The population in a country or given area calculated by births, deaths and migration. More precisely the natural population change is calculated by births minus deaths and net migration is the number of immigrants minus the number of emigrants. Population projections are the calculations of future birth rate, death rate and migration, population based on past and present conditions, They are neither predictions, estimates or forecasts, rather they are in between predictions and forecasts. Population projections show the future course of fertility, mortality and migration

In research the formula is used to expect the future necessities and characterise by groups. Population formula in economics is used to determine the economic activity of the country or area. Population percentage is the formula to divide the target demographic by the entire population, and then multiply the result by 100 to convert it to a percentage. The working age population is defined as those aged 15 to 64. This indicator measures the share of the working age population in total population. Working age population formula is the employment-to-population ratio is equal to the number of persons employed divided by the working-age population and multiplied by 100.

According to uoregon, Calculating Population percent growth rates are The percent change from one period to another is calculated from the formula:

PR = ((VPr - Vpa)/VPa) x 100

Where PR is Percent Rate, VPr is Present or Future Value, VPa is Past or Present Value, The annual percentage growth rate is simply the percent growth divided by N, the number of years.

__Population mean__: The population mean is an average of a group characteristic. Therefore population mean formula as below:

Population mean μ = ( Σ Xi ) / N

where Σ means the sum of, X is all the individual items in the group and N is the number of items in the group. The symbol 'μ' represents the population mean.

__Population standard deviation__: It is a measure of the average distance between the values of the data in the set and the mean. A low standard deviation indicates that the data points tend to be very close to the mean; a high standard deviation indicates that the data points are spread out over a large range of values.

Population standard deviation = σ = √ [ Σ ( Xi - μ )2 / N ]

The symbol 'σ' represents the population standard deviation.

__Population Variance__: It is the average of all data points, The variance measures the average degree to which each point differs from the mean.

Population variance = σ^{2} = Σ ( Xi - μ )2 / N.

__Population proportion__: It is a fraction of the population that has a certain characteristic.

Population proportion P = X/N

__Z-Score__: Z-score is measured in terms of standard deviations from the mean. It is a numerical measurement that describes a value's relationship to the mean of a group of values.

Standardized score Z = (X - μ) / σ

The population decrease and growth formula are as below:

1. If a constant rate of growth be R% per annum, then population
after n years = P x (1+R/100)^{n}.

2. if the growth be R% during first year and Q% during second year the population after 2 years = P x (1+R/100) x (1+Q/100)

3. if the constant decrease in population be R% per annum, then the population after n years = P x (1-R/100)^{n}.

The formula to calculate the future population values if the present population and with unknown growth rate.

VPf = VPr x (1 + i)^{n}

Where VPf is Future population, VPr is Present population, i is Growth rate (estimation), n is number of years.

If a population grows by a constant percentage per year, this eventually adds up to what we call exponential growth. In other words, the larger the population grows, the faster it grows!! A curve of exponential growth is an upward sweeping growth curve.

Population growth rate is the percentage change in the size of the population in a year.

Population growth rate = ((Natural Increase + Net in Migration)/Starting population)) * 100

Natural Increase is the births minus deaths, Net in Migration is immigration minus emigration. If the total number of births equal to total number of deaths in a year or period and there is zero net migration, the growth rate will be zero. If the natural increase is balanced out by net migration, the growth rate will also be zero.

__The Malthusian theory__: The Malthusian theory of population has been widely discussed and criticised during the 19th and early 20th century. The mathematical formulation of Malthus doctrine that food supply increases in arithmetical progression and population increases in geometrical progression, where he did not mention on economy progression with the population. Malthus could not foresee the unprecedented increase in scientific knowledge and agricultural inventions over a period of time which has stayed the law of diminishing returns. Consequently, the food supply has increased much faster than in arithmetical progression. Some of the countries with more GDP can import food from surplus countries.

__The Optimum Theory__: The optimum theory of population was propounded by Edwin Cannan in his book Wealth published in 1924 and popularized by Robbins, Dalton and Carr-Saunders. Unlike the Malthusian theory, the optimum theory concerned with the relation between the size of population and production of wealth. The optimum theory of population is superior to the Malthusian theory on many grounds.

__The Theory of Demographic Transition__: The theory of demographic transition is based on the actual population trends of advanced countries of the world. According to this theory, every country passes through three different stages of population growth.

1. In the first stage, the birth rate and the death rate are high and the growth rate of population is low.

2. In the second stage, the birth rate remains stable but the death rate falls rapidly. As a result, the growth rate of population increases very swiftly.

3. In the last stage, the birth rate starts falling and tends to equal the death rate. The growth rate of population is very slow.

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