Fine Tuning of the Physical Constants of the Universe
Parameter Max. Deviation
Ratio of Electrons

rotons 1:1037
Ratio of Electromagnetic Force:Gravity 1:1040
Expansion Rate of Universe 1:1055
Mass Density of Universe1 1:1059
Cosmological Constant 1:10120
http://www.godandscience.org/apologetics/designun.html
These numbers represent the maximum deviation from the accepted values, that would either prevent the universe from existing now, not having matter, or be unsuitable for any form of life.
Degree of fine tuning
Recent Studies have confirmed the fine tuning of the cosmological constant (also known as "dark energy"). This cosmological constant is a force that increases with the increasing size of the universe. First hypothesized by Albert Einstein, the cosmological constant was rejected by him, because of lack of real world data. However, recent supernova 1A data demonstrated the existence of a cosmological constant that probably made up for the lack of light and dark matter in the universe.2 However, the data was tentative, since there was some variability among observations. Recent cosmic microwave background (CMB) measurement not only demonstrate the existence of the cosmological constant, but the value of the constant. It turns out that the value of the cosmological constant exactly makes up for the lack of matter in the universe.3
The degree of fine-tuning is difficult to imagine. Dr. Hugh Ross gives an example of the least fine-tuned of the above four examples in his book, The Creator and the Cosmos, which is reproduced here:
One part in 1037 is such an incredibly sensitive balance that it is hard to visualize. The following analogy might help: Cover the entire North American continent in dimes all the way up to the moon, a height of about 239,000 miles (In comparison, the money to pay for the U.S. federal government debt would cover one square mile less than two feet deep with dimes.). Next, pile dimes from here to the moon on a billion other continents the same size as North America. Paint one dime red and mix it into the billions of piles of dimes. Blindfold a friend and ask him to pick out one dime. The odds that he will pick the red dime are one in 1037. (p. 115)
The ripples in the universe from the original Big Bang event are detectable at one part in 100,000. If this factor were slightly smaller, the universe would exist only as a collection of gas - no planets, no life. If this factor were slightly larger, the universe would consist only of large black holes. Obviously, no life would be possible in such a universe.
Another finely tuned constant is the strong nuclear force (the force that holds atoms together). The Sun "burns" by fusing hydrogen (and higher elements) together. When the two hydrogen atoms fuse, 0.7% of the mass of the hydrogen is converted into energy. If the amount of matter converted were slightly smallerâ0.6% instead of 0.7%â a proton could not bond to a neutron, and the universe would consist only of hydrogen. With no heavy elements, there would be no rocky planets and no life. If the amount of matter converted were slightly largerâ0.8%, fusion would happen so readily and rapidly that no hydrogen would have survived from the Big Bang. Again, there would be no solar systems and no life. The number must lie exactly between 0.6% and 0.8% (Martin Rees, Just Six Numbers).