Once Siegel and Shuster introduced a character whose most obvious trait was, if not his goodness, his strength, the question has been obvious: How strong is Superman? (Curiously, no one ever asks "How good is Superman?")
Disappointingly, the answer will not be easy to summarize with a number. Three key points:
1) The depictions of Superman's strength have varied over the years, from writer to writer, and even in stories by the same writer. Roughly speaking, he started off in 1938 much stronger than any real man, but weaker than he's ever been portrayed since. He was already strong enough to move a planet in 1949. In 1972, a story cut his power in half. In 1986, John Byrne's reboot depowered Superman considerably. Since then, his power levels have more or less crept back up toward his previous highs.
2) Sometimes strength can be measured by a direct statement of a number, but more often, we just see Superman do things, and then we can infer how strong he must be. If he lifts a truck, though, that doesn't tell us that he can ONLY lift a truck -- he might be much stronger than that. You really only find out exactly how strong he is if you see a point where he tries to do something and just barely succeeds or just barely fails.
3) If you don't want to think about this any further, that's fine. As William Shatner said on Saturday Night Live, "It's just a show!" (Well, just a comic book.) It's not real, and there are no real answers. But "How strong is Superman?" keeps coming up again and again. People want an answer. That's going to require some science, or pseudoscience, so I'll talk about some of the issues first:
In real physics, although not in comic books, these things are true:
1) It's impossible, using hands the size of human hands, to pick up a very, very large object and have it hold together. If you tried to pick up the Great Pyramid by its top stone, you would only lift the top stone off of the pile and carry it away while leaving 99.99% of the pyramid behind. If you tried to grab it by two bottom stones, you'd only end up with those two and perhaps some other slice of blocks that were carefully balanced on top, but you sure wouldn't get the whole pyramid. Large objects lack structural integrity compared to their bulk.
If you'd like a comparison, try to use a toothpick to lift a cake. It's impossible -- the toothpick will slice through the cake, carrying almost no cake with it. That's what would happen if an incredibly strong being tried to lift a huge object.
Therefore, if Superman's really strong, he will be able to lift any object that is capable of being lifted, but larger objects will simply crumble. That certainly includes a planet. If he tried to push a planet, he should just end up drilling a hole through it, and maybe end up holding a piece that's not very big.
John Byrne wrote that Superman's ability to carry things was actually a form of telekinesis, so that he was holding the object together in some way other than with his hands. Not many writers allude to that, and it's more that they ignore the issue than take any particular approach to it.
2) The oft-cited test of "moving a planet" is naive with respect to physics.
First, the ability to push a planet at all involves the flying power, not the use of very strong arms. If a very strong being without flying power (say, Doomsday, or the Hulk) tried to push a planet, nothing would happen. Newton's laws (if we pay any attention to real physics at all) dictate that something has to be pushed against. An airplane pushes against air. A rocket pushes against the exhaust that it expels. Because Superman can fly in space, and change directions, we have to imagine that he has some unreal ability to push and pull against something, through some unspecified force (electromagnetic or gravitational?) and large astronomical bodies seem to be the only candidates.
Second, if any force pushes on an object in space, the object will move. The question is not whether the object will move or not. The question is how much the pusher is able to accelerate the planet.
This is different from the physics of everyday objects because of things like friction. Heavy objects are "stuck" to the Earth's surface, creating a force that resists meager efforts to move them. If you apply 50 lbs of force to move a parked truck (with the brakes locked), you will not move it at all. If you apply 200 lbs of force, you still will not move it at all. (At least, you won't move the wheels. You may rock it slightly, while the wheels remain fixed.)
However, in outer space, if you applied 50 lbs of force to a truck, you would move it, and the longer you kept pushing, the more it would speed up. In fact, if you applied 50 lbs of force to a planet, you would push it, but by some incredibly small amount.
When Superman has been seen to move a planet, the real assertion is that he moves it a significant amount in a fairly short time. If he were "weak" and he only moved a planet one inch after pushing for a week (which is still way beyond normal human strength), it wouldn't match the feats we've seen him perform in the past.
The ability to move a planet is a pretty good match to the top strength levels in Superman's past. We first see Superman moving a planet in 1949, in Superman #58. The planet has human-like inhabitants, so it's probably roughly the size of Earth. While the post-Byrne Superman admitted outright that he was unable to move a planet, the ability came back later, even if the writer (Joe Kelly) didn't intend it. In JLA vol. 3 #75 (the end of Obsidian Age), Superman, Martian Manhunter, and Wonder Woman move the Earth. Unlike the physics of everyday objects (like you and two of your friends moving a couch), the physics of bodies in space means that the contribution of forces is more or less linearly additive. That is, if 3 equal parties moved the Earth at a certain level of acceleration, then one of them alone could move it at 1/3 that acceleration.
Presumably, Superman is stronger than 1/3 of the total in that group, but that doesn't matter too much. Whether he's only 1/3 of the total (exactly equal to Wonder Woman and Martian Manhunter) or 99% (much stronger than the two of them combined), that nails down his strength level pretty closely.
One might wonder how fast and how hard Superman (and his friends) pushed those planets. In both cases, he needed to push the planets in order to adjust the orbit significantly (in one case, the planet was too far from its star; in the other case, too close). The stories don't provide the boring details of how long he has to push to make the needed change, but you certainly feel like it happens pretty quickly -- minutes or hours, not days or weeks.
Unfortunately, we hit another clash between real physics and the storytelling, because if Superman (or anyone) pushed a planet hard enough to move it significantly in minutes, the acceleration would absolutely devastate the people, trees, buildings, etc., on the planet. Over large portions of the planet, the force would be sideways, which is exactly what causes damage during an earthquake.
1% of the Earth's distance from the Sun is 1.5 million kilometers. To change a planet's temperature noticeably in a short time, it would have to move at least about that far. If Superman pushed at 1/10th of a G force, this would require 48 hours of pushing. That is actually too hard of an acceleration (it would devastate objects on the surface of the planet), too little of a change in the orbit (no one would notice the change in temperature for a long time), and yet too long of a delay (Superman doesn't say, "I'll see you in a couple of days!") to match the details in the stories, and if we loosen any of those assumptions, the other details become even more inconvenient. Let's say, though, that pushing an Earth-sized planet by 1/10th of a G is a good trade-off between the contradictory details. Let's say that Superman pushes the planet for 48 hours, it somehow holds together, and applying 1/10th G, he saves the day. (Given the nature of orbital mechanics, a single push is not the right answer, because making the orbit as close to circular as the Earth's is now would require a much more sustained effort, but we've already fudged on the precise details in imagining that it causes the necessary climate change without wrecking objects on the surface.) Let's say that pushing Earth at 1/10 G is the level of Superman's strength.
The Planet-Moving Answer
If Superman is just capable of pushing the Earth at 1/10th G, then his strength could be expressed in the following terms:
1) How much could he lift if he were lifting a weight against the 1 G gravity we experience on the surface of the Earth?
Very simple: It must be 1/10th of the mass of the Earth. That is 6 x 1024 kg, or, if you want to see the big number:
6,000,000,000,000,000,000,000 metric tons.
2) How much stronger is he than a normal man?
The current world record in weightlifting (of any kind) is the 390 kg back squat by Hossein Rezazadeh. That makes Superman 15 sextillion times stronger than the strongest actual man. Of course, Rezazadeh is much stronger than an ordinary man, maybe ten times stronger.
"Sextillion" is a very rare term, so to rewrite that in more common terms, Superman is 15 billion trillion times stronger than Rezazadeh, and about 150 billion trillion times stronger than an average man.
Really Big Numbers
All told, there are more digits than you would expect in the sorts of numbers we're talking about. Let's say that Superman got into a fight with an opponent who was very strong, but not as strong -- someone who could lift a small mountain (1 mile cubed of rock). What would the fight look like between Superman and that enemy? A decent fight? Would the enemy get in some good blows before eventually losing?
Given that premise, Superman would be about 500 billion times stronger than the enemy. To put that in perspective, compare a man and a fruit fly that is 3 mm long and weighs 3 milligrams. Flying, it can just support its own weight, so we'll call that its strength. Hossein Rezzadeh is only 130 million times stronger than the tiny fruit fly. Superman would have a much bigger advantage over the mountain-lifting enemy than Rezazadeh would have over the fruit fly. The edge that Rezazadeh has on a fruit fly, planet-moving Superman would have on an opponent who could lift a mountain range (3000 mountains).
Basically, for an opponent to tangle with Superman, in terms of sheer strength (and not magic or some other angle) the opponent would have to be a planet-mover, too. An opponent with 1/10th of Superman's strength would push a planet as much in 20 days as Superman pushes it in 48 hours. (If the opponent had flying power at all.)
Superman's strength (and other powers) have been explained in a number of ways over the years.
1) A "physical structure" that is "millions of years advanced" (Action #1). This implies that great strength is a form of perfection that evolution naturally leads to, overlooking the fact that natural selection does not lead to perpetually increasing strength in all species, because sheer strength is not the sole determinant of survival. For example, gorillas do not have an inherent evolutionary advantage over squirrels.
2) That "the smaller size of [Earth], with its slighter [than Krypton's] gravity pull, assists Superman's tremendous muscles in the performance of miraculous feats of strength" (Superman #1). Alas, modern planetary science does not lend support to this idea. Even an extremely large planet would not have gravity so much stronger than Earth's so as to explain Superman's planet-moving strength. While some planets orbiting other stars have been found with masses about 3000 times that of the Earth, those are gas giant planets (like Jupiter) that lack solid surfaces. Even if a planet the size of Jupiter were made of solid iron, its surface gravity would be less than 20 times that of the Earth. Superman's strength is far greater than that, so a better explanation is needed. (Of course, powers like telescopic vision also require a better explanation, no matter what the numbers.)
3) That "ultra solar rays" of the Earth's Sun, a yellow star, have an effect on Kryptonians that empowers them instantly. (Action #262)
4) In John Byrne's Man of Steel #1, Jor-El explains that his son, as a Kryptonian, will "grow ever more powerful" because "Kryptonian cells will become living solar batteries". This implies that the power output of a Kryptonian would be about the same as if human-sized solar panels were used to charge a battery. Solar panels are not very efficient, so we might expect, somehow, for Kryptonians to extract power more efficiently, and from a larger portion of the spectrum. But that is ridiculously less power than Superman is seen to display, and would moreover imply that feats of strength would exhaust the stored energy.
So of the offered explanations, (3) actually works best, mainly by being sufficiently evasive about how it might operate.
Eat, Eat, Eat Your Way to Super Strength
One bedrock truth of physics is that for a force to act upon a body, some source of energy must be expended, and therefore some mass must be expended. When a person walks up a flight of stairs, chemical reactions that power the muscles cause a tiny amount of mass that is bound in molecular bonds to be converted into the energy that powers their climb (this should not be confused with the measurable weight loss that takes place through exercise; even in all of the exercise you perform in your life, less than one gram of mass is actually converted into energy). When dynamite explodes, a larger yield comes from other chemical reactions. When a hydrogen bomb explodes, nuclear binding energy is expended to create the explosion. Each of these events causes some mass to be converted into energy. For example, the atomic bomb dropped on Hiroshima converted about 0.6 grams of matter into energy. When you walk up a flight of stairs, the amount of matter converted into energy is tiny, but not zero.
This truth of physics was introduced into the Flash series starring Wally West in the late Eighties. Bursts of super speed left the Flash hungry, needing to eat vast quantities to replenish what he had burned. Energy does have to come from somewhere and for people, food is the explanation. For feats like Superman's, solar batteries are not going to cut it.
But the amount of fuel required depends on how good you are at extracting energy from it. Chemical energy tends to be vastly weaker than nuclear energy, by a factor of up to 100 million. People (and dynamite) use chemical energy. Nuclear weapons and stars use nuclear energy. But it is possible in principle to use all of the energy in an energy source. An explosion like 1945's atomic bombs would result if 0.6 grams of matter were completely annihilated. (0.3 grams of antimatter, in the Earth's atmosphere, would accomplish that task by annihiliating an equal mass of matter.)
The greatest imaginable source of power for Superman would be if his cells could completely convert some fuel into energy, as efficient as a matter/antimatter explosion, and considerably more efficient than the fusion of hydrogen that powers the stars. This is where explanation (3) comes closest to succeeding, because it does not stipulate that the Sun's rays directly power Superman, but that they enable him to begin to display super powers. We can imagine a super metabolism that is normally turned off, but that is turned on a like a switch by the presence of yellow starlight. Then his super metabolism could tap into some unspecified manner of turning fuel into pure energy -- there could be no more potent way of powering a superman.
So when Superman performs a super feat, he, like us, must burn up some mass, and because he uses much more energy than a normal person, he must lose mass at a much greater rate. For Superman to exert a force that pushed the Earth at 0.1 Gs, he would have to convert a certain amount of mass into energy every second, given by Einstein's famous equation E = mc2. The bad news is, for Superman to push a planet with the force described above, he would have to burn up 2 quintillion tons of matter each second. That would require that he weigh an enormous amount before undertaking the task. If he were that heavy, he would crash through the floors of buildings and into the center of the Earth whenever he slept.
If you take the energy-mass equation seriously and work backwards, you have to conclude that planet-pushing is not a feat for human-sized beings even if you hope for a perfectly-functioning super metabolism.
So, if we imagine that Superman burns up several grams of matter in this perfectly efficient way, we find that he produces energy on the scale of hydrogen bombs (which do not adjust the planet significantly in its orbit). This leads us to a more modest and in fact Byrne-like calculation of Superman's strength. Imagine that a ship were sinking and Superman flew into Metropolis Harbor to lift it and carry it to safety. Upon landing, we should hope that he did not burn so much matter as to look emaciated to Lois Lane. Let's say that Superman weighs 100 kg (220 pounds... very close to what he says in Superman The Movie) and that lifting the ship for 100 seconds leads him to lose only 1 kg (2 lbs, not quite noticeable). With those assumptions, how much could he lift?
Burning 10 grams a second, Superman could lift 20 billion tons. That's a tiny little fraction of the mass of a planet, but it's not too shabby. In fact, it's a lot stronger than the Byrne Superman. Instead of being 15 billion trillion times stronger than Hossein Rezazadeh, he would "only" be 45 billion times stronger. "Realistic" Superman would be weaker than a fruit fly compared to planet-moving Superman. In fact, he would be precisely mountain-moving Superman, capable of lifting about one cubic mile of rock. (That's the size of a mountain in the Appalachians, not in the Himalayas.) Ships would be no problem. He could still "move" planets, but not so much that you'd notice, unless he pushed for years.
Does It Matter?
Does it matter how strong Superman is? To most people, of course not, and that even includes a lot of the writers who have handled him over the years. Superman is science fiction, not a physics textbook. But the attempt to include a "real science" explanation for his power goes all the way back to the first page of Action #1. This is an attempt to talk about his feats in terms of real science. If you got this far and aren't interested in the topic... sorry.