Doubling time calculator

The formula

$$N = N_0 \cdot 2^{t/T_d} \qquad\Longleftrightarrow\qquad T_d = \frac{t}{\log_2(N/N_0)}$$

$N_0$ is the starting count, $N$ the count after time $t$, and $T_d$ the doubling time.

Where it comes from

In exponential growth every individual divides at the same average rate, so the population multiplies by the same factor in every equal stretch of time. Call the time for one doubling $T_d$.

After one doubling time the count is $2N_0$, after two it is $4N_0$, and after $k$ doublings it is $2^k N_0$. In a time $t$ there are $t/T_d$ doublings, so

$$N = N_0 \cdot 2^{t/T_d}$$

To find $T_d$ from two counts, divide by $N_0$ and take $\log_2$ of both sides:

$$\log_2\frac{N}{N_0} = \frac{t}{T_d} \quad\Rightarrow\quad T_d = \frac{t}{\log_2(N/N_0)}$$

If your calculator only has natural logs, use $\log_2 x = \ln x / \ln 2$, which gives the common form $T_d = t \ln 2 / \ln(N/N_0)$.

Worked example

Cells go from $2 \times 10^5$ to $1.6 \times 10^6$ in 72 hours. That is 8 times more, and $8 = 2^3$, so there were three doublings:

$$T_d = \frac{72\ \text{h}}{\log_2 8} = \frac{72}{3} = 24\ \text{h}$$

Watch out for

• Only use the log phase. Lag phase after seeding and plateau at confluence both make the doubling time look longer than it is.
• Compound interest is the same maths. Money at rate $r$ doubles in $\ln 2 / \ln(1+r)$ years, which is where the rule of 72 comes from.

Last checked November 11, 2026