Heart-Rate Zones: 220 − Age, Karvonen, and Zone 2

Nearly every heart-rate zone you will meet — on a watch face, in a training plan, on a gym poster — is assembled from two ingredients: an estimate of your maximum heart rate, and a rule for turning that estimate into percentages. Both are conventions, and both are routinely mistaken for measurements. This guide takes them apart: where 220 − age comes from and how wide its spread really is, why the Karvonen heart-rate-reserve formula always returns a higher number at the same nominal intensity, and what the 50–85% ladder and the zone 2 band look like in actual beats per minute.

The estimate underneath every zone

Zones are percentages of something, and that something is the maximum heart rate — the highest rate the heart reaches at all-out effort. Establishing it properly means a supervised maximal exercise test, so the conventional 220 − age rule stands in for it. For a 40-year-old it returns 180 bpm, and every boundary below descends from that one number.

Calling that an estimate is not a hedge. The rule is a population average with wide individual spread — being off by 10–15 bpm is common — which is to say the figure it returns is the centre of a distribution of measured maximums, not a prediction about whoever typed the age in. Nothing in the arithmetic can tell how far from that centre a particular person sits, because the arithmetic never received anything except the age.

What follows from that is worth spelling out, because a boundary printed to the beat is easy to read as though its precision were real. A percent-of-max boundary is the estimated maximum multiplied by an intensity fraction and nothing else, so whatever error the estimate carries is multiplied by that same fraction on the way into the boundary — the 85% boundary inherits more of it than the 50% boundary does, in the ratio of the two intensities. The multiplication is exact to the last decimal. The figure it operates on is not, and no amount of exactness downstream puts back information the input never carried.

Two further caveats travel with the convention, both taken up at the end of this guide: it was characterized in adults rather than teenagers, and where a supervised test has produced a measured maximum, that figure always beats the estimate. Neither difficulty is peculiar to heart rate — the BMI guide makes the same argument about a ratio built from two measurements instead of one estimate.

The 50–85% ladder and the gap between its columns

The Target Heart Rate Calculator builds a ladder of 6 intensities from 50% to 85%, and its result box holds one ladder at a time. Enter an age alone and every rung is percent of maximum: the estimated maximum multiplied by the intensity fraction, and nothing else. Add a resting heart rate and the same rungs are recomputed by Karvonen, with the result naming the method that produced them rather than leaving the convention in force to be inferred. The resting rate swaps the ladder over; it does not append a second one to the first.

Seeing both at once therefore means running the engine twice, which is what the table below does at build time: the function that calculator calls, once for a 40-year-old with no resting rate, then again with a resting rate of 55 bpm. The third column is simply the subtraction — how far apart the two conventions land on each rung, in beats.

Two properties of that last column matter more than any single row. It is positive on every rung, so the columns never cross and never meet inside this ladder. And it shrinks on every step upward, from 28 bpm at 50% to 8 bpm at 85%. Neither is a coincidence of the inputs chosen here; both are forced by the algebra in the next section, and both are asserted at build time, so changing the age or the resting rate above would stop the build rather than leave this paragraph describing a table beside it that says otherwise.

Karvonen and the heart-rate reserve

Karvonen's method applies the same intensity percentages to a different quantity. Written out it is (maximum − resting) × intensity + resting. The bracket is the heart-rate reserve: the working range between the rate the heart holds at rest and the rate it reaches at maximum effort. For the 40-year-old above, 180 bpm of estimated maximum less a resting rate of 55 leaves a reserve of 125 beats. The intensity fraction is applied to those 125 beats rather than to the 180, and the resting rate is put back on at the end — without that last step the result would name a position inside the reserve instead of a heart rate.

Why Karvonen always returns the higher number

Both calculator pages state the conclusion. This is the working behind it, one step at a time. Write i for the intensity fraction, so that 70% intensity is i = 0.7.

1. Start from the formula as written: (max − rest) × i + rest.
2. Multiply the bracket out. The i distributes across both terms inside it, leaving i × max − i × rest + rest.
3. The last two terms both contain rest, so collect them: i × max + rest × (1 − i).

Nothing has been approximated — those are the same expression written three ways. But the last one has the percent-of-max figure sitting in plain view as its first term, i × max. Everything Karvonen adds to a plain percentage is therefore the single remaining term, rest × (1 − i): the resting rate, kept back in proportion to however much intensity is left below 100%. Four consequences fall straight out of it, and the table above shows each one happening.

• The term is positive whenever the resting rate is above zero and the intensity below 100%, so Karvonen is not occasionally the higher figure. It is higher by construction, on every rung the ladder prints.
• It is largest where (1 − i) is largest, at the bottom of the ladder — which is why the difference column opens at 28 bpm on the 50% row.
• It shrinks as i climbs and reaches zero only at i = 1, where both conventions return the maximum itself. The ladder stops at 85%, so its last row still shows the two columns 8 bpm apart: they converge, but not inside the printed range.
• At i = 0 the two expressions differ by the whole resting rate. Percent of maximum returns zero, while Karvonen returns the resting rate — one convention measures effort upward from an arithmetic floor the engine never accepts as an input, the other from the resting rate entered.

So a plan quoting "70% intensity" has not yet named a heart rate. It has named a percentage and left the convention implicit, and two plans can both say 70% while meaning figures as far apart as the difference column records for that rung. Nothing on this site splits the difference between them, because the midpoint of two conventions is an answer to neither question. What the two tools do instead is put the convention into their output: the Target Heart Rate Calculator's result names the single method behind the ladder it has just printed, and the Zone 2 Calculator's result carries both bands once a resting rate is entered. The one-rep-max guide describes the same refusal to average, applied to four equations rather than two.

Zone 2, the easy-aerobic band

Zone 2 in the five-zone model is the 60–70% band, the easy aerobic end of the ladder. The Zone 2 Calculator computes it from an age by percent of maximum, and its result carries the Karvonen band alongside as soon as a resting heart rate is entered. Run for the 40-year-old used throughout this guide, the same nominal band comes back as 108–126 bpm under the first convention and as 130–143 bpm under the second at a resting rate of 55.

Those two ranges do not overlap. The lower edge of the Karvonen band sits above the upper edge of the percent-of-max one, so a band quoted with no convention attached is not merely imprecise — the two readings of it can share no beat at all. The reason is already in the expansion: rest × (1 − i) does its heaviest work where i is smallest, and 60–70% is the smallest i on the ladder. That non-overlap is checked against the engine at build time for the inputs used here rather than left standing as prose.

The label is worth separating from the thing it is sometimes used to name. In the five-zone model zone 2 is a percentage band, which is the only reason arithmetic can produce it from an age at all. The same term is also applied to a boundary particular to an individual, which is not derivable from an age and is a different quantity from the percentage band. What the band above reports is the first of those. It is not a measurement of the second.

What the resting rate adds, and what it cannot

Percent of maximum is a function of one variable. Karvonen is a function of two, and the second one arrives from outside the formula rather than out of a subtraction from 220 — which is what makes its bands responsive to something the calendar does not control.

Raise the resting rate from 55 to 75 bpm with the age left at 40, and the zone 2 band that came back as 130–143 bpm returns instead as 138–149 bpm. Both terms of the expansion moved, in opposite directions. The reserve being scaled fell from 125 to 105 beats, so the same 60–70% slice of it covers fewer of them and the band narrows from 13 to 11 bpm. Meanwhile the resting rate added back at the end is larger by the full 20 bpm, so the whole band sits higher. Neither movement is a judgement about the two entries; both are what the expression does when one of its two inputs changes.

What that second input does not do is improve the first. The maximum underneath a Karvonen band is still 220 − age, carrying the same spread it carries anywhere else, and the reserve is that estimate minus an entered number — so the uncertainty in the estimate passes straight through the subtraction and into the reserve. A Karvonen band is more responsive than a percent-of-max band. It is not built on a firmer maximum. The engine accepts resting rates from 30 to 150 bpm and requires the entry to sit below the age-predicted maximum, because a reserve of zero or less leaves no span for the intensity fraction to scale.

Where a formula zone stops carrying information

Three limits are worth stating plainly, because a zone number carries none of them on its face.

• Teenagers. The 220 − age convention was characterized in adults rather than teenagers. The engine accepts an age from 10 upward and will return a full ladder for it, but the ladder it returns for a teenager rests on a rule that was not characterized on them.
• Heart-rate-affecting medication. Medications such as beta blockers make formula zones misleading. The arithmetic is untouched and returns the figures it always would; what changes is whether those figures still stand for intensity. That is a question for a qualified healthcare professional rather than for a calculator.
• A measured maximum. Where a supervised test has established one, it always beats the estimate, and the same intensity percentages can be applied to that figure directly — which takes the largest source of error out of everything above.

Heart rate is also not the only variable a plan can be written against. The Pace Calculator solves for any one of pace, time, and distance given the other two, with no estimated input anywhere in it: every figure it returns descends from numbers that were entered rather than from a rule applied to an age.

Four common misreadings

1. Treating a boundary as a wall. With 10–15 bpm of spread in the maximum underneath it, a boundary printed to the beat is more precise than its own input. Drifting a few beats across such a line is not something the arithmetic can distinguish from the error already inside it.
2. Comparing bands from different conventions. A percent-of-max figure and a Karvonen figure at the same nominal percentage differ by rest × (1 − i), which the difference column above prints rung by rung. Set side by side with no label attached, one effort can look like two.
3. Averaging the two methods. The midpoint of the two bands is not a compromise between them. It is a figure neither convention produced, and it answers neither of the questions they were each answering.
4. Reading a band as a fitness score. Two numbers went into the arithmetic and no observation of anyone did. What comes out is where a rule placed two lines, and a rule that received an age and a resting rate can describe nothing beyond those lines.

Every figure in this guide came out of the same tested functions the two calculators run in the browser, called at build time on the fixed inputs written into the page rather than on any live reading. The relationships claimed between those figures are asserted to the build as well — that the difference column narrows on every step, that the two zone 2 bands do not overlap, that the higher resting rate produces the higher and narrower band — so the prose cannot quietly outlive the arithmetic it describes.

Frequently asked questions

Not medical advice: this guide provides general educational information about published population formulas. It cannot account for your individual health context and must not be used to diagnose or treat any condition — consult a qualified healthcare professional before intensity-based training, particularly with a cardiac condition or heart-rate-affecting medication such as beta blockers. Calculations on this site are processed locally in your browser and never transmitted. See the methodology page.