How to use it
- Paste the time and the reading, one per line. Two columns straight out of a spreadsheet work.
- Enter the time unit. The doubling time comes back in it.
- Check the window that was chosen and the doubling time. The window is drawn heavier on the chart.
- Look at the other candidates in the table, ordered by how precisely each pins the rate.
- Take the doubling time to the cell seeding calculator for the next passage.
The formulas, and what to watch for
Exponential growth is a straight line once you take logarithms. The arithmetic is one least-squares fit; the hard part is where to cut.
The fit
Least squares of ln(reading) against time. The slope is the growth rate.
- Model
- ln y = ln y₀ + µt
- Doubling time
- ln2 / µ
Choosing the window
Every run of three or more consecutive readings is fitted, and the one that pins µ most precisely wins.
- SE of µ
- s / √Σ(tᵢ − t̄)²
- s
- residual standard deviation
What to watch for
- ⛔ Ranking windows by r² always picks the shortest one. Three points lie on a line whatever they are, and r² calls that the best fit.
- A rule like “the longest window with r² above 0.99” only moves the arbitrariness into the threshold. The standard error has length and straightness pulling against each other with no constant to tune.
- The doubling time does not depend on the unit of measurement. OD or cell count, a constant factor only shifts the intercept.
- Readings at or below zero cannot be logged and are left out, with a count — that count is usually the story.
- Falling stretches are not candidates. Death phase is part of the curve but it is not exponential growth.
- Choosing a window is still a judgement. This ranks the candidates and shows its working; deciding otherwise from the table is fine.
Frequently asked questions
Any three points give an r² near 1. So the ranking uses how precisely the window pins µ instead, and precision improves with more points — so a long window that fits well wins.
Every candidate is in the table, ordered by precision. Decide from the evidence — the reasoning is not hidden.
Either. The doubling time does not depend on the unit. Do remember that OD stops being linear at high values, which can make that stretch look like a plateau.
It is the input the cell seeding calculator asks for — it takes you from “when will this reach my target density” to “what do I seed to have it ready on Friday”.