The mitotic index is the share of cells in a sample caught in mitosis. Multiply it by the length of the cell cycle and you have the usual classroom estimate of how long mitosis lasts. That sum assumes cells are evenly spread in age. We calculated the gap for a population growing steadily, losing no cells, with mitosis at the very end of the cycle. The sum comes out 14.5% low at an index of 0.5 and 30.3% low at 0.01, so a smaller index brings a larger shortfall. These are model figures, and they describe no particular slide.
Index times cycle gives a duration when ages are evenly spread
Count 30 cells in mitosis out of 200 and the index is 0.15, or 15%. With a 24-hour cycle, 0.15 × 24 gives 3.6 hours. This is the taught method: the AQA A-level specification names "calculation of a mitotic index" in Required practical 2. The term has no hits in the Cambridge 9700 syllabus for 2025–2027 or 2028–2030.
The logic holds when every age is equally common, because a stage's share of cells then equals its share of the cycle. By our derivation, that is exact if each division leaves one cell in the cycle and the other leaves at once. A root tip's age mix is unknown. Cells that leave the dividing zone soon after division push it towards even ages, which would shrink the gaps below.
Our cell cycle calculator was changed on 2 November 2026 to set these cases side by side. Enter 30, 200 and 24 hours, leave the stage time blank, and the fixed version gives the index with a 95% counting range of 10.71–20.61%, then 3.6 hours beside two growth estimates. Before that change it said steady division made cell share proportional to time, never printed the index, and returned 36 hours for 300 cells out of 200.
Doubling time is a separate number, from counts over time: 200 to 800 cells in 5 days gives 2.5 days. It equals the cycle only if all cells cycle, none are lost and cycle length does not vary.
Mitosis reads about 30% low when the index is small
In steady growth, cells just after division are twice as common as cells just before it, so a late stage holds fewer cells than its length suggests. Chung and colleagues, in a 1973 paper of which we read the abstract, give tm/g ln 2 = ln (1 + R) for a population "dividing at a constant rate", with tm mitosis time, g generation time and R the fraction in mitosis. Rearranged by us, tm = g × log₂(1 + R).
| Index | Simple sum (h) | If growing steadily (h) | Simple sum low by |
|---|---|---|---|
| 0.01 | 0.24 | 0.34 | 30.3% |
| 0.05 | 1.20 | 1.69 | 29.0% |
| 0.15 | 3.60 | 4.84 | 25.6% |
| 0.50 | 12.00 | 14.04 | 14.5% |
All rows use a 24-hour cycle and are our arithmetic; the shortfall is a share of the growth estimate. As the index falls, the shortfall approaches 1 − ln 2, or 30.7%. For 30 of 200, 4.84 hours is what the count would mean if this population were growing steadily.
Real cycles vary, so we simulated a true 3.6-hour mitosis with the standard deviation of cycle length at 10–30% of the mean. The simple sum stayed 24–27% low. By our derivation the equation is exact once g is the population doubling time, which variation pulls just below the mean cycle.
G1 comes out high whenever it opens the cycle
The sign reverses for a phase at the start, where the young cells pile up. At 15% on 24 hours the simple sum gives 3.6 hours and the growth model 2.70, so the sum is 33.4% high. A very short phase sitting 47.1% of the way through the cycle shows no gap at all.
Laughlin set doubling aside in 1919 because his samples averaged it out
The problem was raised in Harry Hamilton Laughlin's study of onion root tips, Carnegie Institution Publication 265. The title page places him at the Eugenics Record Office. Truman State University's finding aid to his papers records him as its superintendent, then director, until 1940 and calls him "one of the leaders in the eugenics movement". The Cold Spring Harbor Laboratory archive describes him lobbying for eugenic legislation.
A cycle starts with one cell and ends with two. "Must rectifications be made", he asked. For his own material, he decided not. Because he had sampled a small part of each tissue and seen that indices fluctuated over time, he argued "this otherwise sudden doubling effect is entirely lost" in the average. The argument concerns his sampling.
His preliminary study, 13,000 counts over two morning hours at about 18 °C, gave 172.2 minutes for ten active stages, 33.88% of a 508.26-minute cycle. His main results were for 10, 20 and 30 °C.
A larger count stops closing the gap once the sample passes about 184 cells
On 30 of 200, counting alone gives a 95% Wilson range on the simple sum of 2.57 to 4.95 hours. The gap to the growth estimate is 1.24 hours. On a normal approximation with cells as independent draws, the 95% half-width shrinks to that size at about 184 cells for an index of 0.15, and about 439 for 0.05. Counting more cells past that point only tightens the range around the same offset. Slide cells are clustered, so these crossings are best cases.
Onion root counts lose meaning unless the start of prophase stays fixed
Laughlin marked his ten stages with "arbitrary but definite boundaries", and in the preliminary study the earliest took 77.02 of his 172.2 minutes, 45% on our arithmetic. He named the line after it as the likeliest place for error. Two students who place the start of prophase differently measure different things. He also quotes Kellicott's 1904 finding of two maxima and two minima a day in Allium root division, so a morning count samples one part of a rhythm.
Cells that have stopped dividing, which Laughlin tried to avoid by counting close to the tip, dilute a mitosis count. That pushes the sum further short, the same direction as the age mix and often by more: if half the cells at an index of 0.15 were cycling, the growth estimate would be 9.08 hours, and at 30%, 14.04. In a G1 or interphase count they can look like a longer stage instead. A squash can show the relative share of stages in one root, prepared one way.
Tumour grading stays outside this sum because it counts mitoses in a defined area
Elston and Ellis's 1991 abstract lists "an accurate mitotic count using a defined field area" among the grading features, assessed in 1831 patients. An NHS screening poster based on that paper, dated 2005 and marked archived in August 2016, describes finding the "area with most mitotic activity" and counting mitoses in 10 consecutive fields. We did not open a current protocol, so treat both as history, and nothing here interprets a pathology report. That method tallies per field in the busiest area, with no total of cells beneath it, so no fraction exists to multiply by a cycle time.
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