To make a space elevator would require somewhat more than 25 miles of cable. It would require about 44,472 miles of cable.
The FAI has defined that space starts where the Earth’s atmosphere ends, at the Karman line, 100km (about 62-63 miles) up. Low Earth Orbits (LEOs) start somewhat above that, perhaps 120 miles or so.
Objects stay in orbit not because they’re starting at a particular altitude but because they’re traveling so fast sideways that as they fall towards Earth, they miss the ground. The lower the orbit, the faster they have to travel.
The first problem is that if you tried to put a space elevator in a 120 mile LEO, the tip of the cable will need to travel over 17,000 MPH in order to stay in that orbit. But the Earth isn’t turning that fast; it spins at only about 1000 MPH at the equator. So if you tried tying a big rock to a 120 mile long rope, it’ll just fall down and land about 120 miles away.
So we need our space elevator’s orbit to match the spin of the Earth. Such an orbit is called a Geosynchronous Orbit. We already have a bunch of satellites in geosynchronous and geostationary orbits; they’re very useful. And we also know that orbit is 22,236 miles from earth. That’s a long cable.
So if the orbit is 22,236 miles away from Earth, your cable has to be 22,236 miles long, right? Nope. The center of the cable’s mass has to be 22,236 miles from Earth. That means the cable has to be twice as long, 44,472 miles. Not only would a cable that long weigh a lot, it has to be strong enough to not break in the middle from its own weight.
Most space elevator concepts call for the elevator to support its own weight by being in orbit, instead of trying to swing a heavy rock tied at the end of a rope. That eliminates a whole lot of nasty problems that a tethered rope has, such as creating radical weather patterns near the tip, a static electricity charge the size of all the lightning on the planet concentrated in one place, and trying to steer the remote end of a 44,472 mile cable so it remains perfectly centered above the terminal point. So the cable would be terminated a few kilometers short of the ground, and would only be accessible from the air. Boarding the cable car would require you to take a shuttle aircraft up to the bottom end of the cable.
The good news of all the static electricity in the cable is that power that could be harnessed to operate the cars that are running up and down the cable. The bad news is that taking a 44,472 mile journey by electric car is going to be a very long trip, no matter how fast the cars can safely climb. And once you reach the upper terminus of the cable, that just got you out of Earth’s gravity well – you are still no closer to Mars than you were when you started! Those weeks of driving straight up would then be followed by months of space flight.
The most realistic sounding versions feature some kind of tapered cable or ribbon, thickest and strongest in the middle and thinnest at the ends, possibly made of carbon nanotubes (because if you’re this far into Science Fiction territory, why not use the most Space Age of materials, right?) But everything described to date is really far-fetched.