Population growth calculator
Calculate change from two compatible observations. Use the actual elapsed interval, including a fractional year if the dates require it.
Calculate growth from two population figures
Enter the starting and ending totals from compatible observations. The interval controls annualized growth. The scenario rate is a separate mathematical illustration and does not affect the historical growth calculation.
Prefilled with Texas, July 1, 2020 to July 1, 2025 (Census PEP Vintage 2025). Scenario is a mathematical illustration, not an official demographic projection.
How to calculate population growth rate
Absolute change = ending population − starting population. Percentage change = 100 × (ending population / starting population − 1). Annualized growth = 100 × ((ending population / starting population)1 / elapsed years − 1).
The annualized result describes the constant rate that would connect the two totals over the interval. It is a mathematical summary, not proof that each year's growth followed that rate. A ten-year percentage change should not be called annual growth. July 1, 2020 to July 1, 2025 is five years; an April 1 census count and a July 1 estimate do not form the same exact interval.
Percentage growth is invalid when the starting population is zero or missing. Annualized growth requires positive populations and a positive elapsed interval. The calculator suppresses unsupported results rather than printing infinity or a misleading zero. A zero ending population can produce a valid percentage decline, but an annualized rate is withheld under the positive-population rule.
Worked example: Texas, 2020–2025
The Census Bureau estimates that Texas had 29,237,895 residents on July 1, 2020 and 31,709,821 on July 1, 2025. The absolute change is 31,709,821 − 29,237,895 = +2,471,926 people. The percentage change is 100 × (31,709,821 / 29,237,895 − 1) = +8.45%. Spreading that over five elapsed years gives an annualized growth rate of 100 × ((31,709,821 / 29,237,895)1/5 − 1) = +1.64% per year. Dividing 8.45% by five (1.69%) gives a slightly different, simple average that ignores compounding.
Constant-growth scenario
The scenario uses starting population × (1 + annual rate / 100)elapsed years. It illustrates a rate you enter. It does not account for births, deaths, migration, age composition or boundary changes and is not an official Census projection. Rates greater than −100% are required; the output should not be treated as a validated forecast.
For factual change, select observations from the same population universe, source vintage and compatible geography. Use the comparison tool for compatible PEP observations, and read the growth and percentage-point guide before comparing shares.