This document describes 7 common methods for estimating and projecting population sizes: (1) inflow-outflow, (2) natural increase, (3) rate of natural increase, (4) arithmetic, (5) relative increase, (6) geometric, and (7) exponential. These methods use variables like birth rates, death rates, and growth rates to calculate future population estimates. The document also provides examples of applying these methods and notes that the world population doubled around every 25 years between 1750 and 1975.

1. Population Estimation and ProjectionPopulation Estimation and Projection

2. (I) Methods(I) Methods
• 1. Inflow outflow method1. Inflow outflow method
• 2. Natural increase2. Natural increase
• 3. Rate of natural increase3. Rate of natural increase
• 4. Arithmetic method4. Arithmetic method
• 5. Relative increase in population5. Relative increase in population
• 6. Geometric method6. Geometric method
• 7. Exponential method7. Exponential method
MnemonicMnemonic →→ (RAINGER)(RAINGER)

3. • 1. Inflow outflow method1. Inflow outflow method
Pt = Po + (B - D) + (I – O)Pt = Po + (B - D) + (I – O)
Pt = Population count at a later time (t)Pt = Population count at a later time (t)
Po = Population count at an earlier time (o)Po = Population count at an earlier time (o)
B = Number of birth between time t and oB = Number of birth between time t and o
D = Number of death between time t and oD = Number of death between time t and o
I = Number of immigrant between time t and oI = Number of immigrant between time t and o
O = Number of emigrant between time t and oO = Number of emigrant between time t and o

4. • 2. Natural increase:2. Natural increase:
Difference between numbers of birth and deathDifference between numbers of birth and death
3. Rate of natural increase3. Rate of natural increase
Yearly net relative increase in population size due to excessYearly net relative increase in population size due to excess
of birth over death. This is computed as (CBR – CDR).of birth over death. This is computed as (CBR – CDR).
4. Arithmetic method4. Arithmetic method
Pt = Po + btPt = Po + bt
Pt = Population at time (t)Pt = Population at time (t)
Po = Population at an earlier time (o)Po = Population at an earlier time (o)
b = Absolute increase in population / yearb = Absolute increase in population / year
t = Length of timet = Length of time

5. • 5. Relative increase in population5. Relative increase in population
Relative increase in population =Relative increase in population = [(Pt - Po) / Po][(Pt - Po) / Po] × 100× 100
6. Geometric method6. Geometric method
Pt = Po ( 1 + r )Pt = Po ( 1 + r )tt
Pt = Population at time (t)Pt = Population at time (t)
Po = Population at an earlier timePo = Population at an earlier time
r = constant rate of growthr = constant rate of growth
t = time interval between Po and Ptt = time interval between Po and Pt
7. Exponential method7. Exponential method
Pt = Po ePt = Po ertrt
(e = 2.718)(e = 2.718)

6. • Example1: Population of year Y = 10.4 milExample1: Population of year Y = 10.4 mil
Population growth rate = 2.1% per yearPopulation growth rate = 2.1% per year
Population 10 years later = ?Population 10 years later = ?
Pt = Po ( 1 + r )Pt = Po ( 1 + r )tt
Pt = Po ( 1 + r )Pt = Po ( 1 + r )tt
= 10.4 (1 + 0.021)= 10.4 (1 + 0.021)1010
= 12.8 mil= 12.8 mil
[Alternative:[Alternative: Pt = Po ( 1 + r )Pt = Po ( 1 + r )tt
log Pt = log Po + t log ( 1 + r )log Pt = log Po + t log ( 1 + r )
log Pt = log 10.4 + 10 log (1 + 0.021)log Pt = log 10.4 + 10 log (1 + 0.021)
log Pt = 1.017 + 10 log (1.021)log Pt = 1.017 + 10 log (1.021)
log Pt = 1.017 + 10log Pt = 1.017 + 10 × 0.009026× 0.009026
log Pt = 1.017 +log Pt = 1.017 + 0.090260.09026
Pt = anti-log (1.017 +Pt = anti-log (1.017 + 0.09026)0.09026)
= 12.8 mil ]= 12.8 mil ]

7. • Example2: Population of year Y = 10.4 milExample2: Population of year Y = 10.4 mil
Population growth rate = 2.1% per yearPopulation growth rate = 2.1% per year
Population 10 years later = ?Population 10 years later = ?
Pt = Po ePt = Po ertrt
(e = 2.718)(e = 2.718)
Pt = 10.4 (2.718)Pt = 10.4 (2.718)0.0210.021 × 10× 10
= 12.8 mil= 12.8 mil

8. • Example 3: Population of 1983 = 38 milExample 3: Population of 1983 = 38 mil
Population of 1995 = 44 milPopulation of 1995 = 44 mil
Growth rate (r) = ?Growth rate (r) = ?
Pt = Po ( 1 + r )Pt = Po ( 1 + r )tt
Pt/Po = ( 1 + r )Pt/Po = ( 1 + r )tt
44/38 = ( 1 + r)44/38 = ( 1 + r)1212
1.1579 = ( 1 + r)1.1579 = ( 1 + r)1212
log 1.1579 = 12 log (1 + r)log 1.1579 = 12 log (1 + r)
0.0637 = 12 log (1 +r)0.0637 = 12 log (1 +r)
log (1 +r) = 0.0637/12log (1 +r) = 0.0637/12
log (1 +r) = 0.0053log (1 +r) = 0.0053
(1+ r) = anti-log 0.0053(1+ r) = anti-log 0.0053
1+ r = 1.01231+ r = 1.0123
r = 1.0123 – 1r = 1.0123 – 1
r = 0.0123 (ie 1.23% per year)r = 0.0123 (ie 1.23% per year)

9. • (II) Estimated Population and Doubling Time(II) Estimated Population and Doubling Time
Year ADYear AD Population (bil)Population (bil) No of year to doubleNo of year to double
1 0.25 16501 0.25 1650
1650 0.5 2001650 0.5 200
1850 1.1 801850 1.1 80
1930 2.0 451930 2.0 45
1975 4.0 251975 4.0 25
2010 8.0 ?2010 8.0 ?
Population doubling time (n)Population doubling time (n)
2P2P11 = P= P11 (1 + x)(1 + x)n-1n-1

10. • Example 4:Example 4: What is the pop doubling time if growth rate is 2%?What is the pop doubling time if growth rate is 2%?
2P2P11 = P= P11 (1 + x)(1 + x)n-1n-1
2 = (1 + 0.02)2 = (1 + 0.02)n-1n-1
log2 = (n-1) log (1 + 0.02)log2 = (n-1) log (1 + 0.02)
n-1 = 0.301/0.0086n-1 = 0.301/0.0086
n = 35 + 1n = 35 + 1
= 36 years= 36 years
[Alternative or quick method: 0.693/annual growth rate[Alternative or quick method: 0.693/annual growth rate
0.693/0.02 = 34.65 years]0.693/0.02 = 34.65 years]

11. ReferenceReference
11.Lecture notes on population estimation and projection.Lecture notes on population estimation and projection,,
MMed Sc (P & TM) Course, Institute of Medicine (I), Yangon,MMed Sc (P & TM) Course, Institute of Medicine (I), Yangon,
1993.1993.

12. THE ENDTHE END