Cell Doubling Time Calculator
Calculate doubling time (how long it takes a cell population to double) during exponential growth. Use N = N₀·2ⁿ and n = log(N/N₀) / log(2). Includes quick picks, steps, a mini growth-curve visual, and a doublings table.
Background
In exponential growth, each “doubling” multiplies the population by 2. If your population starts at N₀ and ends at N after time t, you can compute the number of doublings (generations) n, then: doubling time = t/n. This model is commonly used for cells, bacteria, or any population growing approximately exponentially.
How to use this calculator
- Pick a mode (doubling time, final population, time, or doublings).
- Enter the values you know (usually N₀, N, and t).
- Click Calculate to get the answer, plus a visual + table (optional).
How this calculator works
- Exponential growth model: N = N₀·2ⁿ
- Doublings: n = log(N/N₀) / log(2)
- Doubling time: DT = t/n
- Predict N from DT: N = N₀·2^(t/DT)
Formula & Equation Used
Exponential growth model: N = N₀·2ⁿ
Doublings (generations): n = log(N/N₀) / log(2)
Doubling time: DT = t/n
Predict final population (from DT): N = N₀·2^(t/DT)
Solve elapsed time (from DT): t = n·DT
Example Problem & Step-by-Step Solution
Example 1 — Find doubling time
A cell culture grows from N₀ = 1.0×10⁵ to N = 8.0×10⁵ in t = 24 hr. Find the number of doublings n and the doubling time DT.
- Compute ratio: N/N₀ = 8.0
- Doublings: n = log(8)/log(2) = 3
- Doubling time: DT = t/n = 24/3 = 8 hr
Because 8× is exactly three doublings (1→2→4→8), the answer is perfectly clean.
Example 2 — Predict final population
Starting at N₀ = 5.0×10⁴, the doubling time is DT = 12 hr. After t = 3 days, what is N?
- Convert time: 3 days = 72 hr
- Doublings: n = t/DT = 72/12 = 6
- Final population: N = N₀·2⁶ = 5.0×10⁴·64 = 3.2×10⁶
Example 3 — Solve elapsed time
A population grows from N₀ = 1.0×10³ to N = 1.0×10⁶. If the doubling time is DT = 30 min, how long did it grow?
- Doublings: n = log(N/N₀)/log(2) = log(10³)/log(2) ≈ 9.966
- Time: t = n·DT ≈ 9.966·30 ≈ 299.0 min
Real data rarely lands on exact powers of 2 — decimals for n are totally normal.
Frequently Asked Questions
Q: Is doubling time the same as generation time?
In binary fission / ideal exponential growth, yes — “generation time” is essentially the doubling time.
Q: Does it matter if I use ln or log₁₀?
No. In n = log(N/N₀)/log(2), the log base cancels out.
Q: When should I NOT use this model?
If growth isn’t close to exponential (lag phase, stationary phase, death phase), this can be misleading.
Q: What does a fractional number of doublings mean?
It means the population increased by a factor between two powers of 2. For example, n = 2.5 corresponds to a multiplier of 2^2.5 ≈ 5.66.
Q: Can I use this for decreasing populations?
This calculator assumes growth (N > N₀). If your count decreases, that’s decay and you’d typically use a half-life / decay model instead.