Doubling Time Calculator
How long until it doubles? Work it out from a growth rate or from two counts, for bacteria, cell cultures, populations or savings.
By Manzoor Ahmad, Pharmacist Turned Web Specialist · Updated How do you calculate doubling time?
From two measurements: Td = Δt × ln 2 ÷ ln(N₂ ÷ N₁). From a growth rate of r% per period: Td = ln 2 ÷ ln(1 + r/100). A culture growing from 1,000 to 64,000 cells in 120 minutes doubles every 20 minutes; something growing 7% a year doubles in 10.2 years (Rule of 70 says 10).
Doubling time by growth rate
| Growth per period | Exact doubling time | Rule of 70 | Rule of 72 |
|---|
Typical doubling (generation) times in biology
| Organism or system | Typical doubling time | Conditions |
|---|---|---|
| Escherichia coli | ≈ 20 min | rich broth, 37 °C |
| Staphylococcus aureus | ≈ 25–30 min | laboratory medium |
| Baker’s yeast | ≈ 90 min | glucose medium, 30 °C |
| Mycobacterium tuberculosis | ≈ 15–20 h | laboratory culture |
| HeLa cells | ≈ 24 h | cell culture |
Generation times are approximate and change with temperature, nutrients and strain. Counting live bacteria? Prepare the plates with the serial dilution calculator.
Doubling time FAQs
For growth of r percent per period, doubling time T_d = ln 2 ÷ ln(1 + r/100). For continuous growth at rate k, T_d = ln 2 ÷ k ≈ 0.693 ÷ k.
T_d = Δt × ln 2 ÷ ln(N₂ ÷ N₁). If a culture grows from 1,000 to 64,000 cells in 120 minutes, that is 6 doublings (2⁶ = 64), so the doubling time is 20 minutes.
Doubling time ≈ 70 ÷ growth rate (in percent). At 2% per year something doubles in about 35 years. It is most accurate for small rates and continuous growth.
Doubling time ≈ 72 ÷ percentage rate, popular in finance because 72 divides evenly by many numbers. At 8% per year, money doubles in about 9 years (exactly 9.01).
Around 20 minutes in rich medium at 37 °C, though it ranges from about 20 minutes to several hours depending on nutrients and temperature. In the body, bacteria usually grow much more slowly.
N = N₀ × 2^(t ÷ T_d). One bacterium dividing every 20 minutes becomes about 16.8 million after 8 hours (24 doublings), if nutrients never ran out.
Growth rate says how much something grows per unit time; doubling time says how long it takes to grow by 100%. They are inversely related: halve the rate and the doubling time roughly doubles.
They are mirror images. Doubling time describes exponential growth, half-life exponential decay, and both use ln 2.
The time for a tumor to double in volume, used in oncology to describe growth speed. It is calculated with the same two-measurement formula from imaging volumes taken at two dates.
Only during true exponential growth. Real populations and cultures slow down as resources run out (the stationary phase in bacteria), so doubling time lengthens.
Growth per period r = 2^(1/T_d) − 1, or continuous rate k = ln 2 ÷ T_d. A 10-year doubling time is 7.18% per year compounded, or 6.93% continuous.
Because each doubling adds as much as everything before it. After 10 doublings something is 1,024 times bigger; after 20, over a million.
Sources
- OpenStax Microbiology, Section 9.1: How Microbes Grow
- OpenStax Biology 2e, Section 45.3: Environmental Limits to Population Growth
- Sezonov, Joseleau-Petit & D'Ari (2007), Escherichia coli Physiology in Luria-Bertani Broth, Journal of Bacteriology
- US Census Bureau: International Database (population growth rates)
- Khan Academy: Exponential growth and decay
Doubling-time math assumes steady exponential growth. Real cultures, tumors, populations and investments slow down, speed up or plateau; treat projections as illustrations, not forecasts or medical or financial advice.