🛁 Bathtub Calorimeter

How do I use the calculator?

It's meant to be used with an actual bathtub and a thermometer.

The proceedure is simple:

1. Fill a bathtub with room-temperature water (or wait for it to reach room-temperature)
2. Submerge yourself in that water for as long as you can stand it
3. Take the final temperature after you get out
4. Enter those values in the calculator to see how much calories you may have burned

How does it work?

This calculator is inspired by the coffee cup calorimeter.

It works on the principle that the energy in a system can be measured by its rate of heat exchange. This is because all energy eventually becomes heat. Since energy is never created or destroyed, the energy being released from a chemical reaction can be measured by the heat it transferred to its surroundings. The rate of human metabolism can be measured this way.

A Calorie (or kCal) is a measurement of the amount of energy it would take to heat up 1 Liter of water by 1. This means that the energy of the human metabolism can be measured by the rate at which it can heat up a volume of water.

Let's assume we have an average-sized bathtub filled with 136 Liters (~36 gallons) of water. When a person is submerged in the water, we can take the initial temperature of the water (let's say 21.1), measure the final temperature (ex. 23.1), and then multiply this temperature difference of 2 by the water volume to determine the number of calories expended.

When it comes down to measuring how much energy was transfered into the water, the math is really simple. This is a very basic form of direct calorimetry.

How could I be burning so many calories at room temperature?

If you use the calculator with water starting at room temperature or colder, you will discover that you'll have burned more calories than you may have expected.

Although the ambient temperature in your home may not feel cold, this is because air is a poor conductor of heat. Water, on the other hand, is an excellent conductor of heat, so it will draw heat away from you much faster even if it's the same temperature as the air.

Since humans are warm-blooded, our metabolism generates a lot of heat to maintain a healthy core temperature. When the environment we're in is cold, we lose heat faster, thus the metabolism needs to burn more calories faster to maintain that internal temperature. This increase of metabolic rate to generate body heat is called thermogenesis.

This explains why this calculator usually calculates a greater calorie burn than would be predicted by your basal metabolic rate (BMR).

Using the same calculation we talked about earlier, and some additions on top of it, we can not only calculate the total calories burned but also how many extra calories were burned through cold thermogenesis.

The calculator on this page does this by estimating the user's Basal Metabolic Rate, which is the daily rate at which one burns Calories why lying still and doing absolutely nothing. There are devices one can use to determine their metabolic rate, but we will use the Mifflin-St Jeor formula, which is close enough for this purpose.

Here's the formula:

For a biological male, we need to add 5. For a biological female, we subtract 161.

Let's pretend that I, a 32 year old male who is 179 cm tall and weighs 70.3 kg, take a bath in 136 liters of water at 15 for 1 hour, at which the final temperature is 17.5. These are actual values from a cold bath I took in real life.

If we multiply the volume water by the 2.5 temperature difference, we get a total burn of 340 calories.

Now let's estimate my BMR:

Divide the daily BMR by 24 to get the hourly rate and we get 69.4 Calories per hour

To figure out the number of extra calories burned in the cold water experiment, we subtract this from the total calories:

What happens if you use colder or warmer water?

Put simply, the colder the bath, the more calories you will burn.

However, this doesn't mean that colder is better. Water that is too cold can cause hypothermia, a dangerous condition where the body fails to warm itself up. Colder water can also be very uncomfortable.

If you use warmer water, you will notice the measured calorie burn decreases significantly the closer you reach human internal body temperature of 37. This is because the body doesn't have to fight against heat loss. It should be noted that calculation becomes more complicated with warmer water because the rate of heat loss needs to be compensated for.

Why would someone want to do take a cold bath?

Cold-induced thermogenesis can be used to burn calories without exercise. While many might not prefer it as a weight loss method alone, it can be a beneficial therapy on top of diet and exercise. I particularly enjoy watching videos and meditating while burning calories in a cold bath. It's literally "Netflix n' Chill"!

This approach to burning calories may be especially helpful for those with mobility issues or joint pain. Even if one can't fit in a normal tub, similar benefits can be had from cold showers or even turning down your thermostat.

Cold exposure can turn regular body fat into brown adipose tissue, which is fat that is adapted to burn more calories to generate heat.

A cold bath or shower may also be helpful for depression.

How do I measure how much water is in my bathtub?

Someone measuring their calories with this calculator for the first time, in my opinion, should not worry much about the exact volume of water in their tub. You can just assume that a tub holds roughly 136 Liters (36 gallons) at the level one would normally fill it at. If one decides to make a habit out measuring bathtub calories, then a more precise volume is called for.

The only real way to get a measurement of water volume is by using a vessel of a known capacity. When I measured my tub's capacity, I used a standard 5 gallon bucket to fill my tub, counting however many times it took to fill the bucket until the water in the tub got to the right level. I discovered that a 5 gallon bucket actually holds 5.75 gallons, so I had to figure out the height for 5 gallons and mark a line on the interior.

Since then, I've repeated the process but I put a measuring stick in the tub to measure where the water level stood at every time I added a bucketfull. I figured out that there's roughly 6.23 liters present for every vertical centimeter of water, so if I somehow end up with more or less water I just use the measuring stick to get the water volume.

What about a cold shower?

Cold showers may have similar benefits to a cold bath and, theoretically, the calculator can still be used if the bathtub drain is plugged and the water volume is measured. However, cold showers are not as efficient or precise for measurement as a cold bath. A simple cold shower can be an excellent alternative when a bathtub isn't availble or those who can't use a bathtub.