The Navy equation
The 1980s US Navy circumference equation relates body density to a few circumference measurements. In the common form used here it works from the log of (waist minus neck) for men, and (hip plus waist minus neck) for women, against height.
It was fitted on large groups, which is exactly why the page keeps saying "estimate": the equation predicts well for a group and only roughly for any one person in it.
There is more than one published form of the Navy equation, and this version follows the layout most reference tables use. Feeding the same measurements into a slightly different edition can shift the result by a point or two, which is one more reason the page prints a band around the number instead of a confident single digit.
Taking the measurements
The neck is measured just below the larynx, the tape level and snug but not tight. The waist is at the navel for men and the narrowest point for women; the hip is the largest circumference around the buttocks.
The tape is where most of the error lives. A pull a bit looser moves the answer by a point or two, so measure a few times and treat the middle reading as yours. The ±3 points band on the page is the equation being honest before that tape even gets involved.
The direction of the error usually makes sense even when the digit wobbles: a slack tape around the waist runs high and a tight tape around the neck runs low, and either one moves the difference at the heart of the equation. Being deliberate about where the tape sits matters more than chasing the last millimeter.
Measuring yourself is harder than it looks, and the waist is the awkward one. The navel is an easy landmark but it is not the same point on every body, and turning to look in a mirror twists the torso and moves the tape. Measure standing relaxed, tape parallel to the floor, and if a second pair of hands is available, use them for the neck - the one place where you cannot easily see what you are doing.
The bands, which are softer than they look
Charts that call a range "athletes" and the next "fitness" look exact, but the boundaries differ between sources and were never precise lines on a body. The page prints the common version and flags where your estimate falls, so you can see the band rather than feel judged by it.
A percentage does not say where fat sits, and it says nothing about muscle, fitness or what is around the organs. Two people at the same number can be different bodies - which is the point of reading the whole chart, not the line.
The category labels are drawn from the same kind of population data the equation itself comes from, so a high reading is a flag to pay attention to rather than a verdict about anyone. Over months, measured the same way each time, your own trend carries more meaning than the label a single sitting earns.
Different methods disagree
Skin-fold callipers, bioelectrical impedance scales and a DEXA scan will each give a somewhat different number for the same body. None of them is automatically the truth; each measures a proxy for fat and carries its own error.
This is why the page narrows its claim to "the circumference method says" rather than "you are". Tracking your own number over time with the same method is more meaningful than comparing one number across methods.
Because every method measures a proxy and the ranges overlap, the honest takeaway is a position on a scale, not a conclusion. When two methods disagree or the number sits near a boundary, the page’s point is to hold the full picture rather than let a single instrument have the last word.
What the equation is actually doing
Strip the constants away and the male form is a comparison: how large is the waist next to the neck, corrected for height. The female form adds the hip, because the female body stores fat differently and the 1980s fit needed a second girth to hold. Both are the same shape - a difference of circumferences, a logarithm, a division and then the 450 subtraction that turns body density back into a percentage.
The subtraction and the logarithm are why the near-boundary cases behave strangely. When the waist barely exceeds the neck the logarithm approaches zero, the denominator grows, and the percentage dives below zero. A negative body fat is not an extremely lean person; it is two measurements that cannot both be right, which is why the page says so instead of printing the number.
Nothing in the equation knows about muscle, bone, water, or where the fat sits. It is a tape measure standing in for a scan, and it is only as good as the two or three numbers typed into it. That is not a reason to distrust it - it is a reason to read it as a rough position on a chart rather than a measurement of your body.
Where the error actually comes from
Waist and neck enter the male equation with opposite signs, so their errors add rather than cancel: a waist measured too loosely and a neck measured too tightly both push the estimate up. That is why the page asks for a snug tape and repeats the instruction in each field - the technique is doing more work than the arithmetic.
Breathing and time of day matter more than most people expect. A waist taken at the end of a normal exhale can be one or two centimeters smaller than one taken at full inhale, and the same waist measured in the evening is often a centimeter larger than in the morning. Pick one moment - morning, before eating, after the bathroom - and keep it.
Rounding is the smallest of these, but it is visible: the page prints one decimal, and half a centimeter of tape tension moves the answer by roughly a tenth of a point. Reading the second decimal, or comparing two numbers recorded a week apart with different tape tension, is noise wearing the costume of a measurement.
Reading the trend instead of the reading
A careful tape measurement varies by a point or two from day to day on the same body, which is the same size as the change many people hope to see in a fortnight. A single reading therefore says very little about progress; a four-week average of weekly readings says a great deal, because the day-to-day noise averages out while a real change does not.
Keep the conditions fixed - same time of day, same tape, same place on the body, same breath - and write the number down instead of holding it in your head. If the average waist falls while the average percentage falls with it, the equation is agreeing with the tape, which is the most that a circumference method can offer.
And when the number stops being useful, stop taking it. If a measurement starts driving meals, mood or exercise in a way that feels out of proportion, the useful next step is a conversation with a clinician or a dietitian, not a fourth decimal place on a calculator.
Danfio