I climb stairs to work (20 floors) every day . The least amount of work my body is doing my gaining potential energy (P.E) = mgh where m is mass , g is acc. due to gravity and h is height . Assuming every floor is 1 metre high . Mass -> 70kg Work Done Comes out to 70*10*20 = 14000J . 1 calorie = 4.2 Joules . So I am burning somewhere around 3000 calories . Right ? But this calculation seems way off . I do not feel this tired after climbing 20 floors . What am I missing ? Thanks.
14000J = 3346 calories = 3.346 kcal.
Unfortunately, you forget that our calorie measurements are commonly done in kilocalories, so you're off by a factor of 1000.
Other than that, your physics calculation is solid enough. Energy spent during ascension is simply proportional to the change in elevation, or more precicely, change in potential energy.
But I highly doubt that each floor is only 1 meter. That must be wrong.
While Alec is close, there is one factor that is not taken into account. The body is about 25% efficient, so for kcals to joules, it's about a 1:1 conversion ratio.
A typical set of household stairs is 8 feet in height, so to get meters multiply by .305 = 49 meters climbed for 20 flights. Plug that into your equation, and you get 33,476.8 joules of potential energy, which is about how many small calories (defined as the energy needed to raise 1g of water 1 degree C.
So, take your 33,476.8 joules, divide by 1000 to get kilocalories, and you're burning ~ 33.475 or 33.5 food calories to climb 20 flights of stairs.