Enter the initial population, the annual decrease rate, and the time span into the calculator to determine the final population after the specified period.

Population Decrease Calculator

Enter any 3 values to calculate the missing variable

Population Decrease Formula

The population decrease calculator estimates how many individuals remain after a population declines by the same percentage each year. This is a compound decrease model, which means each year’s decrease is applied to the remaining population, not the original population.

FP = IP * (1 - DR/100)^{TS}
Variable Meaning
FP Final population after the decrease period
IP Initial population at the starting point
DR Annual decrease rate entered as a percent, such as 2 for 2%
TS Time span in years

In practical terms, the formula multiplies the initial population by the yearly retention factor. If the decrease rate is 2%, then the population keeps 98% of its size each year.

Equivalent Forms

If you know any three values, the missing value can be solved with these rearrangements:

IP = \frac{FP}{(1 - DR/100)^{TS}}
DR = 100 * \left(1 - \left(\frac{FP}{IP}\right)^{1/TS}\right)
TS = \frac{\ln(FP/IP)}{\ln(1 - DR/100)}

These forms are useful when the calculator is being used to estimate a starting population, infer the annual decline rate, or determine how long it takes to reach a target population.

How to Use the Calculator

  1. Enter the initial population.
  2. Enter the annual decrease rate as a percentage.
  3. Enter the time span in years.
  4. Calculate the final population, or leave one field blank and let the calculator solve for it.

For most population problems, the decrease rate should be between 0% and 100%. A value of 0% means the population stays constant. A value of 100% means the entire population is lost in one period.

Example

A town begins with 100,000 residents and declines by 2% per year for 5 years.

FP = 100000 * (1 - 2/100)^{5} \approx 90392.08

Rounded to whole people, the final population is 90,392. That means the town loses about 9,608 residents over the 5-year period.

You can also measure the total number lost and the percent remaining:

L = IP - FP
R = \frac{FP}{IP} * 100

Here, L is the total population lost and R is the percentage of the original population still remaining after the decline period.

Total Percentage Decrease Over the Full Time Span

The annual decrease rate and the total decrease across the full period are not the same thing. To find the overall percentage drop from start to finish, use:

TD = \left(1 - (1 - DR/100)^{TS}\right) * 100

In the example above, the annual decrease rate is 2%, but the total 5-year decrease is about 9.61%, not exactly 10%. This happens because each year’s decrease is applied to a smaller remaining population.

When This Calculator Is Appropriate

  • City or regional population projections
  • School enrollment decline estimates
  • Wildlife population reduction modeling
  • Subscriber, customer, or membership attrition
  • Any scenario with a constant percentage decrease over equal time intervals

Important Assumptions

  • The decrease rate stays constant for every year in the time span.
  • The model assumes percentage-based decline, not a fixed number lost each year.
  • The formula uses yearly compounding because the time span is entered in years.
  • Population values should be positive, and final answers can be rounded to whole individuals when appropriate.

If your problem involves losing the same number of individuals each year rather than the same percentage, a linear decrease model would be more appropriate than this calculator.

Common Questions

Is this a linear or exponential model?
This calculator uses an exponential decay model because the decrease is compounded over time.

Why is the final population not equal to the initial population minus rate times years?
Because the rate is applied to the remaining population each year, not to the original population only once.

Can I use decimals for the rate?
Yes. For example, 1.5 means 1.5% per year.