My cat is about 1' high at the shoulder, and I am a little over 6', but my cat can easily jump onto something as high as I am. That is 6x it's height. If a cat can do this, then Why can't I jump up onto my barn roof? That is a little less than 36' up. I have a hard time jumping onto even a 4' platform. Now if my cat had trouble jumping onto an 8" platform, I would think that pathetic. Do cats have muscles 20x stronger than humans, for their mass? Is it just their skeleton providing leverage?
Cats have different body structure than human beings. Its body-kinetics are quite different from us. Yes, muscles are quite strong, but this not the only reason. To know in-depth about the reasons behind the cats’ extreme jumping abilities, you can just refer this online article - "The Glory of the Cat – adidarwinian" at http://adidarwinian.com/the-glory-of-the-cat Along with the flexible spine, strong muscles, flexible joints, they have a peculiar trait known as righting reflex. The same article has information on this peculiar trait. Due to the righting reflex instinct, cats can even survive falls from the high rise buildings.
There is not a linear relationship between the size of a muscle and its power. The cat weighs significantly less, but the decline in muscle power is not identical. If he weighs 20x less than you, but his muscle generate 1/5 as much force, he will still be able to jump way higher than you.
Both the mass of an animal and the amount of energy their muscle can release rapidly are proportional to their volume. The height to which they can jump is proportional to the ratio of the two, so most animals can jump as high as any other to within a small factor. The remaining difference between those who can who can jump about 6' such as your cat or Javier Sotomayor, and yourself, is practice.
Shortwinded answer: Cats are not exceptional jumpers. Their mystique fits a pattern defined by physics and illusion.
Medium-winded answer for cat lovers: I care for cats who began feral and now come and go as they please. My territory-marked (tattered) curtains show exactly how high these cats can reach without jumping. They are amazing, with marvelous agility, senses, personalities and wits. These acrobats cannot, however, jump as high as it looks.
Longwinded . . .
To compare the jumping abilities of humans and cats, and countless other animals, requires more than measuring the altitude of a platform.
Two pertinent factors easy to overlook are:
A. How much did the center of mass rise?
B. Did the maneuver include climbing as well as jumping?
A misleading factor is:
C. How does jump height compare to body size?
Considered in reverse order, comparing a human who can reach 7 feet without jumping to a cat who can reach 3 feet:
C.   How does jump height compare to body size? This is surprisingly irrelevant.
Physics alone determines that jump height is generally independent of body size, down to smaller than a mouse, where limiting factors become the fluid properties of air resistance and viscosity, not the kinetic factors of gravity and musculoskeletal physiology.
Under the neutral assumptions of power laws, a 7/3-as-long human is expected to produce roughly 49/9 ≈ 5.4 times the jumping force of a 3/7-as-long cat. This force acts over a muscle contraction approximately 7/3 as long, delivering ∼343/27 ≈ 13 times the jumping energy.
The weights of this human and cat likewise have somewhere near a 13 :1 ratio, which happens to cancel out the difference in energy, and that is not a coincidence. It is physics. [Somewhat ugly mathematical formulas to be added if requested.]
B.   Did the maneuver include climbing as well as jumping? The cat is quicker than the eye.
A human’s jumping onto a meter-tall platform typically ends with a footed landing. No climbing involved.
When a human gains a three-meters-above-ground tree branch, though, that branch is first grabbed by the hands, followed by a lot of pulling and climbing before the feat is complete.
When a cat bounds upon a two-meter-tall fence, the same sequence of pulling and scrambling occurs, only quicker.
Here are two slow-motion videos. One shows a cat climbing more than jumping. The other shows a cat reaching a high target purely by springing.
Beautiful! And note that the highest leap reaches perhaps 7 feet.
Which leads to . . .
A.   How much did the center of mass rise? Cats have an edge on humans, but not by much.
Cats who can reach 3 feet without jumping and 7 feet on the fly raise their centers of mass by 7−3 = 4 feet. This is impressively comparable to the best human athletes, but this does not reach a separate realm of ability.