How doubling time is calculated
During exponential growth a population doubles at a steady interval. From a starting count N₀ and a later count N taken a time T apart, the doubling time is DT = T × ln 2 ÷ ln(N ÷ N₀). The same two counts give the number of population doublings, log₂(N ÷ N₀), and the specific growth rate μ = ln(N ÷ N₀) ÷ T, so DT = ln 2 ÷ μ.
Counts can be total cells, cells per mL or per cm², CFU/mL or OD600 readings, as long as every value uses the same measure. If you have raw chamber counts, turn them into cells per mL with the hemocytometer calculator first.
Worked example: 2 × 10⁵ cells to 1.6 × 10⁶ in 72 hours
Seeding 200,000 cells and counting 1,600,000 three days later is an 8-fold increase: log₂ 8 = 3 doublings in 72 hours, so the doubling time is 24 hours. The growth rate is ln 8 ÷ 72 = 0.02888 per hour, or 0.6931 per day.
If the culture started at population doubling level 12, it ends at PDL 15. ATCC writes the same step as PDL = 3.32 (log Xe − log Xb) + S, where 3.32 is 1 ÷ log₁₀ 2, rounded.
Fit a whole growth curve
Two counts describe one interval. With counts at several times, choose Doubling time from a growth curve and paste the time and count columns from your spreadsheet. The calculator fits a straight line through ln(count) by least squares, then reports the doubling time, R² and the doubling time over each interval, so points from the lag phase at the start or the stationary phase at the end stand out. Leave those points out and fit again.
The example is a bacterial culture read at OD600 every 20 minutes, rising from 0.050 to 0.466 over 100 minutes. The fitted doubling time is 30.96 minutes, with R² 0.9999.
Cells and bacteria: what the number means
For cultured animal cells, ATCC defines the population doubling time as the interval, during the logarithmic phase, in which the cells double in number. It is not the same as the cell generation time, the interval between one cell's divisions: cells that die or stop dividing make the population double more slowly than a single dividing cell. For bacteria, which divide by binary fission, the generation time is the doubling time, and after n generations Nₙ = N₀ × 2ⁿ.
Either way, the counts must come from exponential growth. Counts that include the lag after seeding or a crowded, stationary culture give a doubling time that is too long. Keep OD600 readings within your spectrophotometer's linear range and dilute dense cultures before reading.
Plan ahead: counts and times
With a known doubling time, Count after a growth time projects forward: 200,000 cells doubling every 24 hours reach 800,000 after 48 hours. Time to reach a target count runs the other way: going from 200,000 to 1,000,000 takes log₂ 5 = 2.322 doublings, or 55.73 hours. Both assume growth stays exponential, so add any lag after seeding and expect cultures to slow near confluence.
To split cells to a target density, use the dilution calculator. For plating bacteria to count CFU, plan the tubes with the serial dilution calculator.
Sources: ATCC, Animal Cell Culture Guide, "Passage number and population doubling level" (DT = T ln 2 / ln(Xe/Xb); PDL = 3.32 (log Xe − log Xb) + S) and its glossary. Roth V. 2006. Doubling Time Computing. OpenStax, Microbiology, 9.1 How Microbes Grow (generation time; Nₙ = N₀ × 2ⁿ).