Now there has always been the ages long debate over who would win in a fight The Man of Steel, Superman, or the Savior of Humanity, Kakarot. Now there have been feasible arguments on either side as to who would but I am about to attempt to end this argument the best way I can, and that way involves the most infallible method there is, and that method iiiiiiiiiisssssss...... MATH!!!!!
We all know that both Heroes possess immense amounts of power each and that both Heroes are nigh on impossible to beat in combat. However, I am going to attempt to break down these Heroes of humanity's abilities down mathematically as well as taking into to consideration both hero's various techniques and skills in order to figure out who would win in fight.
Back-Story time! Just kidding if you don't already know just a little backstory on these characters you most likely shouldn't be here, but if you are then just look 'em up real quick and you'll get some idea.
So I'll start with Goku. Goku is an alien child sent from his home planet to destroy yada yada yada changes is his ways after an accident and protects the planet. He's is incredibly strong and always shows immense potential to get stronger with every fight he takes part in. He usually starts out weaker than the opponent that he is fighting and then gets strong enough to beat them with ease. Now I'm going to be using the power level system (and I know that Toriyama said that the power levels have no real meaning to them, but I am going to be using them anyway) Now according to the Dragonball Wiki:
When he competed in the 22nd World Martial Arts Tournament, Goku's power had increased to 180 thanks to his training..... In terms of physical strength: as a child he could push extremely large rock formations with ease for Master Roshi's training, easily over 100 tons each.... Thanks to training, Goku's power had increased to 90,000 by the time of his battle with the Ginyu Force. It then takes a leap to 3,000,000 thanks to a Zenkai, and it increases to 150,000,000 while utilizing his Super Saiyan form against Frieza. Dragon Ball Z: The Anime Adventure Game states that Goku's base power rose to 8,000,000 by the time of theTrunks Saga.
Now if we do the the math on this one Goku can lift 1 ton for every 1.8 power level. And at his full potential and his final power level he is at 8,000,000 with his Super Saiyan form boosting him to 150,000,000. With the math done there (and assuming that every boost thereafter is by the same increment) each SSJ boost is by an amount approximately equivalent to 1666 time each boost. Now his Kaio Ken multiplies his power by each respective multiplier so, 16,000,000, 24 mil, so on and so forth.
Now here comes the fun part and all the huge numbers:
- At SSJ his power is multiplied by 1666 thus bringing him to a power level of 13,328,000,000 which, if the same rules of 1 ton for every 1.8 power level apply, would allow him to lift approximately 7,404,444,444 tons.
- At SSJ2 his power is multiplied by another 1666 bringing us to 22,204,448,000,000 allowing him to lift around 12,335,804,444,444 tons. Hot damn
- In SSJ3 form his power level is brought up by 1666x bringing us to around 36,992,610,368,000,000 which would then allow him to lift 20,551,450,204,444,444 tons
I'm not going to use SSJ4 seeing as its is only used in GT and most people don't consider that canon and the use of Super Saiyan God form has a bunch of other un-quantifiable variables.
He also has his kamehameha, Instant transmission, the use of Senzu Beans,
and the use of the dragon balls ( given that they have one use unless Goku can fight for a full year without tiring out or having them destroyed in stone form). And the fact that he can travel faster than the speed of light as is stated in the dragonball wiki:
In the anime, it was implied that he was able to move faster than light, as King Kai was unable to track him when he fought Frieza, but was previously able to track a ship moving through space at what was apparently light speed.
And lastly He is a Master Martial Artist
Now on to The Great Superman
Superman, born on the planet krypton sent to the planet earth, grows up to save the planet from various dangers. He fights various baddies on a daily basis continues to amaze us with extensive feats and amazing powers. He is known to fly faster than a speeding bullet and leap over tall buildings, but how strong is he really. He has been known to withstand explosions that are equivalent to that of five supernovas. Has survived flying into the sun and can fly in space with no oxygen.
He can bench press the equivalent of the earth's mass for five days straight hardly breaking a sweat (which by the way people is around 6 septillion tons) He can fly faster than the speed of light, but doesn't do so in fear of causing any lasting environmental destruction. He is an excellent martial artist adept in kryptonian martial arts of Torquasm-Rao and Torquasm-Vo. Which give him an extensive physical and mental advantage in any form of combat.
Now the actual fight. When it comes to physical strength Superman by far outclasses Goku, however, that has never really been an issue for Goku when it comes to fights, because when it comes to opponents that are stronger than Goku, he has been able to outlast and eventually beat those opponents with ease. Such opponents include Frieza, Cell, and Beerus.
Speed goes to Goku. Even though Supes goes as fast or faster than the Speed of light he wont due to his need to preserve the earth and its people. Goku doesn't have to abide by those rules. He can and will use all any power that he has at his disposal in order to get the job done.
When it comes to martial arts it don't matter. They're both masters in their respective martial arts so.... yeah.
So most of the fight comes down to stamina and durability and the fact that Goku can be brought back to life if killed with a wish from the dragonballs then the battle will most likely end in some sort of stalemate.