Population growth rate calculator
This population growth rate calculator finds the average yearly rate between two population counts: a town that grew from 100,000 to 121,000 in 10 years grew by 1.92 % a year. It also projects the population forward and shows how long it takes to double.
Example: Calculate: Annual growth rate from two counts · Population at the start 100,000 · Population at the end 121,000 · Years between the counts 10 · Method: Geometric (compound, once a year) → Result: Growth rate 1.924 % per year (geometric). Source: BPS & UNFPA, Proyeksi Penduduk Kabupaten/Kota Provinsi Papua 2010–2020 (Jakarta 2015), Bab I/II: metode geometrik for Kabupaten/Kota (national and per province: metode komponen), P_t = P_0 (1 + r)^t, r = (P_t/P_0)^(1/t) − 1, Laju pertumbuhan equal for every year (read 10.10.2026). Updated: .
How it is calculated
Geometric growth rate r = (P_t ÷ P_0)^(1/t) − 1; exponential rate r = ln(P_t ÷ P_0) ÷ t. P_0 is the population at the start, P_t the population t years later. The geometric method works like compound interest with the same rate every year – Indonesia’s statistics office BPS describes it this way for its district and city projections, P_t = P_0 (1 + r)^t; its national and provincial projections use the component method with births, deaths and migration. The UN Demographic Yearbook gives the annual rate of population increase as the average annual exponential rate, in percent; there the projection is P_t = P_0 · e^(r·t).
Growth rate examples
| Start | End | Years | Geometric rate per year |
|---|---|---|---|
| 100,000 | 121,000 | 10 | 1.92 % |
| 1,000,000 | 1,104,081 | 5 | 2.00 % |
| 500,000 | 600,000 | 8 | 2.31 % |
| 80,000 | 72,000 | 6 | −1.74 % |
The exponential rate is always a little lower for growth: 100,000 to 121,000 in 10 years gives 1.91 % instead of 1.92 %. A negative rate means the population shrank.
Projection and doubling time
At 2 % a year, 100,000 people become 100,000 × 1.02^10 = 121,899 after 10 years with the geometric method, or 100,000 × e^0.2 = 122,140 with the exponential one. The doubling time follows from the same formulas: ln 2 ÷ ln(1 + r) years (geometric) or ln 2 ÷ r (exponential).
| Rate per year | Doubling time, geometric | Doubling time, exponential |
|---|---|---|
| 1 % | 69.7 years | 69.3 years |
| 2 % | 35.0 years | 34.7 years |
| 3 % | 23.4 years | 23.1 years |
| 5 % | 14.2 years | 13.9 years |
- Both methods assume the same rate every year. BPS states this assumption explicitly for the geometric method.
- The growth rate includes migration. The rate of natural increase only compares births and deaths – the UN notes the two can differ.
The maths is the same as in the exponential growth calculator; logarithms come from the logarithm calculator, and percentage changes from the percentage calculator.
Frequently asked questions
How do you calculate the population growth rate?
Geometric: r = (P_t ÷ P_0)^(1/t) − 1. From 100,000 to 121,000 in 10 years: 1.21^(1/10) − 1 = 0.0192, so 1.92 % a year.
What is the exponential growth rate formula?
r = ln(P_t ÷ P_0) ÷ t, the method of the UN Demographic Yearbook. For 100,000 to 121,000 in 10 years it gives ln 1.21 ÷ 10 = 1.91 %.
How do I project a population?
Geometric: P_t = P_0 × (1 + r)^t. At 2 % for 10 years, 100,000 × 1.02^10 = 121,899.
How long does a population take to double?
ln 2 ÷ ln(1 + r) years with the geometric method: about 35 years at 2 % and 23.4 years at 3 %.
Why do the two methods give different rates?
The geometric method adds growth once a year, the exponential one continuously. For the same two counts the exponential rate is slightly lower when the population grows.
Sources and legal basis
- BPS & UNFPA, Proyeksi Penduduk Kabupaten/Kota Provinsi Papua 2010–2020 (Jakarta 2015), Bab I/II: metode geometrik for Kabupaten/Kota (national and per province: metode komponen), P_t = P_0 (1 + r)^t, r = (P_t/P_0)^(1/t) − 1, Laju pertumbuhan equal for every year (read 10.10.2026)
- UN Statistics Division, Demographic Yearbook 2019, Technical notes Table 3: annual rate of population increase = average annual exponential rate, in percent (read 10.10.2026)
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