Doubling Time Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/6/2026
Doubling time is calculated as t = ln(2) ÷ r, where r is the continuous growth rate expressed as a decimal. For a growth rate of 5% per period, a population doubles in about 13.86 periods.
Explanation
Doubling time indicates how many periods (hours, days, years — depending on the unit of the growth rate entered) are needed for a population undergoing continuous exponential growth to reach twice its initial size, regardless of that starting size: the remarkable property of exponential growth is that this time depends only on the growth rate, not on the current population. The exact formula uses the natural logarithm of 2 (ln(2) ≈ 0.693) divided by the growth rate as a decimal. It's sometimes approximated by the 'rule of 70' (70 divided by the growth rate as a percentage), a practical mental-math approximation but slightly imprecise; this calculator applies the exact formula rather than this approximation. This model assumes continuous exponential growth and a constant rate over the entire period — a common simplification in population biology (bacterial cultures in their exponential growth phase, for example), but one that departs from reality as soon as limiting factors (resources, predation, competition) slow growth down.
Example: bacterial culture growing at 5% per hour
Inputs
Growth rate: 5% per hour.
Calculation
Doubling time = ln(2) ÷ (5 ÷ 100) = 0.6931 ÷ 0.05 ≈ 13.86.
Result
The population doubles approximately every 13.86 hours, as long as the 5% per hour growth rate stays constant.
Frequently asked questions
Why doesn't the result have a fixed time unit (hours, days, years)?
Because the result is expressed in the same period unit as the growth rate entered: a rate 'per hour' gives a doubling time in hours, a rate 'per year' gives it in years. The calculator doesn't automatically convert between time units.
What's the difference with the 'rule of 70'?
The rule of 70 is a quick approximation (70 ÷ rate as a percentage) that gives a close but not exact result, convenient for mental math. This calculator uses the exact formula with the natural logarithm of 2, more precise, at no extra computational cost.
Does this calculator work for a declining population?
No, it's deliberately limited to positive growth rates. For a population declining exponentially, the equivalent concept is 'half-life' (the time needed for the population to be cut in half), which uses the same formula but is interpreted differently and isn't covered here.
Does real biological population growth always follow this model?
Rarely over the long term. The continuous exponential model describes an unconstrained growth phase well (for example, the start of a bacterial culture in rich medium), but most biological populations eventually slow down as resources become limited, predation increases, or competition intensifies — a phenomenon better described by logistic growth models, outside the scope of this calculator.