HOW MANY PEOPLE HAVE LIVED ON THE EARTH?

NATHAN KEYFITZ·

RESUMENUna f6rmula simple es propuesia para estimar el numero de personas que han vivido. Em­

pleando suposiciones que parecen ser razonables, se obtuvo un estimativo de 69 billiones-para1960. La poblacion actual del mundo es alrededor del 4% de eete numero.

SUMMARYA simple formula is proposed for estimating the number of people who have ever lived. Using

assumptions that seem reasonable, an estimate of 69 billion (1960) is obtained. The present worldpopulation is about 4 percent of this number.

The number of people who have livedon the earth is found from a single formu­la, which may be applied to the successiveintervals between (guessed) populationnumbers.

If at time t1 the population was nl, andat time t2 (t2 > t l ) the population was n2,

then the annual rate of growth r satisfies

n2 = eT(I,-I.)

nl

or

If during the interval from time tl to t2

the rate of increase was r, then at anygiven time the population was nleT( t- t. )

and the total person-years lived were• University of Chicago.

Substituting the value of r from equa­tion (1) in equation (2) gives for the per­son-years lived the very simple result

n2 - nl:= (n2 - nl)(t2 - tt> (3 )r in n2 -In nl

To proceed from person-years to per­sons, we divide by the expectation of life,which may be taken as about 25 years.

Applying this to the set of data belowgives for the several intervals the person­years of the last column, which add to1.72 X 1012 man-years, or, on dividing by25 as the average expectation of life, to69 billion. On this total the 3 billion nowalive would be about 4 percent of thenumber who ever lived.

The result is not very sensitive to the

CALCULATION OF PERSON-YEARS LIVED, WHEN PERIOD Is INFOUR INTERVALS, AND IN ONE INTERVAL

t by Calendar (n,-nl)(h-h)years of the n In nChristian Era In n,-In nl

-1,000,000 2 0.6980.34XlOIS

-5,000 5,000,000 15.425 .31 X 1012

0 250,000,000 19.337.63XI01s

1650 545,000,000 20.1160.45 X 1Q12

1960 3,000,000,000 21.822

1. 72XI012

-1,000,000 2 0.698142 X 1012

3,000,000,000 21.822..

581

582 DEMOGRAPHY

expectation of life we assume, between 20and 35 years, which seems to me to coverthe range of possibilities. It is very sensi­tive, however, to the way in which wedivide the total time to fit the successivegeometric curves implicit in the method.If, for instance, we do not divide the in­terval at all but simply take it that twopeople living a million years ago havenow increased to 3 billion, then the num­ber of man-years is 142 X 1012, about 80times as many as we found.

In reading Professor Winkler's article,1

I do not believe that he was aware of this.The point probably makes my own resultsomewhat high; if I had taken morepoints of time, I could well have foundfewer people. 1 would also have foundsomewhat fewer people (half as manybefore 1650) if I had assumed that therace started half a million years agorather than a million.

1 Wilhelm Winkler, "Wieviele Menschen ha­ben bisher auf der Erde gelebt?" lnw-natitmalPopulatioa Conference, Vienna 1959 (Vienna:Union Internationale pour l'Etude Scientifiquede la Population, 1959), pp. 73-76.