17 is very very close to zero. Just round the number.

Answer 2

The output of

Math.cos(90 * Math.PI/180)

is

6.123031769111886e-17

Notice the e-17 at the end, which means that this number is 6.123 x 10^-17. This is a number so vanishingly close to 0 that it's effectively 0. The reason that it's not identically 0 is due to rounding errors in the IEEE-754 double format which prevents you from getting an exact representation of π / 2 and causes minute rounding errors in the calculation of the cosine.

By the way - I was pretty surprised as well when the result came back starting with a 6! It's only after I looked at the very end that things started to make sense.

Hope this helps!

Answer 3

6.123233995736766e-17

is scientific notation for a very small number, close to zero. It is not exactly zero because of rounding errors and so forth.