WHY ARE BELT SIZES DIFFERENT THAN PANT SIZES?

When shopping for a belt, many people get confused by belt sizing.  The common rule of thumb, as well as our sizing guide, says that your belt size is generally 1 - 2 inches larger than the waist size of your pants, but why? The answer lies back in your high school geometry class.

I DON’T CARE ABOUT THE MATH, JUST TELL ME THE ANSWER

The very small thickness of your pants and belt increase the necessary length of the belt to encircle your waist compared to your pants, which just have to go around your skin and underbritches.

EXPLAIN THE GEOMETRY TO ME!

Remember this formula:  c=2πr?  That is the calculation to determine c, the circumference of a circle, where r is the radius of the circle.  Because your belt goes outside of your pants, the radius of you-wearing-pants-and-a-belt is slightly bigger than you-wearing-pants-but-no-belt, so r increases.  Using the formula, for every inch r increases, c, the circumference, increases by 2π inches, or about 6.28 inches!  Based on that, you can see that even a small change in the radius increases the circumference meaningfully.  We estimate that pants and a belt add about ¼” to your “radius”, which is what makes your belt size different than your pant size.

Your waist is more of an elliptical shape than a circular one, but the same principle applies.  If you’re interested, the math is explained in more detail below.

VANITY SIZING

Another sizing issue is the concept of vanity sizing, which is when a company intentionally lists a product as a smaller size to play on people’s egos.  This issue is not unique to belt sizing, but it can also confuse shoppers when comparing their pant and belt sizes.  At Never Back, we don’t use vanity sizing and our belts are true-to-size.  You can take out a tape measure and check for yourself: simply measure from the inner end of the buckle to the middle notch.


THE CALCULATIONS

Let’s take a look at an example.  The formula to estimate the perimeter p of an ellipse is

Where a is half of the width of the ellipse (imagine your waist from side to side) and b is half of the length of the ellipse (your waist from front to back), like this

Next, let’s assume that the average person’s waist is about 1.5 times wider than long, so that

Now let’s look at an example of someone who wears pants with a 34” waist.

Substitute (3/2)b for a

and simplify.

At this point we’ve isolated the variable and can solve for b.  To make things simpler, everything will be converted to decimals here.

which gives us

So those are the values for the segments of the major and minor axis of the ellipse that is you-wearing-pants-but-no-belt.  Next we add in the thickness of the pants and belt, estimated to be ¼”.  Even though this is only a little bit, it makes a noticeable difference in the perimeter.  So our variables a and b are now

Now we’ll use the same original formula to determine this person’s belt size, the perimeter of you-wearing-pants-and-a-belt.

Substitute the values for a, b, and π

and simplify.

So there you have it.  Someone with a pant waist size of 34 inches would have a belt size of between 35 and 36 inches.

Jonathan Woo1 Comment