Population Forecast Calculator
With decadal censuses of 40,000 to 77,000, the incremental increase method forecasts 102500 people two decades ahead.
Usually decadal censuses.
102500
- Arithmetic increase P + n x̄
- 95500
- Geometric increase P(1 + r)ⁿ
- 106833.1643
- Average increase x̄
- 9250
- Average incremental increase ȳ
- 2333.333333
- Geometric mean growth rate r
- 17.78979975 % per interval
Step-by-step solution
- x̄ = mean of increases 6000, 8000, 10000, 13000 = 9250
- ȳ = mean of changes in increase = 2333.333333
- Pₙ = P + n x̄ + n(n + 1)ȳ/2 = 77000 + 2 × 9250 + 3 × 2333.333333 = 102500
Population Forecast Formula
Pₙ = P + n x̄ + n(n + 1)ȳ/2
arithmetic Pₙ = P + n x̄; geometric Pₙ = P(1 + r)ⁿ; x̄ average increase, ȳ average incremental increase
Worked Example
Census figures 40,000, 46,000, 54,000, 64,000 and 77,000 over five decades, forecast two decades ahead:
- x̄ = mean of increases 6000, 8000, 10000, 13000 = 9250
- ȳ = mean of changes in increase = 2333.333333
- Pₙ = P + n x̄ + n(n + 1)ȳ/2 = 77000 + 2 × 9250 + 3 × 2333.333333 = 102500
Geometric increase P(1 + r)ⁿ: 106833.1643 · Average increase x̄: 9250 · Average incremental increase ȳ: 2333.333333 · Geometric mean growth rate r: 17.78979975 % per interval
GATE tip
For the geometric method GATE often uses the arithmetic mean of percentage growth rates; this calculator uses the geometric mean, which reproduces the data exactly. State which you use.
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Frequently asked questions
Which method should I use?
Arithmetic suits old, slow-growing cities and gives low values; geometric suits young, fast-growing ones and gives high values; incremental increase sits between and is common in Indian practice (CPHEEO).
What is the design period?
Typically 30 years for water supply and sewerage, so the forecast covers three decades beyond the latest census.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Population Forecast Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/population-forecast-calculator/
IEEE
Scientific Converters, "Population Forecast Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/population-forecast-calculator/