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How many hours do these cells take to double?

Specific growth rate (μ) and doubling time calculator

Takes viable cell density counted at two time points and gives the specific growth rate (μ) and the time the cells take to double (doubling time).

When to use itUse it mid-culture to compare this batch with earlier ones, or to plan the next passage.

Prefilled with an example: CHO cells growing from 0.3 to 2.4 × 10⁶ cells/mL in 3 days (72 hours). Change any value and the result updates.

×10⁶ cells/mL

Live cells per mL at the first count. Any unit works if the second count uses the same one, because only the ratio matters.

×10⁶ cells/mL

The value at the second count. Pick both points from the phase where cells are growing fast (exponential phase).

h

In hours. Multiply days by 24.

h

A later time than the first, also in hours.

Doubling time (td)24 h
Specific growth rate (μ)0.02888 1/h
Doubling time in days1 day
μ per day0.6931 1/day

These cells double about every 24 hours (about 1 days). If that is slower than earlier batches, review the medium, the osmolality and the condition of the cells at seeding.

How to read it

The row that matches your result is marked.

  • Both points in active growthYour resultUse as isThe calculation assumes the cells keep growing at a constant rate (exponential growth). Including the lag right after seeding, or the late phase when growth stops, underestimates the rate.
  • Doubling time close to the usual value for the cell linePlausibleAbout 20 to 30 hours is a common guide for CHO cells, but it varies widely with cell line, medium and conditions, and there is no fixed standard. Compare with your own earlier batches.
  • High osmolality (roughly 350 to 450 mOsm/kg or more)Growth tends to slowOur related Japanese article reports that raising osmolality moderately increases productivity per cell 1.5 to 3 times, while the maximum growth rate falls (one report in the range reviewed saw it drop by about half). Above 500 mOsm/kg, growth stops and cells swell. Read a falling μ as a sign of this trade-off.
  • Times or densities entered incorrectlyCannot calculateThe second time must be later than the first, and both densities must be above 0.

How it is calculated

μ is the growth per hour (unit 1/h), and the doubling time is 0.693 (ln2) divided by μ. To convert to days, multiply μ by 24 and divide the doubling time by 24. The two points are joined by a single exponential curve, so a point from before growth starts (lag phase) or after it stops (stationary phase) underestimates the growth rate.

μ = ln(X2 / X1) ÷ (t2 − t1) doubling time td = ln2 ÷ μ

Source: The specific growth rate in exponential growth, μ = ln(X2/X1) ÷ (t2 − t1), and the doubling time, td = ln2 ÷ μ, are standard bioprocess engineering equations (see, for example, Doran, Bioprocess Engineering Principles).

With your numbers

  1. μ = ln(X2 ÷ X1) ÷ (t2 − t1) = ln(2.4 ÷ 0.3) ÷ (72 − 0) = 0.02888 1/h
  2. td = ln2 ÷ μ = 0.693 ÷ 0.02888 = 24 h

Limits of this calculation

  • The equations for μ and doubling time (μ = ln(X2/X1)/(t2 − t1), td = ln2/μ) are established cell culture standards and are not given in the related Japanese article. That article covers fed-batch feed design and the osmolality trade-off as situations in which μ falls.
  • If either point falls outside active growth (before growth starts, after it stops, or during decline), μ is underestimated. Fitting a line through three or more points (regression) is more reliable.
  • Results shift with the counting method (automated counter or trypan blue staining) and with how live and dead cells are told apart. The calculation assumes the same method and instrument for both counts.
  • Acceptable values for μ and doubling time vary widely with cell line, medium, osmolality and other conditions, and there is no fixed standard. The related article also gives the numbers as ranges.

Primary sources

Every calculator gives an estimate for learning, built on published information and primary sources. Real decisions follow the applicable guidance and expert judgment.