The real-life physics of Super Mario: How could a portly plumber jump that high?

...and run for miles, punch through brick, live off mushrooms...

Able to jump five times his own height, run at a steady 11mph, and punch through solid brick, Mario is capable of wondrous feats. But what is it about the body of the squat plumber that allows such miracles of athleticism? When you peel back the layers of Nintendo’s infamous character you reveal a medical marvel that’s more likely alien than human.

You really only get a sense of Mario’s abilities once you quantify and compare him to his human counterparts.

So, what makes a Mario? With Super Mario Run now leaping up the iPhone App Store charts, we put the anatomy of the world’s most famous plumber under the microscope.

Measuring-a Mario

Canadian personal trainer Evan Ungar holds the Guinness World Record for ‘Highest Standing Jump’, managing to leap a whopping 5’3” with no run up:

Standing 5’10” tall, Ungar jumped nearly his own body height to attain the record. 

Mario does a little better.

In the original Super Mario Brothers (where I’ll be taking all my measurements from) he is able to make a standing jump to five times his own body height:

According to an official Nintendo statue, Mario stands 5’1” tall, meaning with each bound Mario is leaping more than 25’ into the air, or 7.75m. Nearly five times Ungar’s record.

When it comes to running, knowing that Mario is 5’1” tall means we can take his vertical height in the game and use him as a ruler to mark out a horizontal distance and time how long it takes him to run it. 

From there we can extrapolate how far he could travel in a mile and work out his top speed. Anyone who’s played these early Mario games will know that once the man gets up to speed he won’t slow down until he hits a brick wall, so we can be confident he’ll go at a steady pace:

It takes Mario three seconds to cover a distance equivalent to 15m. Over an hour, at that speed, Mario would cover 18km, or 11.2 miles. Compared to Usain Bolt’s 9.58 second 100m dash, which works out at 27.44mph, Mario is practically jogging. However, when you look at Dennis Kimetto’s marathon record of 2:02:57, with an average speed of 12.7mph, you can see the stout Italian is holding his own, especially for someone who’s been at this for 35 years.

It’s the punching through brick that sees Mario at his most impressive, though. While you may have seen videos of martial arts specialists punching through concrete, it will usually be an individual slab, or a stack of them separated by pencils. In Mario the hovering blocks are 4 layers thick, with no obvious gaps between the rows:

Yet, despite this, he is able to shatter them in a single hit.

According to a paper on the Mechanical Properties of Brick Masonry (fascinating late night reading, I’ll tell you), a stack of four high strength bricks can withstand 3,750psi of pressure before cracking, or, 16,681 newtons.

Now, when martial artists punch blocks, they do so at about 24mph, producing 3,000 newtons of force. A great PBS video on the physics of brick breaking demonstrates how that’s enough force to break a concrete block. For Mario to crack a stack of four, he has to produce more than five times that.

Of course, whereas a martial artist is producing all this force from a punch, Mario is producing that 16,681 newtons of force from his jump.

Knowing how much force he requires to impact the bricks to smash them and the velocity of his jump, we can hazard a guess at Mario’s body mass. Consider this equation:

If force equals 16,681, velocity is 7.75m/s, and the time of contact is a single frame, or -.03 seconds, Mario’s mass must be just 33.3kg. That’s just over 5st.

It’s at this point I should probably say that physicists have worked out that the Mario games don’t play by Earth gravity.

In a paper titled ‘Acceleration Due to Gravity: Super Mario Brothers’, a group of students at  Midwood High School at Brooklyn College calculated from the speed at which Mario fell to the ground that he is acting under 9.31g, more than nine times greater than the Earth standard. So while he has a body mass of 33.3kg, on his world, he weighs 310kg, or a more portly 48st.

So, Mario, a 5’1” man is able to run at 11.2mph, jump more than 25 feet, and punch through stacks of four bricks, all while weighing almost 48st.
What sort of body would allow for these feats?

Making-a Mario

The first thing to do is try and work out how much of Mario is made up of muscle. We know his body mass and his height, which is a start, especially if we assume his body is proportioned much like an average person’s.

Back in July, 2000 there was an in-depth study in the Journal of Applied Physiology, that studied 468 different men and women to work out the average skeletal muscle mass of a person depending on their age and gender. Skeletal muscle is the meat that pulls on your bones, moving your joints and providing power to all your activities. It’s there we’ll be able to work out how Mario can jump so high.

The first hitch when placing Mario on this chart is working out how old he is. According to his bio in Super Smash Bros Melee he was 26 in 2002, which would mean he was born in 1976, just five years before his first appearance in the original Donkey Kong, and 40 years old today. 

I think Mario’s a liar.

For one thing, you have to take into account that in his first appearance the man is a qualified plumber. The Chartered Institute of Plumbing and Heating Engineering requires apprentices be at least 16 years old before they start the four years of training it takes to be qualified, meaning in 1981, when he appears in Donkey Kong, he has to be at least 20. I’ll give Mario the benefit of the doubt and say he was born in 1961, making him 55 today.

In that bracket, according to the study, around 35% of his body mass is made up of skeletal muscle. This means that Mario only has 11.7kg, just over 1.8st, of muscle to achieve the feats that he does.

Let’s look again at that jump and the amount of energy it would take to propel a 33kg object 25’ into the air under more than nine times Earth gravity. Energy = mass x gravity x height. So we’re talking about muscles that use 23,563 joules in every jump. As it takes a single second to do this we know that power generated by the muscles is exactly the same.

To put this in perspective, according to Marks’ Standard Handbook for Mechanical Engineers, “a labourer over the course of an 8-hour day can sustain an average output of about 75 watts”. In a single jump Mario uses the same amount of power as a person labouring for five minutes.

Clearly, Mario must have some serious muscles but from the outside he doesn’t appear bulky at all. His arms and legs are slim, his chest is rounded rather than hard.

There is a very rare condition that could go a small way to explaining this: myostatin-related muscle hypertrophy. This condition causes people to have twice as much muscle mass as your average human. You might have seen the World’s Strongest Toddler Documentary that followed Liam Hoekstra, a three-year-old with the condition:

These denser muscles are able to produce twice as much power while taking up half the space.

Even with double the strength of your average man, we’re still several orders of magnitude off what he’d need to produce the power and strength he displays in Super Mario World.

It gets even stranger when you think about Mario’s bones. While Mario is relatively light mass-wise, he is doing all this jumping and punching on a world where he weighs 48st. The constant strain on his joints and bones must be awful.

There have been many studies into the ways we negate the force of an impact of a fall, like how parachutists will roll as soon as they hit the ground or how gymnasts cushion the blow with ankle and hip movements. We don’t need to look at those, though, because Mario lands with both feet together and his legs straight, like every health and safety manual ever has said not to do.

If only there were a study where scientists made people jump from a height without bending their legs, just to see what damage it would do…

Oh, science, you do spoil us.

Back in 2013, a group in Sao Paulo had subjects wear a rig that locked their knees in place and made them jump off a platform to measure the force their knees underwent. The study found that subjects with an average weight of 64kg, jumping from 75cm, put their knees under 6,100N of force.

Mario is nearly six times that weight on his planet and falling from 10 times higher. According to biomedical engineer Cindy Bir at Wayne State University in Detroit in an interview with Livescience, a sharp blow delivering 4000 newtons of force has a 25% chance to crack your femur. Mario is receiving many times that impact with every jump. It’s a wonder his legs don’t snap into a thousand pieces with every landing.

There is actually a real world reason that can explain why Mario isn’t forever in crutches - it could be that he has a mutated LRP5 protein that’s led to increased bone density. According to an article in The Scientist, one case of the mutation was discovered after a person walked away from a severe car crash without a single broken bone. 

Another was found after doctors failed multiple times to fit a patient with a hip replacement, the problem they had was that they couldn’t get the screws for the prosthesis to penetrate his bones. A side effect for those with the mutation is that, with such dense bones, they can’t swim as easily, finding their bodies less buoyant than other people. Considering the way Mario sinks in the undersea levels, this suggests it may be the cause.

Looking beyond his muscles and bones, Mario’s organs are put under extreme stress by his antics. His brain, for instance, is being subjected to the same extreme G-forces as a fighter pilot every time he jumps off a high pile of blocks. He is in danger of passing out as he falls because of the blood that will be pulled up into the blood vessels in his skull. When he hits the ground the sudden deceleration could cause his brain to bruise as it moves inside the skull. Mario must have a thicker meringes layer than the average person, providing more cushioning material inside the skull to prevent it from bruising on impact.

Then there’s his heart. Mario’s blood pressure must be enormous. Not only is he living on a world with more than nine times our gravity, which will put strain on his vascular system just to transport the blood around the body, but, with his denser than normal muscles expelling so much energy with every jump, his heart will need to be working harder to make sure they’re supplied with freshly oxygenated blood. If we sliced the man open his heart and lungs would very likely be both larger and made of denser tissue.

A side effect of all these larger, better-performing muscles and organs is that Mario’s body burns through a lot more energy. As well as his basic calorie spend, each one of his jumps burns at least five calories. Not much in one go but every level sees Mario bounding about like a rabbit, racking up hundreds of calories. 

Then there’s the fact he runs everywhere, all while weighing 48st, which adds a greater effort to all his movements. While likely a very healthy man, he’ll need to be taking in thousands of extra calories every day. All on a world where the only food he can find is mushrooms.

I’m sure Nintendo never put a great deal of thought into the reality of Mario but the creature they’ve built is fascinating. If he played by the same rules as normal people, he’d be dead many times over. His body would be too heavy for life in a world with nine times the gravity, with his muscles, organs, and bones being ill-equipped to function under the intense pressure.

There are lots of questions about Mario but the numbers we can work out from the way he behaves in-game add up to make a man very differently built from your average plumber.