Half your age plus seven, and where it came from

The rule gives a lower bound of half your age plus seven and an upper bound of your age minus seven, doubled. At 30 that is 22 to 46; at 40 it is 27 to 66. It has no research behind it and appears in print as early as the nineteenth century as social advice rather than a finding — but it has one property that is genuinely interesting, which is that it is symmetric.

If someone falls inside your range, you fall inside theirs. That is not obvious from the wording and it is exactly true, because the upper bound is the algebraic inverse of the lower one.

Why is the symmetry exact?

Because the two bounds are inverse functions. The lower bound is age ÷ 2 + 7; the upper is (age − 7) × 2. Apply one and then the other and you return to where you started: at 30 the lower bound is 22, and 22’s upper bound is (22 − 7) × 2 = 30.

That mutuality is the only reason the rule is more than an arbitrary line. A rule of thumb that said one thing from one side and another from the other would be describing a preference; this one describes a relation.

How does the range behave with age?

It widens, and faster than most people expect.

The width grows by 1.5 years for every year of age, because the upper bound rises twice as fast as the lower one falls. By 60 the rule has stopped constraining anything in practice, which is a reasonable sign it was written for a much narrower band of life than it is now applied to.

Does an age gap change over time?

No, and this is the part people consistently get wrong. The difference between two birth dates is fixed: someone born in 1990 and someone born in 1994 are always four years apart, whatever ages they happen to be.

What changes is the ratio, and the ratio is what the intuition is actually tracking. A four-year gap is twice the younger person’s lifetime at six and two, and under a tenth of it at fifty and forty-six. The gap is constant and its significance is not, which is why the same number feels enormous in one decade and irrelevant in another.

The half-plus-seven rule is essentially a ratio rule wearing arithmetic clothes — it widens with age because it is quietly tracking that same proportional effect.

Does the same arithmetic work on anything else?

It works on any pair of inverse functions, and that is the general lesson worth taking from it. A rule that maps A to B and B back to A describes a symmetric relation; one that does not is describing a one-sided preference and should be stated as such.

Compound interest has the same shape: the rate that turns 100 into 150 over three years is the inverse of the rate that turns 150 into 100, and the annualising article works through why that matters when comparing returns.

Where does the rule break?

At both ends. Below about 14 the lower bound exceeds the person’s own age, which is nonsense; above about 60 the upper bound exceeds plausible human lifespan, which makes it vacuous.

It also has nothing to say about anything that actually matters — life stage, independence, or whether the two people involved want the same things. It is a heuristic about numbers being applied to something that is not about numbers, and its persistence probably owes more to being easy to compute than to being right.

Is there a better question?

Life stage, which is what the ratio is a crude proxy for. Two people five years apart at 20 and 25 are frequently at very different points — study, first job, financial independence — while the same five years at 45 and 50 usually is not a stage difference at all.

That is why the rule feels roughly sensible in the twenties and stops meaning anything by the fifties. It is tracking a real thing badly, and the real thing stops varying with age long before the formula does.

Questions people ask

Where does the rule come from? It appears in nineteenth-century advice writing and has no identifiable author or study behind it. Attributions circulate freely and none of them checks out.

Is the gap or the ratio the meaningful figure? The ratio, if either. The gap is fixed and the ratio falls steadily, which matches how the significance of a given gap is actually experienced.

Why does the range widen so fast? Because the upper bound doubles a shrinking subtraction while the lower bound halves a growing number. The two move apart at 1.5 years per year of age.

Is there any evidence behind it? None. It is folk arithmetic, and the honest use of it is as a conversation piece rather than a test.

One clean piece of algebra and no evidence at all, which is a fair description of most rules of thumb. The half your age plus seven calculator shows both bounds, the age gap calculator applies it to two real dates, and the age difference calculator gives the constant that underlies all of it.