Every number this tool produces
How it is calculated, why, what the alternatives are, where the controversy lies, and how to change it.
Peter Gershkovich, M.D., M.H.A. · info@openpathology.tech · Version 1.0 · 2026-08-05
Who this is for
A pathologist who is not a haematopathologist, and who wants to know exactly what the arithmetic is doing before trusting it, or before deciding what their laboratory should configure. Every abbreviation is expanded. No software knowledge is assumed.
The governing principle: where haematology practice genuinely disagrees, this tool does not pick a winner. It ships a documented default, makes the alternative selectable, and states in every report which one produced the numbers. Where you see a blue Configurable note, that is a decision your laboratory owns.
Where these settings live
Every Configurable item below is a field in the configuration profile — a single JSON file that travels with your laboratory's settings. There are three ways to reach it.
| Configuration Editor | This is where the counting policy is set. Its Counting Policy panel holds the differential denominator and per-100 reporting, the rounding rule, the decimal precision, the confidence interval, the diagnostic thresholds and the composition of derived figures such as the myeloid-to-erythroid ratio. Each applies to the specimen type selected at the top of the editor. The panel also edits the cell layout, the keyboard assignment, target counts, report templates, the morphology checklist, handedness, audio and autosave. |
| Export → edit → Import | Use Export Config on the counter, edit the
JSON, then Import Config. This reaches the whole profile, including the
few descriptive fields the editor does not surface —
constituents, categoryNotes,
targetCountBasis, requireCaseNumber and
provenance. An imported profile is validated before it is accepted,
and rejected with reasons if it cannot be counted with. |
| Preset catalogue | A set of complete starting points. A preset changes the layout, the keys and the wording — not the counting convention. Every preset that counts NRBC in peripheral blood keeps them out of the leucocyte denominator, as the built-in profile does. |
Whichever route you use, the profile is validated before it becomes active, and the identifier and version of the profile that produced a count appear in every report.
Abbreviations
| WBC | White blood cell (leucocyte) |
| RBC | Red blood cell (erythrocyte) |
| NRBC | Nucleated red blood cell — an immature red cell still carrying a nucleus, normally confined to marrow but appearing in blood in certain conditions |
| M:E ratio | Myeloid-to-erythroid ratio |
| NDC | Nucleated differential count — the marrow differential as defined by ICSH |
| BM | Bone marrow |
| PB | Peripheral blood |
| LIS | Laboratory information system |
| ICSH | International Council for Standardization in Haematology |
| CLSI | Clinical and Laboratory Standards Institute |
| WHO | World Health Organization (here, its classification of haematolymphoid tumours, 2022) |
| ICC | International Consensus Classification of myeloid neoplasms, 2022 |
| AML | Acute myeloid leukaemia |
| MDS | Myelodysplastic syndrome |
| CI | Confidence interval |
| CV | Coefficient of variation — a measure of reproducibility |
1. The differential percentage
You classify cells one at a time. The tool tallies them and expresses each category as a proportion of a total.
percentage of category X = (cells counted as X ÷ denominator) × 100
Everything else follows from two questions: what goes in the denominator, and how the result is rounded.
1.1 What goes in the denominator
Bone marrow. Every nucleated cell you counted, including erythroid precursors. This is the ICSH definition. Erythroid cells belong in a marrow differential because the balance between red-cell and white-cell production is much of why the marrow is being examined — that balance is the M:E ratio (§3).
Peripheral blood. Leucocytes only. Nucleated red cells are counted but excluded from the denominator and reported separately as NRBC per 100 WBC.
Why NRBC are treated differently in blood
In a healthy adult nucleated red cells do not circulate; they lose the nucleus before leaving the marrow. Their appearance in blood is pathological — severe haemolysis, marrow infiltration, severe hypoxia — or normal in the newborn.
They are not leucocytes. A leucocyte differential describes the composition of the white cell population, and a red cell precursor in that denominator dilutes every leucocyte percentage. There is a practical reason too: analysers historically counted NRBC as white cells, so the reported count needs correcting —
corrected WBC = uncorrected WBC × 100 ÷ (100 + NRBC per 100 WBC)
— and that formula requires NRBC expressed per 100 WBC, not as a percentage of all nucleated cells. Reporting it the other way makes the correction wrong.
The tool performs this correction, and shows its working
When you enter an analyser WBC on the results screen and nucleated red cells were counted, the correction above is applied before any absolute count is derived, and the arithmetic is displayed — the value entered, the factor, and the result. It is never applied silently, because only you know whether your analyser already corrected it; a checkbox says so and the entered value is then used as it stands.
Why it matters. At 20 NRBC per 100 WBC an uncorrected value overstates every absolute count by 20%. The absolute neutrophil count drives neutropenia grading, and a 20% overstatement moves values across the 1.5 and 0.5 ×10⁹/L boundaries — in exactly the population where nucleated red cells circulate.
Correcting the WBC and excluding NRBC from the differential denominator are two halves of one convention. Doing either alone is what produces the error.
A blood film with 180 leucocytes and 20 nucleated red cells
| NRBC in denominator | NRBC excluded (this tool) | |
|---|---|---|
| Denominator | 200 | 180 |
| Segmented neutrophils (120) | 60.0% | 66.7% |
| Lymphocytes (40) | 20.0% | 22.2% |
| Monocytes (15) | 7.5% | 8.3% |
| Nucleated red cells (20) | 10.0% | 11.1 per 100 WBC |
| Report opens | "A 200-cell differential" | "A 180-cell differential count" |
Every leucocyte percentage is understated by about 10% relative when NRBC sit in the denominator, and the error grows with the NRBC count. In a newborn, or a patient with marrow infiltration where NRBC can exceed the leucocytes, the distortion becomes severe.
Controversy, and honesty about the evidence
The convention is not seriously disputed in laboratory haematology. What can and cannot be cited: CLSI H20-A2 specifies two observers counting 200 cells each, quoted verbatim in an open-access ICSH paper. The ICSH flow cytometry reference method treats nucleated red cells as a population distinct from leucocytes, identified by absence of the CD45 antigen. Neither states the reporting rule in words. This is the weakest citation in the design file and is flagged for clinical corroboration.
Configurable
denominatorExcludes — any category can be counted
but kept out of the denominator. per100Reporting sets how it is then expressed. A
laboratory wanting NRBC inside the denominator omits both.
1.2 How the result is rounded
Percentages rarely divide evenly. Three equal categories rounded to whole numbers give 33 + 33 + 33 = 99%, not 100%. Laboratories resolve this differently, so all three approaches are offered.
Fourteen categories with ten cells each — every one truly 7.14%:
| Policy | Result | Total | Worst single-category error |
|---|---|---|---|
| Largest remainder (default) | twelve at 7%, two at 8% | 100% | 0.86 points |
| Largest count | thirteen at 7%, one at 9% | 100% | 1.86 points |
| Independent | all at 7% | 98% | 0.14 points |
Largest remainder (the Hare method, from parliamentary seat allocation): every value is rounded down, then the leftover units go one at a time to the categories closest to rounding up. Totals 100%, and no category is displaced by more than one unit of the last decimal shown. This is the default.
Largest count: the whole rounding difference is added to the category with the most cells. Also totals 100% and is simple to describe, which is why some laboratory procedures specify it. Its weakness is visible above — one category reads 9% against a true 7.14%, which matters where a single percentage meets a diagnostic cut-off.
Independent: each rounded on its own merits. Individually the most faithful; the cost is a report that visibly does not total 100%, which some clinicians read as an error.
Controversy
No standard dictates this — it is a reporting policy. The default is largest remainder because a forced 100% is what readers expect and it achieves that with the least distortion of any individual number. A laboratory whose procedure specifies otherwise should be able to follow its own procedure.
Configurable
rounding: "largest-remainder" |
"largest-count" | "independent". Whichever is chosen is stated in the
report's method note. precision: { "display": 2, "report": 0 }, each 0 to 4.
1.2a How many decimals a count can actually support
The default is two decimal places on screen. It is worth being clear that this is a display convention, not a statement of precision.
A differential of n cells can only produce percentages in steps of 100/n:
| Cells counted | Smallest possible step | 95% interval around an observed 50% |
|---|---|---|
| 100 | 1.0 point | 40.4–59.6% |
| 200 | 0.5 point | 43.1–56.9% |
| 500 | 0.2 point | 45.6–54.4% |
So a 200-cell count displaying 66.67% shows two digits that no possible
count could have changed independently — the next attainable value is 67.00% or 66.00% —
beside an interval roughly twelve points wide. The second
decimal is arithmetic, not measurement.
Two decimals are nonetheless retained as the default for two honest reasons: a low-frequency category such as basophils at 0.50% reads better with them, and a laboratory replacing an existing report format may need to match it. The interval displayed beside each percentage is the figure that states the real precision, and it is why this tool shows one.
A laboratory that finds the extra digits misleading can set
precision.display to 0 or 1. The tool does not impose that choice, but it should not let
the digits imply more than the count carries.
2. How many cells to count
Counting is sampling, so precision improves only with the square root of the number counted: quadrupling the count halves the uncertainty.
Bone marrow — 500 cells. ICSH 2008 §2.6: "At least 500 cells should be counted in at least two smears when a precise percentage of an abnormal cell type is required for diagnosis and disease. At least 300 cells should be counted if the NDC is not essential to the diagnosis." The guidance is conditional, which is often lost when quoted. An American Journal of Clinical Pathology study (2018, 165 cases, five technologists) found 300-cell counts diagnostically equivalent to 500, including 100% sensitivity at the 20% blast threshold — supporting the ICSH 300-cell provision.
Peripheral blood — 200 cells. The CLSI H20-A2 reference method is two independent observers counting 200 cells each.
Controversy
The two-observer element is almost never done in routine practice — it is a reference procedure for evaluating analysers, not a clinical workflow. This tool implements the single-observer count. A two-observer mode is a documented future item, not a current capability.
Configurable
targetCount per specimen type. The target is
advisory and never enforced: you may finish at any count above zero. Finishing
below target produces a note stating the precision achieved rather than blocking you — a
paucicellular aspirate may make a longer count impossible, and you are the one who knows that.
3. The myeloid-to-erythroid ratio
The ratio of white-cell precursors to red-cell precursors. It answers: is this marrow making proportionally too much of one lineage? Conventionally 2:1 to 4:1 is normal. It is always read alongside cellularity, because a proportion says nothing about absolute quantity — a marrow can have a normal M:E ratio and be profoundly hypocellular.
This tool follows ICSH 2008 §2.6 exactly:
myeloblasts + promyelocytes + myelocytes + metamyelocytes
+ band forms + segmented neutrophils + eosinophils
+ basophils + promonocytes + monocytes
M:E = ─────────────────────────────────────────────────────────────
erythroblasts at all stages of differentiation
Lymphocytes, plasma cells and mast cells take no part in either the numerator or the denominator. They are neither myeloid nor erythroid.
Controversy — and it is a real one
ICSH includes monocytes and their precursors. A widely taught alternative excludes them. The argument for exclusion is developmental: that "myeloid" here should mean the granulocytic series specifically. The argument for inclusion — ICSH's position — is that monocytes are myeloid by derivation and the ratio should capture total granulocytic-plus-monocytic production against red-cell production. Both are taught; both appear in textbooks.
| 150 segs, 60 monocytes, 90 erythroblasts | M:E |
|---|---|
| ICSH convention (monocytes included) | 2.3:1 |
| Alternative convention (monocytes excluded) | 1.7:1 |
That difference can move a marrow across the boundary of what a reader considers normal. Comparing an M:E ratio against another laboratory's, or your own from before a change of convention, is meaningless unless both used the same rule.
Configurable
Both conventions ship as selectable presets:
ndc-14 (ICSH, default) and ndc-14 with the alternative M:E composition set in the Configuration Editor (excluding
monocytes). The numerator and denominator are lists of categories, so any other convention can be
expressed. Every report states which convention produced its ratio.
A precision warning specific to ratios. A ratio of two counted proportions carries the sampling error of both, so it is substantially less precise than either percentage alone. You do not have to take this on authority — it follows from the counting model, and the arithmetic is below.
The ratio therefore carries its own interval. The same count of 150 segmented neutrophils, 60 monocytes and 90 erythroblasts, scaled down:
| Cells in the ratio | M:E displayed | 95% interval |
|---|---|---|
| 300 | 2.3:1 | 1.8–3.0 |
| 30 | 2.3:1 | 1.1–5.0 |
| 10 | 2.3:1 | 0.7–8.3 |
The same displayed ratio in all three rows. At 30 cells it is compatible with anything from mild erythroid predominance to marked myeloid predominance. The imprecision is shown rather than merely asserted — the advisory about not over-reading small differences is retained alongside it.
How it is computed. The ratio uses two disjoint groups from one count, so conditioning on the cells that fall in either group leaves a single binomial: M:E is the odds that a cell in the ratio is myeloid. The interval is therefore the odds transform of the same Wilson interval used for every percentage — exact, not approximate, and giving the same answer every time. Fieller's theorem was rejected because it breaks down when there are no erythroid cells, which is the case most in need of a bound; a bootstrap was rejected because it would give a slightly different interval on each run of the same count.
With no erythroid cells the upper bound is shown as ∞. That is the truth, not a failure: the ratio is unbounded above, and the lower bound remains finite and informative.
4. Confidence intervals
You counted 200 cells from a film containing millions. A different 200 cells from the same film would have given a somewhat different answer. That variation is not error in the sense of mistake — it would occur for a perfect observer — it is the arithmetic consequence of sampling. When the tool shows 15.0–26.1% beside an observed 20%, it means: given 40 blasts in 200 cells, true values across roughly that range are consistent with what was observed.
It is not a measure of whether you identified the cells correctly. It cannot detect a misclassification.
| Observed | 100 cells | 200 cells | 500 cells |
|---|---|---|---|
| 20% | 13.3–28.9% | 15.0–26.1% | 16.7–23.7% |
| 5% | 2.2–11.2% | 2.7–9.0% | 3.4–7.3% |
| 1% | 0.2–5.4% | 0.3–3.6% | 0.4–2.3% |
| 0% | 0–3.7% | 0–1.9% | 0–0.8% |
The 20% row. That figure separates acute myeloid leukaemia from myelodysplastic syndrome in the classifications that use it. At 200 cells an observed 20% spans the threshold — the count does not establish which side the true value falls on. At 500 cells it narrows to 16.7–23.7% and still spans it. This is not a deficiency of the software; it is the statistical reality of counting cells, and it is why ICSH directs that the count be extended near a critical threshold.
The 0% row. Counting zero blasts in 200 cells does not exclude blasts. It places them below roughly 1.9%. Reporting a bare "0%" overstates what was established.
Why this method and not the obvious one
The textbook formula is the Wald interval, p ± 1.96 × √(p(1−p)/n). This tool does not use it. Wald performs badly exactly where haematology needs it — small counts and proportions near zero, which is to say rare populations near diagnostic cut-offs. For 2 blasts in 200 cells:
| Wald | −0.38% to 2.38% |
| Wilson (used here) | 0.3% to 3.6% |
A negative lower bound for a blast percentage is not a rounding artefact; it is a result that cannot be put in front of a clinician. The Wilson score interval is bounded within 0–100% by construction and behaves sensibly at zero counts. Brown, Cai and DasGupta's review in Statistical Science (2001) documents Wald's coverage failures at length and recommends Wilson for exactly these conditions.
Not configurable, and why
The interval method is fixed at Wilson. Offering Wald would be offering a method that produces impossible values in this tool's characteristic case — a worse instrument, not a choice. The confidence level is configurable, and interval display can be switched off.
Configurable
confidenceIntervals:
{ "enabled": true, "level": 0.95 } — 0.90, 0.95 or 0.99.
5. The near-threshold advisory
When a confidence interval spans a diagnostic threshold your laboratory has configured, the results screen says so, names the threshold and its basis, and points at Continue Counting.
The reasoning is the ICSH direction to extend the count when an abnormal percentage is very close to a critical threshold. "Very close" had no operational definition until the interval supplied one: an interval that straddles the threshold means the count has not settled the question.
Two deliberate limits. It never blocks you, for the same reason the target count is advisory. And it does not promise resolution — counting more narrows the interval but need not resolve the threshold, since a true value sitting exactly on the line straddles it at any count.
Configurable
thresholds: each with a target category, a percentage,
a label and a citable basis. Shipped defaults are 20% blasts (WHO 2022 / ICC 2022), 5% blasts (the
value ICSH names as an example) and 10% plasma cells. These are defaults, not clinical
instruction — review them against your own reporting practice. Configuring none
disables the advisory.
6. Blast percentage: of what, exactly?
Historically, in marrows with heavily expanded erythropoiesis, blasts were expressed as a percentage of non-erythroid cells — erythroid precursors removed from the denominator. This was the erythroleukaemia rule of the WHO 4th edition. The 2016 revision withdrew it (Arber et al., Blood 2016;127(20):2391–2405), by eliminating acute erythroid leukaemia, erythroid/myeloid subtype. Blasts are counted as a percentage of all nucleated cells. WHO 2022 (5th edition) and the ICC 2022 both retained that denominator; neither made the change.
The two can differ enormously. Take a marrow of 500 nucleated cells: 300 erythroid precursors, and 200 non-erythroid cells of which 45 are blasts.
| Convention | Blast percentage |
|---|---|
| Of all nucleated cells (current, since WHO 2016) | 9.0% |
| Of non-erythroid cells (WHO 4th ed., pre-2016) | 22.5% |
The same slide falls on opposite sides of the 20% boundary depending on the rule. This tool reports blasts as a percentage of all nucleated cells, matching current practice.
Configurable
A subset percentage can be defined as an additional reported figure
— a numerator group over a denominator group of your choosing. The bands-segs-10 preset
demonstrates it, reporting both figures side by side for comparison against historical results.
Because a subset percentage has a real denominator count it also carries a confidence interval, and
it can be given a diagnostic threshold of its own.
7. Which cells belong in the count
ICSH 2008 §2.6 defines the marrow nucleated differential count as: blast cells, promyelocytes, myelocytes, metamyelocytes, band forms, segmented neutrophils, eosinophils, basophils, mast cells, promonocytes and monocytes, lymphocytes, plasma cells, and erythroblasts. The shipped default implements exactly this list, and an automated test holds it there.
ICSH explicitly excludes these from the count
Megakaryocytes, macrophages, osteoblasts, osteoclasts, stromal cells, smudged (lysed) cells, and non-haemopoietic cells such as metastatic tumour cells. Lymphoid aggregates should be commented on but not tallied.
A cell counted into any category enters the denominator. Tally a smudged cell or a tumour cell and every reported percentage falls slightly — including the blast percentage being compared against a threshold. Because the totals stay internally consistent, nothing on screen reveals the error. Record such findings in the morphology comment instead.
Configurable
The category list is entirely yours. A laboratory that considers
"other" too risky can remove it. categoryNotes attaches scope guidance to any category.
8. Known limitations of manual counting
These are limitations of the method, not of this software. The quantified findings come from a four-institution ICSH study of 616 samples comparing manual morphology against flow cytometry and analysers (Hedley et al., 2026).
| Rare populations are least reliable | Blasts correlated well above roughly 10%, but below that suffered "a large degree of imprecision primarily with morphology due to the small number of cells counted". Blasts showed the largest reproducibility variation of any category, a CV just over 15% — exactly the range where diagnostic thresholds sit. |
| Band vs segmented is observer-dependent | Variability attributed partly to "high variation between morphologists in differentiating band and segmented neutrophils". |
| Immature granulocytes lack a standard | "The lack of a traceable standard for what are arbitrary morphologic features." Two competent morphologists may legitimately disagree. |
| Basophils are too few to be precise | Poor correlation between methods, "in part due to the relatively small number of basophils counted by morphology". |
| The smear introduces error | Non-uniform distribution, staining quality and dysplastic features all act before counting begins. ICSH recommends at least two smears where a precise abnormal percentage matters. |
A practical consequence: if your laboratory does not rely on the band/segmented distinction, configure a single combined granulocyte category. Counting what can be distinguished reliably is better than splitting what cannot.
9. What the software does not do
- No cell recognition. Every classification is yours. Press the wrong key and it records the wrong cell; nothing in it can detect that.
- No diagnostic decision. It reports thresholds you configured; it does not interpret them.
- No confidence interval for the M:E ratio (§3).
- No two-observer reference workflow (§2).
- No absolute counts without your input — computed only when you supply an analyser white cell count, and never derived for categories outside the differential.
10. Chosen versus fixed
| Decision | Status | Default |
|---|---|---|
| Cell categories | Configurable | ICSH 2008 §2.6, fourteen categories |
| Keyboard mapping | Configurable | Left-hand ergonomic |
| Target cell count | Configurable | BM 500, PB 200 |
| Denominator: which categories count | Configurable | BM all; PB excludes NRBC |
| Per-100 reporting | Configurable | NRBC per 100 WBC in blood |
| Rounding policy | Configurable | Largest remainder |
| Decimal precision | Configurable | Display 2, report 0 |
| M:E numerator and denominator | Configurable | ICSH, monocytes included |
| Additional subset percentages | Configurable | None by default |
| Diagnostic thresholds | Configurable | 20% and 5% blasts, 10% plasma cells |
| Confidence level, and whether shown | Configurable | 95%, shown |
| Report wording | Configurable | Three institutional templates |
| Confidence interval method | Fixed | Wilson score — §4 |
| That percentages derive from counted cells | Fixed | — |
References
- Lee S-H, Erber WN, Porwit A, Tomonaga M, Peterson LC, for the International Council for Standardization in Haematology. ICSH guidelines for the standardization of bone marrow specimens and reports. Int J Lab Hematol 2008;30(5):349–364.
- Hedley BD, Keeney M, Gambell P, Qu C, Mao J, Davis BH, Wood BL. White Blood Cell Enumeration and Differential by Flow Cytometry: The ICSH WBC Reference Method. Int J Lab Hematol 2026;48(1):93–101. Open access.
- CLSI H20-A2. Reference Leukocyte (WBC) Differential Count (Proportional) and Evaluation of Instrumental Methods, 2nd ed. Wayne PA: CLSI; 2007.
- Brown LD, Cai TT, DasGupta A. Interval estimation for a binomial proportion. Statist Sci 2001;16(2):101–133.
- Is a 500-Cell Count Necessary for Bone Marrow Differentials? Am J Clin Pathol 2018;150(1):84–89.
- WHO Classification of Haematolymphoid Tumours, 5th ed., 2022; and the International Consensus Classification, 2022.
- Comar SR, Malvezzi M, Pasquini R. To follow or not to follow the recommendations regarding microscopic analysis of the CLSI H20-A2… Rev Bras Hematol Hemoter 2015;37(1):69–70. Open access.
WBC ΔΣ is a counting and calculation aid for trained laboratory personnel. It performs no cell identification and makes no diagnostic decision. Any laboratory deploying it should validate it locally under its own quality management system.