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In short: std(A) returns the sample standard deviation of the data in A, dividing by N−1. Pass 1 as the second argument (std(A,1)) to divide by N instead. This guide is for researchers and analysts who need to compute, check and report a standard deviation in MATLAB and avoid the common dimension, missing-value and cross-software mistakes.
What std is used for in research
The standard deviation summarises how spread out values are around their mean. In research it is reported alongside means in descriptive tables, used to standardise variables, and used as the scale for error bars and effect sizes. MATLAB’s std function computes it for vectors, matrices and N-dimensional arrays. Per the MathWorks reference page (read 2026-11-08), the default definition is S = √( (1/(N−1)) Σ|Aᵢ − μ|² ), where μ = (1/N) Σ Aᵢ: the mean always uses N, and the default sum of squares is divided by N−1.
Install or access
std is part of base MATLAB, so no toolbox is needed. The official reference is the MathWorks documentation page for std (listed under Sources). GNU Octave, a free program with a largely compatible syntax, also provides std (see the alternatives table below).
Step-by-step: computing a standard deviation
1. Standard deviation of a vector or of matrix columns
Call std(A). With no dimension given, MathWorks documents that it operates along the first array dimension whose size is not 1. For a matrix, that means one value per column. The documentation example uses A = [4 -5 1; 2 3 5; -9 1 7], and std(A) returns 7.0000 4.1633 3.0551.
2. Choose N−1 or N (sample or population)
The second argument is the normalisation weight w. w = 0 (the default) divides by N−1; w = 1 divides by N, giving the square root of the second moment about the mean. Use the default when your data are a sample and you want to estimate the spread of the wider population; use w = 1 when your data are the whole population of interest. A worked check by hand, for the eight values x = [2 4 4 4 5 5 7 9]: the mean is 5 and the squared deviations sum to 32. std(x,1) is √(32/8) = 2, and std(x) is √(32/7) ≈ 2.1381.
3. Standard deviation along rows
To choose a dimension while keeping the default normalisation, pass 0 as the second argument: std(A,0,2). The documentation example A = [6 4 23 -3; 9 -10 4 11; 2 8 -5 1] gives 11.0303; 9.4692; 5.3229, one value per row. Do not write std(A,2) expecting dimension 2: the second argument is always the weight w.
4. Several dimensions, or every element
Pass a vector of dimensions, as in std(A,0,[1 2]), to reduce over several dimensions at once (for a 3-D array this returns one value per page). Pass "all", as in std(A,0,"all"), to use every element in A.
5. Ignore missing values
The default missingflag is "includemissing": if a slice contains a missing value, its output is NaN. Add "omitmissing", as in std(A,0,"omitmissing"), to ignore missing values; a slice that is entirely missing still returns NaN. For numeric and duration data the older flag names "includenan" and "omitnan" are also documented, and "includenat"/"omitnat" for datetime.
6. Weighted standard deviation
Give w as a vector of nonnegative weights whose length matches the operating dimension. With A = [1 5; 3 7; -9 2] and w = [1 1 0.5], [S,M] = std(A,w) returns S = 4.4900 1.8330 and the weighted mean M = -0.2000 5.2000.
Output and how to read it
Shas the same units as the data, and is never negative.- The optional second output
Mis the mean (the weighted mean when you supply weights), so[S,M] = std(A)gives both for a descriptive table. - A scalar input returns
0, and a 0-by-0 input returnsNaN. - Report which normalisation you used. The sample (N−1) version is the usual default for inferential work.
Troubleshooting
| Symptom | Cause per the documentation | Fix |
|---|---|---|
| Output is NaN for a column or the whole result | A missing value is in the slice and the default is "includemissing" |
Use std(A,0,"omitmissing") |
| Still NaN after omitting | The slice is entirely missing | Check that column or row of the data |
| Got one value per column when you wanted per row | Default operates along the first non-singleton dimension | Use std(A,0,2) |
std(A,2) does not give row results |
The second argument is the weight w, not the dimension |
Write std(A,0,2) |
Result is 0 |
Scalar input (or a single observation) | Confirm you passed the full data array |
| Weighted call errors | The length of w must match the operating dimension |
Resize the weight vector |
Free alternatives, and a cross-tool trap
The same data give different numbers in different programs if the default normalisation differs. The NumPy documentation notes that other libraries often default to ddof=1, unlike NumPy’s default of ddof=0.
| Tool | Call | Default divisor | Switch to the other |
|---|---|---|---|
| MATLAB | std(A) |
N−1 | std(A,1) for N |
| GNU Octave (free) | std(x) |
N−1 (w = 0) |
std(x,1) for N |
| NumPy (free) | np.std(a) |
N (ddof=0) |
np.std(a, ddof=1) for N−1 |
For the array [[1,2],[3,4]], np.std(a) is √(5/4) ≈ 1.1180 while ddof=1 gives √(5/3) ≈ 1.2910 (hand-calculated). Octave’s std also accepts w, a dimension, "all" and a nanflag ("omitnan" excludes NaNs).
Related CASRAI guides: MATLAB normal distribution, fitting in MATLAB, polyval in MATLAB, NumPy polyfit.
FAQ
Does MATLAB std use N or N−1?
N−1 by default (w = 0). Use std(A,1) to divide by N.
How do I get the standard deviation of each row?
Use std(A,0,2). The 0 keeps the default normalisation and 2 selects the row dimension.
How do I get one standard deviation for a whole matrix?
Use std(A,0,"all").
Why does std return NaN?
By default any missing value in a slice makes that output NaN. Use the "omitmissing" flag.
Why is my MATLAB result different from NumPy?
NumPy divides by N by default, MATLAB by N−1. Set ddof=1 in NumPy to match.
Sources
- MathWorks, std: Standard deviation (MATLAB documentation), read 2026-11-08.
- NumPy, numpy.std, read 2026-11-08.
- GNU Octave, Descriptive Statistics, read 2026-11-08.
