# Why is walking up stairs harder than walking normally?

I must admit, I'm pretty new to studying physics and I know this is a simple concept but I'm having difficulty understanding it. I've tried reading the questions here but I just need a little bit of help and a push in the right direction. So my question is:

Why is walking up stairs harder than walking normally? Could you give me an equation and/or comparison between the two?

• each time you go up you need extra force to raise the body up against gravity. For each vertical distance h you need an extra energy equal to $mgh$ – user83548 Nov 5 '15 at 15:42
• To walk, you just have to lift one foot barely above the ground, tilt forward, and land on the foot. To climb a stair, you have to lift a foot to the next step, and then that leg has to lift your entire body up so that your other foot can be lifted. – mbeckish Nov 5 '15 at 15:44
• Warning: The accepted answer is wrong. – user4552 Jan 12 '19 at 15:20
• Different muscles are involved. When climbing stairs, your glutes and quads work hard. When walking, your psoas swings the leg forward, and landing is not as much work. – Bert Barrois Jan 12 '19 at 17:06

You have to lift up your body mass under the presence of gravity, so you have to overcome the force of gravity.

While climbing up the stairs you have to put force on ground, more then your weight, which put same force but in opposite direction i.e. on you.

Suppose your mass is $m$, then while climbing up, if you resolve the forces then,

$$N-mg=ma\text{, } N=-F$$

$F$ is the force you apply on the stair and $N$ is the force exerted by the stair on you. Newtons' third law, or the magnitude of $N$ is equal to that of $F$

So in $y$-direction, if you want to move up then the $N$ should be more then your weight ($mg$) and according to this equation you will have some acceleration.

However when you are walking (moving along x-axis) $N$ goes equal to your weight ($mg$) and both balance each other along $y$-axis so you have to only care about exerting force to move along $x$-axis.

That's why walking up stairs harder than walking normally.

• Thanks, that makes sense. I appreciate you taking the time to write that. – FirstLegion Nov 5 '15 at 15:51
• This is wrong. You don't need a nonzero vertical acceleration in order to move upwards. – user4552 Jan 12 '19 at 15:19

When moving up you are pushing yourself in the opposite direction of the force of gravity. Therefore you do a positive work which is approximately $mgh$ ($h$ is the height of the step). While coming down gravity will do the same work for you.

It is more difficult because it requires more energy. Once you are up to speed, walking on a flat surface requires only enough energy to overcome friction, air resistance, and the energy to move your legs. Walking up stairs is more difficult because you additionally have to provide the energy to lift your body weight up the stairs. It's the difference between pushing a car and trying to lift it in the air. The relevant equation relates the mass, $m$, the height it is lifted, $h$, and the acceleration due to gravity $g=9.81m/s$ to the gravitational potential energy, $U$. $$U=mgh$$