220 minus your age is a rule of thumb, not a formula
Almost everyone who has been near a treadmill knows the rule: take 220, subtract your age, and that is your maximum heart rate. It is one subtraction, it needs nothing but a birthday, and it is quoted with a confidence that the number itself does not earn.
What the arithmetic actually does
The free Max Heart Rate tool implements exactly that one line. Give it an age of 32 and it computes 220 − 32 = 188 beats per minute, then prints two percentage bands of that figure: sixty to seventy percent, which is 188 × 0.6 = 112.8 rounded to 113 and 188 × 0.7 = 131.6 rounded to 132, and seventy to eighty-five percent, which runs from that same 132 up to 188 × 0.85 = 159.8, rounded to 160.
Notice what happened there. Every one of those bands is a percentage of a single estimated number. Whatever error is in the 188 is carried straight through into all four band endpoints, multiplied by the percentage. The bands look more specific than the estimate they came from, and they cannot be.
It was a description of a population, not a law
The subtraction is a straight line drawn through measurements taken from a lot of different people of a lot of different ages. A straight line through a cloud of points describes the middle of the cloud. It says nothing about how wide the cloud is, and the width is the part that matters when the reader is one person rather than a population.
That width is the reason the rule is called a rule of thumb rather than a formula. Measured maximums for people of the same age differ from one another by an amount large enough that the estimate can sit well away from any particular person's real figure. The tool's own note puts the individual spread at roughly 10 to 20 beats per minute. This page will not improve on that number, because improving on it would mean inventing one.
The later formulas fit better and change nothing about you
Because the fit was known to be rough, other lines have been drawn through larger and better-chosen samples. The most widely quoted is 208 − 0.7 × age. Another in circulation, derived from a sample of women, is 206 − 0.88 × age.
Run all three at the same age of 32 and the disagreement is immediate:
220 − 32 = 188208 − 0.7 × 32 = 208 − 22.4 = 185.6206 − 0.88 × 32 = 206 − 28.16 = 177.84
That is a spread of 188 − 177.84 = 10.16 beats per minute produced entirely by the choice of formula, before a single real heart has been considered.
The two most common lines are also worth comparing across ages, because they cross. Set them equal: 220 − a = 208 − 0.7a gives 12 = 0.3a, so a = 40, where both return 180. Away from forty they pull apart in opposite directions. At twenty, 220 − 20 = 200 against 208 − 14 = 194, a gap of 6. At seventy, 220 − 70 = 150 against 208 − 49 = 159, a gap of 9 the other way.
Nine beats is not a rounding detail once it is multiplied through a band. Seventy percent of 150 is 105; seventy percent of 159 is 111.3. Same person, same age, same percentage, two answers six beats apart, decided by which line somebody typed into the calculator.
Why a better line still cannot tell you your own maximum
This is the point the whole subject turns on. A newer formula fits the population better — the cloud of points sits closer to the line on average. It does not narrow the cloud. Individual variation is a property of people, not of the arithmetic, and no amount of refitting removes it. Swapping 220 − age for 208 − 0.7 × age gets you a better estimate of the average person your age. It gets you no closer to yourself.
The only thing that produces an individual's actual maximum is measuring that individual, which is a physiological test rather than a calculation, and is not something a static page can do or advise about.
How to read the tool's output
Treat the number as a rough scale rather than a threshold. It is the middle of a wide range for people of your age, quoted to the nearest beat because that is what the arithmetic produces, not because the precision is real. The band endpoints are percentages of that same rough figure and inherit all of its uncertainty.
The tool is transparent about this: its own text describes the rule as a rough average with wide individual variation, and it is labelled informational. That is worth taking at face value. A number that comes from your birthday alone knows nothing else about you, and the arithmetic cannot supply what the input never contained.