The formula
Doubling time is the time a growing population takes to double. From a count N1 at the start and N2 after time t:
doubling time = t × ln 2 ÷ ln(N2 ÷ N1)
ln is the natural logarithm and ln 2 is 0.693. The same formula works for cells counted on a hemocytometer, bacteria measured by OD600, or any population growing exponentially.
A worked example
A flask seeded with 2 × 105 cells holds 1.6 × 106 cells 72 hours later.
- N2 ÷ N1 = 1.6 × 106 ÷ 2 × 105 = 8.
- ln 8 = 2.079.
- Doubling time = 72 × 0.693 ÷ 2.079 = 24 hours.
A quicker check: 8 is 23, so the cells doubled three times in 72 hours, once every 24 hours.
Growth rate and generation time
The growth rate constant is k = ln(N2 ÷ N1) ÷ t, here 2.079 ÷ 72 = 0.0289 per hour, and doubling time is ln 2 ÷ k. Microbiologists call the doubling time of bacteria the generation time; it is the same number.
Typical values
- E. coli in rich medium at 37 °C: about 20 minutes.
- Yeast: 90 minutes to 2 hours.
- HeLa, HEK293 and CHO cells: 20 to 24 hours.
- Primary cells and slow lines: 30 to 60 hours or more.
Getting a reliable number
Count only while the cells are in log phase. Freshly seeded cells pause before they start dividing, and cells near confluence or in spent medium slow down, both of which stretch the apparent doubling time. Use counts at least two doublings apart, count the same way each time, and for adherent cells count only live, attached cells. Seeding density and passage number change the result, so note them when you report it.
Calculators
The Cell Doubling Time Calculator gives the doubling time, growth rate and number of doublings from two counts. Count cells with the Hemocytometer Calculator, and for bacteria turn OD600 readings into cells per mL with the OD600 Calculator.