Introduction: Measure Body Fat % Via Underwater Weighing

About: I'm just your average 20-something working in the real-world as an engineer in the nuclear industry. I have a B.S. in Engineering Science & Mechanics and an M.S. in Engineering Science. I function as a mechan…

Obesity is currently one of the largest health problems in America.  Numerous studies positively link obesity with diabetes, heart disease, acid reflux, uncomfortable plane rides, being shunned from amusement park rides, etc. Normally the Body Mass Index (BMI) is used to determine if you are a healthy weight, but the BMI is really an inadequate system.  It is not very difficult for someone to fall into the overweight category of the BMI because they have a higher than normal ratio of muscle to fat.

Body composition or your body fat percentage is a much more reliable indicator of health and fitness, but it can be difficult to measure.  The three most common methods of calculating body fat % are:
-hydrostatic (underwater) weighing
-skinfold (caliper) measurements
-Bioelectrical impedance

All of these methods have their inherent strengths and weaknesses, but underwater weighing is the "gold standard" for accuracy.  If you want to achieve the best possible accuracy you would need a much more elaborate set-up, but in this instructable I will show you how you can estimate your body fat % with fairly good accuracy using nothing but a spring-based bathroom scaleand this instructable!

NOTE: I have a tendency to try and convey to much information.  If you just want the big picture/to give this a quick try, read only what's written under "Essential Info".  If you would like to improve accuracy and learn a bit check out what's written under "Additional Info".

Step 1: Theory

Essential Info

The two equations in this picture are the equations that will be used to calculate your body composition.  The steps in this instructable will show you how to estimate or calculate the different variables in the equations.  If seeing these equations gives you nightmares about high school/college math classes, have no fear.  Step 7 has a spreadsheet which will automatically do all the calculations necessary, and all you have to do is plug in the appropriate figures: Gender, Dry Weight, Underwater Weight, Age and Height (or Vital Capacity), and Water Temperature (or density of the pool water).
I have also attached the spreadsheet to this step if you would like to open it up and play around with it as you go through; however, more explanation of how it works will be in Step 7.

Additional Info

This test is really to determine the density of an individuals body.  By plugging the density of our body into a well studied equation (Siri Equation) we can determine an individuals body composition (%BF).  You can determine our density (as I will show you in the following steps) by taking a ratio of our weight in the air to our weight underwater.  The difference in our weights will result from what is known as buoyancy force.  The buoyancy force is related to our density through Archimedes' Principle. 

According to Archimedes' Principle things with a larger density than water will sink (in water), that with a smaller density than water will float, and things with the same density as water are what's known as neutrally buoyant (aka it will hover at any depth until you give it a push up or down); 
FUN FACT: NASA has what's known as a neutral buoyancy lab where astronauts train for space missions because neutral buoyancy is very much like zero gravity...but anyway.

Unlike a piece of metal, out bodies are composed of different materials with different densities.  Luckily our bodies are composed primarily of water, and thus the majority of our components (skin and organs) have a density very similar to that of water and won't contribute to our weight underwater.  The parts of our body that have significantly different densities than water are our muscles, fat, bones, lungs, and GI tract.  

These parts of our body contribute to our underwater weight (UWW) by either helping us to sink or float, and their densities are approximately as follows: fat floats (density approximately 0.9 g/cc), muscles sinks (1.1 g/cc), and the air inside out lungs and GI tract floats (0.0012 g/cc).  The volume of a human being's GI tract is relatively small and constant across most sized people, so this factor is built right into the density calculation.  After exhaling all of the air we can from our lungs they are not completely empty; what's left is known as the Residual Volume (RV) of our lungs.  Our individual RV can be estimated based on size, age, and sex; this information is generally known to an individual and the attached spreadsheet will make it easy for you to approximate this.  Alternatively you could estimate your RV as a certain percentage (contained in the spreadsheet) of your Vital Capacity (the maximum amount of air you can exhale in one breath) which I will show you how to measure in Step 6.

After accounting for the buoyancy of our lungs and GI tract, the only factors left are the amount of fat, bone, and muscle we have.  We can then solve for them in terms of a ratio of the mass of fat we have, to the amount of fat-free mass we have (muscle and bones); this ratio is more commonly referred to as our body composition or body fat percentage (BF%).

This is a relatively brief overview of the science behind this process.  If you are interested in a more detailed explanation of the process using a professional set-up check out the following link (it's a brilliant explanation actually):

A lot more information about different methods of calculating body fat % as well as the sources for the equations I'm using came from the following source:

You can also always check out Wikipedia:

Step 2: Materials

Essential Info
All you really need to complete this instructable is a Spring-based scale, a pool of water large enough to submerge your whole body, and a method of reading the scale (most likely a friend wearing a pair of goggles).  Below is a lot more information about why you need certain equipment and how your results could be impacted by the way you perform the measurements.

I keep saying a "spring-based scale". The reason is because a spring based scale gives you a reading of your weight based on the deformation of a spring. This type of scale will not be affected by the water pressure because it is an open system. If you try to seal an electronic one in a plastic bag it be affected by the water pressure and could break. If you try to use an electronic one underwater, it will likely short out. I had some ideas after the fact about how I could make this more accurate; those will be covered in the last step.

Additional Info

As with most projects, your results will depend a lot on the tools that you have available to you.  The more accurate all of your equipment is (a graduated cylinder vs. a kitchen measuring cup), the more accurate your final results will be.  
That being said, the only thing your really need to complete this instructable is a spring-based scale and a pool.  
(You might be able to use a balance based scale, but they are larger, slower, and good luck finding someone who you can convince to let you lower 4 foot tall, 40 pound piece of equipment into their pool.)

 The measuring cup and the digital scale are for measuring the density of the pool water I used, and I will discuss other options for that in the next step.

The second picture is of a bottle, a sink, and a plastic tube.  This is for measuring the Functional (Vital) Capacity of your lungs which can be related to your Residual Capacity; this equipment is also not necessary and will be discussed further in step 6.

Step 3: Calculate the Density of Your Water

Essential Info

Estimate or measure the temperature of the water in your pool.  Record that in the spreadsheet, and it will automatically estimate the density of pure water based on that temperature.  This method does have it's drawbacks, so read the addition info section if you get a chance.

Additional Info

To calculate the density of your pool water you need to measure out a known amount of pool water in milliliters (write that down) and weigh it in grams (write that down); be sure to either tare your scale or subtract out the weight of your container.  Now divide the mass (weight) by the volume and you have the density in grams/ml or grams/cubic centimeter(cc).  This will be done for you in the spreadsheet.

I would recommend, if possible, measuring the density of your pool water because it can vary quite a bit based on temperature and what type of pool chemicals you use (chlorine or salt water). Option 1 neglects the effects of whatever pool chemicals are used and introduces some error. However, in my case, I measured the density of my pool water to be 0.983 g/cc which was lower than pure water should have been at that temperature. This isn't possible, so the only explanation is that there was too much error in my scale and measuring cup. Instead I used 0.997 g/cc (calculated on my spreadsheet) because a difference of 0.014 g/cc in density makes a huge difference in the end BF% calculation.
In summary, when I say measure the density if possible, that means measure the density only if you have a graduated cylinder that can measure at least 100ml and a calibrated scale that is accurate to the 0.1 grams; otherwise you won't have enough accuracy/significant figures to offset the potential difference the chemicals would make.

Step 4: Measure Your Dry Weight

Essential Info

Weigh yourself wearing as little as possible on a hard surface out of the water.

Additional Info

Some tips:
-the most accurate time to weigh yourself is in the morning after you go to the bathroom, but before you eat.
-you should record your dry weight and your wet weight as close together as possible and in that order; don't measure your dry weight while soaking wet.
-Make sure your scale is on a hard level surface (even a slight incline will give you incorrect results)
-You should be naked. If not possible, the less clothes the better.
-The weight a spring scale gives can change if you repeatedly load and unload it.  This is because various mechanical factors; before taking your measurement lightly bounce up and down on the scale a few times to ensure that there are no sticking points in the mechanism (this could be especially true if you have used this in the pool before and the scale has experienced some corrosion) .  Now, if possible, calibrate the scale to the weight of a known object; then record your dry weight.

Step 5: Measure Your Wet Weight

Essential Info

Time for the trickiest and most crucial part of all of this, so you might want to consider reading the additional info here.
 1.  Get into the water wearing as little clothing as possible with the scale.
2.  Shake/turn the scale around in every direction to ensure you release any trapped air.
3.  Fully submerge yourself and hang out in the water for a bit.  Rub your hands through your hair and make sure you shake any trapped air bubbles free from your clothing, hair, body hair, etc.
4.  Time to take a measurement.  As the pictures indicate you can do this in either deep or shallow water, but the important thing is that when the measurement is taken every inch of your body is full submerged and you have exhaled all of your air.  You can do this seated or standing, but make sure you don't interfere with the motion of the scale platform.

Additional Info

Now for some Tips on making this process easier and more accurate.

Consider that even a very large person (250 lbs) with very low body fat % (7%) won't weigh much more than 16 lbs underwater (I weighed about 9 lbs); this means that it will be difficult to balance motionless on the platform in the limited amount of time you will have (cuz you exhaled all of your air) with even the most subtle underwater currents or misaligned body position.  If you are a smaller female you could end up having an UWW 1 pound or less.  For that reason I recommend...
-Do this in shallow water with a substantial weight belt on (or you could hold a large rock or 25 lb weight plate).  That way you won't have to go very far to submerge your head or to stand up and get air.  You will just have to place the weight belt on the scale underwater and subtract it's underwater weight from the underwater weight you recorded while wearing it to get your true underwater weight.
-A lot of pools have subtly sloped bottoms, do this in the most level region possible; like the bottom of the deep end, near the start of the shallow end, or on the bottom step to get in.
-Have a partner read the measurement on the scale so you don't have to wear goggles which will contribute to error in your reading.
-Measure your weight as many times as possible (like 10 times) and once you begin getting consistent readings average your 3 or so heaviest readings. (but be sure the needle is always motionless when the reading is taken!)  This is because it's tough at first to get used to balancing motionless on the scale without oxygen, and most people are hesitant to expel all their air (but the more you exhale the heavier your reading will be and the lower your body fat %).
-Exhale all your air before going underwater; it makes things less chaotic than blowing a ton of bubbles in your face while trying to sit still.  Plus it's easier to see (from the bubbles) if you can exhale anymore air once your on the scale if you only have a little bit left in you.

Step 6: Estimate or Calculate the Residual Volume of Air in Your Lungs

Essential Info

AKA, the easy way
Plug your gender, age, and height into the spreadsheet and it will spit out your RV in the Intermediate Calculations section.

Additional Info

The Harder Way (still easy)
The pictures give you a sequence of events, but I'll detail it step by step here.
1.  Obtain a large container with a semi-tight lid.  Aim for something at least 5 Liters or 1.5 gallons; otherwise you may need to use multiple containers which adds complexity and error.
2.  Fill the sink, tub, or submerge the whole thing all the way in a pool
3.  Flip the container over so the opening is facing down under the water.  If you can't get any last stubborn air bubbles out use the tube to suck them out.
4.  Situate one end of the tube above the water to put your mouth on.  Put the other end of the tube under the opening of the container.
5.  Take several deep breaths and on the last one draw and hold as much air as you can.  Exhale every last bit you physically can through the tube and into the container.  Make sure the open end of the tube stays under/inside the container the whole time.  A nose clip could help to ensure that you don't cheat and take any extra air in through your nose when your forcing out the last bit of air from your lungs.
6.  You now have a bubble the size of your Vital Capacity (VC) trapped in the container.
7.  With the open end of the container underwater, put the lid on your container.
8.  Quickly flip the container over so that the water left from the opening of the container to the bottom of your VC bubble stays inside the container.
9.  Fill a measuring cup with a known amount of water and fill the container to the brim with water.  Keep track of how much water you add to the jar.
10.  The volume of water that you added to the container to fill it to the brim is the Volume of your VC.  Enter this value into the spreadsheet in either liters or US fluid ounces.

NOTE:  I was surprised to find that my VC was surprisingly low; about 1.3 liters smaller than the average man.  This resulted in a RC about 0.5 liters lower than the equation estimates.  I may need to seek the advice of a doctor if some other people don't encounter a similar issue.  In the end it only affects the calculation by about 3.6% which is within reason for this method.

Step 7: Calculate Body Fat %

Essential Info

The first picture below is a screen shot of the spreadsheet which will calculate your BF% for you.  Go over the picture notes on it from top to bottom to understand how you must put in the information you acquired throughout this instructable to get your results.

Additional Info

I reproduced the picture from the first slide here to show you all of the variables that go into the calculation.  I have told you about a few different methods of calculating/estimating some of these variables.  Play around with them on the spreadsheet and see how it affects your results.

The spreadsheet has 3 tabs or work sheets.  The Control (green) tab is write protected on all but the necessary input cells so you can mess around with different inputs without worrying about screwing up the formulas.  The other two tabs are places where you can play with the different equations I used to come up with error and the water density interpolation.  You can also see my results for two different sets of inputs and the impact they had on the final calculation as an example.

I made it so that you could put in either English or SI units for any one of the variables, but don't try to put in both; I'm not sure what result it will have, but it will likely be incorrect.

Step 8: Verify and Interpret Results

Essential Info

The first images are of norm charts according to the American College of Sports Medicine.  You can think of it like grades in school: everyone should shoot for an A (90%), but a lot of people are fine just by barely passing with a D (60%).  For example, I am 24 years old with approximately 10% BF.  This means that I am in between the 70th and 80th percentile, so call it a 75%; not bad but I'm still shootin' for the A...

Additional Info

Plus some general facts, Women require and naturally store more fat than men.  They tend to store it in their hips and legs while men store it in the midsection and chest; consequently this contributes to higher instances of heart disease in men.

But lets get down to whats really important...or what most people are programmed to care about (whether they know it or not): looks.
The distribution of fat on your body is hard coded into your DNA.  One man might have a sick Six-pack at 7% BF while another can have it at 9%.  BUT THE ONLY WAY TO HAVE A SIX-PACK IS WITH A LOW BF%!!! So just go ahead and shoot for the 90th percentile; notice how women can have a six-pack at 14.5% BF while men have to go to 7.1%...good times, haha.

The last picture is of a little study I did of the impact of the different variables on the spreadsheet.  First I looked at the impact each variable would have on your final BF% calculation if your measurement was off by 5%.  This could result in some tremendous error because some of the numbers are naturally small; like your UWW compared to your BW.  So then I changed that to some likely errors you might encounter with certain everyday measuring instruments: like a bathroom scale, thermometer, or measuring cup. 
It ended up not being too bad, with the underwater weight (UWW) probably being your most critical step SO BE CAREFUL THERE.
In the end the total error was approximately 20% which at my measurement of 10% BF amounts to a +/-2% BF.  This is actually a great error for something as simple as a bathroom scale; also notice it's enough to tell you whether you inside a given percentile on the norm chart.
For those with higher BF% will have higher error ranges, +/-5% BF is still way better than a cheap Bioelectrical Impedance bathroom scale or the caliper method (unless it's done by a professional).
Consequently I had my BF% measured by a certified trainer at my gym using the caliper method and it came out to be 9.5%, so I am pretty confident in this method and my results!

Step 9: Summary and Potential Improvements

Accuracy could be further improved not only by using a weight/weight belt, but also a more sensitive scale.  Below is a crude sketch of how you could use a diving board and some other more sensitive scales to get a better reading of your underwater weight.  This method would also make remaining motionless and repeating the UWW measurement easier.

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