Some Math for You

luisprieb

For all of those out there in their second half of their weight loss journey, many of you will notice that your weight loss speed will drop, but don't worry! Math is here to help you. It turns out that the smaller you are, the less fat you need to lose to make a noticeable change. Now, I'm sure all of you will say "Oh, I already knew that!" but I'm going to show you why this is true and how much improvement there really is.

First of all, for simplification, I'm going to represent the mass of a man with a sphere (this is not so off from the shape people take when they are heavier. Of course, as they lose shape, they approach the characteristic shape of their body, but bear with me with this representation).

Ok, so let's assume a sphere with a radius of 8 inches. This would produce a volume of about 2144.6606 (V=(4/3)(pi)r^3). The density of fat is about 0.03316 pounds per inch cubed. So lets say you lose 20 pounds of fat. ((1/0.03316)*20)That would equal a volume loss of 603.048 inches cubed ((1/0.03316)*20). That means the new volume is about 1541.613 inches cubed. Now, if you recalculate the radius from that (cuberoot(1541.613*(3/(4pi)))). The new radius would be 7.166309207 in. That would mean a loss of 0.833690793in. in radius. Now, if you lose another 20 pounds, lets see what happens. The new volume is 1541.613. Since you are still loosing the same amount of fat, the volume loss would be another 603.048. Thus, the new volume would be 938.5645206. If you recalculate the radius from that you would get 6.0738 inches. That would be a loss of about 1.0925 inches now! If you did this a third time you would find that the new radius loss would be of 1.763 inches! That's more than twice the original radius loss. We compare radii because I believe loss in radii is what people really see from weight loss (waist circumference is directly proportional to the radius (2(pi)r), so that's the connection there).

Now, there is something else as well! This has to do with perception. If you compared yourself losing 1 inch at your original weight and losing 1 inch at the second, the inch would be much more noticeable at the second instance. That is due to the fact that 1 inch represents a greater percentage of the total radius. At 8 inches, 1 inch represents 12.5% in radius loss, while at 7.166, 1 inch represents a 14% radius loss.

From these mathematical notions we can see how even though the rate at which you lose weight is slower, the rate at which you look better may be faster! So stay motivated and keep going so that that rate increases and you see some serious radius loss!

PS: Keep in mind a sphere is a very rough representation of the human body, so changes may not be as drastic as shown here, but the principle holds! The more weight you lose, that more size you will lose with the same weight loss.