RDW-CV to RDW-SD Calculator
RDW-CV to RDW-SD Calculator
Estimate RDW-SD in femtolitres from the RDW-CV your analyser printed and the MCV — with the Gaussian coefficient most versions of this conversion leave out, and an honest account of where the estimate fails.
Estimate RDW-SD from RDW-CV and MCV
RDW-CV + MCV → RDW-SD (fL)RDW-CV 13.0%, MCV 90 fL — an ordinary healthy adult
Formula and where the coefficient comes from
= 3.5882 × RDW-CV × MCV ÷ 100 (fL)
- RDW-CV
- the percentage your analyser printed. It is defined as (1 standard deviation of the red cell volume distribution ÷ MCV) × 100, so it is a relative measure and depends on the MCV
- RDW-SD
- not a standard deviation, despite the name. It is the width of the red cell volume histogram at 20% of peak height, in femtolitres, measured directly off the curve and independent of the MCV
- 1 SD
- = RDW-CV × MCV ÷ 100, which is the RDW-CV definition rearranged. This is the step that puts the MCV back into an absolute width
- 2√(2 ln 5)
- = 3.588245… — the full width of a Gaussian at one fifth of its peak height, in standard deviations. Set exp(−(x−μ)²∕2σ²) = 0.20 and you get |x−μ| = σ√(2 ln 5), so the full width is twice that
- why it matters
- the version of this conversion circulating without the coefficient — RDW-CV × MCV ÷ 100 — returns about 11.7 fL for a normal adult, roughly a quarter of the lower reference limit of 39 fL. It would report profound uniformity in every healthy person
- the assumption
- that the volume distribution is Gaussian. It is not, and it is least Gaussian in the dimorphic and skewed populations where an RDW is most interesting — which makes this an estimate rather than a conversion
Worked example
RDW-CV 13.0%, MCV 90 fL — an ordinary healthy adult
Recover the standard deviation of the volume distribution: 1 SD = RDW-CV × MCV ÷ 100 = 13.0 × 90 ÷ 100 = 11.7 fL
For a Gaussian, the full width at 20% of peak height is 2√(2 ln 5) standard deviations. ln 5 = 1.6094, so 2 ln 5 = 3.2189, √3.2189 = 1.7941, and twice that is 3.5882
RDW-SD ≈ 3.5882 × 11.7 = 42.0 fL
42.0 fL sits inside the published RDW-SD reference interval of 39 to 46 fL, which is the check that the coefficient belongs there
Now the error this page exists to correct. The version of the formula circulating without the coefficient gives RDW-CV × MCV ÷ 100 = 11.7 fL — that is the standard deviation, not the histogram width, and it is about a quarter of the lower reference limit. Applied to a healthy adult it reports a profoundly narrow distribution
The 11.7 fL figure is not meaningless; it is simply a different quantity. It is the actual standard deviation of this patient's red cell volumes, which is a useful number and is not what a report labelled RDW-SD contains
And the caveat that goes with the answer: 42.0 fL assumes the volume distribution is Gaussian. A patient with two populations of cells has a distribution with two peaks, for which no standard deviation describes the width at any particular height, and that is exactly the patient whose RDW someone is looking at
The two indices, side by side
| RDW-CV | RDW-SD | |
|---|---|---|
| What it is | Coefficient of variation of the red cell volume distribution | Width of the red cell volume histogram at 20% of peak height |
| How it is obtained | Calculated: (1 SD ÷ MCV) × 100 | Measured directly off the distribution curve |
| Unit | Per cent | Femtolitres |
| Depends on the MCV? | Yes — arithmetically, by construction | No |
| Reference interval (Cleve Clin J Med) | 11% to 16% | 39 to 46 fL |
| Reference interval (ClinLabNavigator) | 11.0% to 15.0% | 36 to 47 fL |
| Reference interval (StatPearls) | 11.5% to 15% | Not given |
| Reported by | Almost every analyser; usually printed as ‘RDW’ | Some analysers, alongside or instead of RDW-CV |
| Behaviour in microcytosis | Rises partly because the denominator fell | Unaffected by the MCV |
| Sensitivity / specificity for iron deficiency anaemia in one 271-patient series | 45.2% / 68.5% | 33.2% / 64.8% |
What the estimate does across the MCV range, at three RDW-CVs
| MCV | RDW-CV 13% (normal) | RDW-CV 16% (raised) | RDW-CV 22% (markedly raised) |
|---|---|---|---|
| 60 fL | 28.0 fL | 34.4 fL | 47.4 fL |
| 70 fL | 32.7 fL | 40.2 fL | 55.3 fL |
| 80 fL | 37.3 fL | 45.9 fL | 63.2 fL |
| 90 fL | 42.0 fL | 51.7 fL | 71.0 fL |
| 100 fL | 46.6 fL | 57.4 fL | 78.9 fL |
| 110 fL | 51.3 fL | 63.2 fL | 86.8 fL |
| 120 fL | 56.0 fL | 68.9 fL | 94.7 fL |
Why 3.5882, step by step
| Step | Expression | Value |
|---|---|---|
| Gaussian height relative to peak | exp(−(x−μ)² ∕ 2σ²) | — |
| Set it to 20% of peak | exp(−(x−μ)² ∕ 2σ²) = 0.20 | — |
| Take logs | (x−μ)² ∕ 2σ² = ln 5 | ln 5 = 1.60944 |
| Half-width in standard deviations | |x−μ| ∕ σ = √(2 ln 5) | 1.79412 |
| Full width in standard deviations | 2√(2 ln 5) | 3.58825 |
| Standard deviation from RDW-CV | 1 SD = RDW-CV × MCV ∕ 100 | 11.7 fL at 13% and 90 fL |
| Estimated RDW-SD | 3.58825 × 1 SD | 42.0 fL |
RDW-SD is not a standard deviation, and that is the whole problem
Two red cell distribution widths appear on full blood count reports and they are different quantities with confusingly similar names. RDW-CV is a percentage: it is the coefficient of variation of the red cell volume distribution, the standard deviation of that distribution divided by the mean cell volume and multiplied by a hundred. Almost every analyser reports it, and most reports label it simply ‘RDW’. RDW-SD is a width in femtolitres, and despite the name it is not a standard deviation. It is the width of the red cell volume histogram measured at 20% of its peak height, read directly off the curve and independent of the mean.
That difference has a consequence the rest of this page is about. RDW-CV has the MCV in its denominator, so at a constant absolute spread of cell volumes it rises as the cells get smaller and falls as they get larger. A microcytic patient’s RDW-CV is therefore inflated partly for arithmetical reasons, and a macrocytic patient’s is deflated. RDW-SD has no such dependence, which is exactly why it was introduced and why it is described as the purer measure of anisocytosis. If you have one and want the other — because a paper, a protocol or a colleague quotes the one your analyser does not print — the conversion has to put the MCV back in.
And that is where the commonly circulated version goes wrong. Recovering the standard deviation from the RDW-CV is straightforward: 1 SD = RDW-CV × MCV ÷ 100, which for a normal adult at 13.0% and 90 fL is 11.7 fL. The mistake is to stop there and call 11.7 fL the RDW-SD. It is not: 11.7 fL is the standard deviation, and RDW-SD is the width of the curve at a fifth of its height, which for a Gaussian is 2√(2 ln 5) = 3.5882 standard deviations. The correct estimate for that patient is 42.0 fL, comfortably inside the published reference interval of 39 to 46 fL. The version without the coefficient returns 11.7 fL, roughly a quarter of the lower limit, and would report profound uniformity of red cell size in every healthy person who used it.
The coefficient is derived rather than quoted, because no source was found that publishes it. Set the Gaussian height function exp(−(x−μ)²∕2σ²) equal to 0.20, take logs, and the half-width at one fifth of peak height is σ√(2 ln 5); double it for the full width. The derivation is printed on this page so it can be checked. What cannot be derived away is its single assumption: that the red cell volume distribution is Gaussian.
It is not, and it is least Gaussian in exactly the anaemias in which anybody would want this conversion. A combined iron and B12 deficiency produces a distribution with two peaks, and a curve with two peaks has no standard deviation that describes its width at any given height. A recent transfusion does the same. A brisk reticulocytosis skews the curve to the right rather than widening it symmetrically. In all three cases the estimate on this page will be wrong by an amount that cannot be predicted from the inputs. There is direct evidence that the two indices are not interchangeable: in 271 consecutive patients on a single analyser, RDW-CV reached 45.2% sensitivity and 68.5% specificity for iron deficiency anaemia against 33.2% and 64.8% for RDW-SD. If one were a fixed multiple of the other at a given MCV, they could not rank the same patients differently, and they do.
So this page computes the estimate, prints both published intervals beside it so the two can be compared directly, and states plainly what it is: a translation that is good enough to read a paper or a protocol with, and not a substitute for the analyser’s own RDW-SD when a decision depends on it. If the question is clinical rather than arithmetical, the RDW is far more useful read beside the other indices than converted — the MCV-based anaemia type classifier does that with the reticulocyte count and iron studies, the red cell indices interpreter with the MCV and MCHC, and the MCV calculator computes the mean this conversion needs.
Frequently asked questions
How do you convert RDW-CV to RDW-SD?
Multiply the RDW-CV by the MCV, divide by 100 to recover the standard deviation of the red cell volume distribution, then multiply by 3.5882 — the full width of a Gaussian at 20% of its peak height, expressed in standard deviations. So RDW-SD ≈ 3.5882 × RDW-CV × MCV ÷ 100. At RDW-CV 13.0% and MCV 90 fL that gives 42.0 fL, inside the published interval of 39 to 46 fL. It is an estimate, not an exact conversion.
Why is the 3.5882 coefficient needed?
Because RDW-SD is not a standard deviation. It is the width of the red cell volume histogram at 20% of peak height, and for a Gaussian that width is 2√(2 ln 5) = 3.5882 standard deviations. Leaving the coefficient out returns the standard deviation instead — 11.7 fL for a normal adult, against a reference interval of 39 to 46 fL. That version would call every healthy person profoundly uniform in red cell size.
What is the difference between RDW-CV and RDW-SD?
RDW-CV is a percentage, calculated as the standard deviation of the red cell volume distribution divided by the MCV, times 100; it therefore depends on the MCV and rises in microcytosis for arithmetical reasons. RDW-SD is a width in femtolitres, measured directly off the histogram at 20% of peak height, and is independent of the MCV. Published intervals are roughly 11% to 16% for RDW-CV and 39 to 46 fL for RDW-SD, though sources differ.
Is the estimated RDW-SD reliable?
It is reliable enough to read a paper or a protocol with and not reliable enough to base a decision on. It assumes the red cell volume distribution is Gaussian, and that assumption fails in dimorphic populations, after transfusion and with a brisk reticulocytosis — which are the situations in which somebody would want the number. The evidence that the two indices are not interchangeable is that they perform differently as tests: in one 271-patient series, RDW-CV reached 45.2% sensitivity for iron deficiency anaemia against 33.2% for RDW-SD.
Which RDW does my report show?
If it is a percentage, it is RDW-CV — that is what almost every analyser reports and it is usually printed as ‘RDW’ with no suffix. If it is in femtolitres, it is RDW-SD. Some analysers report both. If the report gives a number around 13 it is a percentage; a number around 42 is femtolitres.
What does a high RDW mean?
That the red cells vary in size — anisocytosis. The common causes are iron, B12 and folate deficiency; a raised RDW often appears in iron deficiency before the MCV falls, which makes it an early clue. Reticulocytosis after bleeding or haemolysis widens it because reticulocytes are larger than mature cells, and recent transfusion widens it by mixing two populations. A low RDW is not consistently associated with any haematological disorder.
Related calculators
References
- Three neglected numbers in the CBC: the RDW, MPV, and NRBC count. Cleve Clin J Med. 2019;86(3):167 — the RDW-SD reference interval of 39 to 46 fL and the RDW-CV interval of 11% to 16%, the statement that the RDW is the width of the distribution curve of corpuscular volume rather than of the cell, and the behaviour of the RDW in iron deficiency against thalassaemia.
- ClinLabNavigator. Red cell distribution width — RDW-CV = 1 SD × 100 ÷ MCV with a reference range of 11.0% to 15.0%; RDW-SD as the actual measurement of the width of the red cell distribution curve, in femtolitres, reference range 36 to 47 fL, and not influenced by the MCV.
- The Blood Project. Red cell distribution width (RDW) — RDW-SD as “the actual width (in fL) of the red cell size distribution curve (measured at the 20% height level)”, RDW-CV as a relative measure inversely proportional to the MCV, and the behaviour of both in bimodal red cell populations.
- Curry CV. Red cell distribution width. Medscape Reference — the definition of RDW-SD as the width of the red cell size distribution histogram at the 20% height level, in femtolitres.
- A review of RDW-CV and RDW-SD measurements in patients with iron deficiency anaemia in an acute care hospital in Singapore. Clin Chem. 2023;69(Supplement_1):hvad097.133 — 271 patients on a Sysmex XN-9000; RDW-CV sensitivity 45.2% and specificity 68.5% against RDW-SD 33.2% and 64.8%, with RDW-SD reference limits taken from a College of American Pathologists survey.
- Normal and abnormal complete blood count with differential. In: StatPearls (NBK604207) — normal RDW 11.5% to 15%, elevated above 15%, and the MCV × RDW classification of anaemia.
Medical Disclaimer: The tools and content provided here are for educational and reference purposes only. They are not intended to substitute for professional medical advice, diagnosis, or treatment. Clinical decisions should always be based on the comprehensive assessment of a qualified healthcare professional.