How much would it cost to build a space elevator?

It would take BILLIONS(possibly trillions) of dollars and resources to build such an elevator. Also, much notably research has to be done to accomplish that feat.

Trillions just do to the research needed to make the necessary
construction materials but could we yes if we wanted to bad enough and in 20 years.( i have faith in the ingenuity of the human race when it really wants to do something.)

I bid the job for $8.93…checks, cash or money orders accepted.

Okay. Let’s see. The Saturn V weighed about 6.7 Million lbs and could lift about 200 thousand lbs into LEO. That is about 3%. Yes, a tether should be much more efficient. If it were practical.

The greatest tensile strength material that is commonly available is Kevlar. The problem is that if we take any thickness of Kevlar cord it will reach breaking strength in 400 miles. In other words, when the cord gets 400 miles long the weight of the cord equals the breaking strength of the Kevlar. If you taper the cord you can reach 800 miles. However, 800 miles is quite a bit short of the necessary 22,000 to reach geosynchronous orbit.

Okay, now let’s look at gravity. Gravity decreases with the square of the distance. The Earth’s surface is about 3,500 miles from the center. If you go up 3,500 miles above the Earth’s surface the gravity is only 1/4. At about 1,500 miles up the gravity is about 1/2. This is why the tether concept is so frustrating.

With the gravity at 1/2 and decreasing to nothing as you go out toward geosynchronous orbit Kevlar is strong enough. So, the last 20,500 miles is no problem. The problem is the first 1,500 miles where gravity is 1/2 and increases to 1. The Earth’s gravity is still at 80% at 400 miles so you do get a littel help. However, even taking into account the reduction in gravity the Kevlar will still break at about 1000 miles. However, if a material is developed that is twice the strength per weight of Kevlar then a tether could reach to about 4,000 miles. If you can increase the strength by about 3 then you would have some left over for payload.

There are other practical considerations like how you would pull against the tether to raise the car without abrading the tether. Also, in space temperature would be a problem because Kevlar would melt if got too hot and would risk being brittle if it were too cold.

A more practical near term vehicle might be something like a linear accelerated vehicle that would essentially be shot out of a magnetic canon. For example, you put one in the Rockies and you can clear one mile of atmosphere and have plenty of time to accelerate to a nice speed. This would also relieve the inefficiency of having to carry the weight of the reaction fuel. The downside is that I’m not so sure about hitting the atmosphere at hypersonic velocities as you exit the barrel.

Third on the list is an air breathing lifter. The reason why this is nice is because with typical liquid hydrogen/liquid oxygen rockets the oxygen weighs 8X as much as the hydrogen. If you could get the oxygen from the atmosphere the efficiency would go up tremendously. This has been done with a bomber with the X-15’s and more recently with the lifting craft on Spaceship 1. However, the ultimate would be a SCRAMJet engine which would allow you to get higher and boost the space vehicle to a higher initial speed.