gives lists of the elements of data whose values lie in successive integer bins.


gives lists of the elements of data whose values lie in successive bins specified by binspec.


gives the lists of the labels inds specified by the binning of data.


  • BinLists drops elements whose values do not correspond to real numbers.
  • The following bin-width specifications binspec can be given:
  • dxbins of width dx »
    {xmin,xmax,dx}bins of width dx from xmin to xmax »
    {{b1,b2,}}the intervals [b1,b2), [b2,b3), »
    xbins,ybins,bin specifications for multivariate data understood as {{x1,y1,},{x2,y2, },} »
  • BinLists[data,dx] takes the bin boundaries to be integer multiples of dx, with the first bin starting at Ceiling[Min[data]-dx,dx] and the last bin ending at Floor[Max[data]+dx,dx].
  • BinLists[data] is equivalent to BinLists[data,1].
  • In BinLists[data,{xmin,xmax,dx}], elements are placed in bin i when their values satisfy .
  • BinLists[data,{xmin,xmax}] is equivalent to BinLists[data,{xmin,xmax,1}].
  • In BinLists[data,{{b1,b2,}}], elements are put in bin i when their values satisfy .
  • In the form BinLists[data,{{b1,b2,}}], the bi at each end can be -Infinity and +Infinity.
  • If the bi do not form an increasing sequence, they are automatically sorted by BinLists.
  • If data consists of length-n sublists, then n bin specifications must be given, and BinLists[data,] yields an array of lists of depth n.
  • Within each bin, elements appear in the same order as in the original data.
  • The data can have the following forms and interpretations:
  • {x1,x2,}list of real numbers or quantities »
    {{x1,y1,},{x2,y2,},}list of vectors of the same dimension »
    SparseArrayan array equivalent to Normal[data] »
    QuantityArrayarray of column-compatible quantities »
    TimeSeries, TemporalData,vector or array of values (the time stamps ignored) »
  • Labels inds for the input elements xi can be given in the following formats: »
  • {x1,x2,}use the xi themselves (no labels by default)
    {x1,x2,}Automaticuse integer labels
    {x1,x2,}{v1,v2,}a rule between all the elements and all the labels
    {x1v1,x2v2,}a list of rules between the element xi and its label vi


open allclose all

Basic Examples  (3)

List elements in bins of a specified width:

Make lists of elements in bins of width 1 from 0 to 10:

List elements in a sequence of ranges:

Scope  (12)

Basic Uses  (8)

List squares mod 3 and 5 in two-dimensional unit bins:

List random pairs in bins of width 0.25 in both dimensions:

List multidimensional data in ranges:

Bin data in any dimension:

Bin data, ignoring values that are not real:

Bin data of any precision:

SparseArray data can be used just like dense arrays:

Bin data from a time series:

The time stamps are ignored:

Data with Quantities  (3)

Bin quantity data:

Automatic bins:

Specify bin width:

Bins of fixed width, minimum and maximum:

Specify bin intervals:

Bin mixed-type data:

The units are compatible for each dimension:

Specify bin width for each dimension:

QuantityArray can be used just like arrays:

Automatic bins:

Specify bin width in compatible units:

Data with Labels  (1)

Bin data with output as an array of labels:

Bin data with default integer labels:

Applications  (1)

Visualize two-dimensional data in bins:

Properties & Relations  (1)

The length of BinLists is equivalent to the results from BinCounts:

For a list of vectors:

Possible Issues  (4)

Binning intervals are closed on the left:

For data involving quantities, the bin specification must be given in compatible units:

Matrix data must have unit-compatible columns:

The bins obtained using the specification {min,max,dx} may not include all data points:

Specify the min and max so all data points are included in the bin covering:

Alternatively, use the width-only bin specification dx:

Wolfram Research (2007), BinLists, Wolfram Language function, (updated 2023).


Wolfram Research (2007), BinLists, Wolfram Language function, (updated 2023).


Wolfram Language. 2007. "BinLists." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023.


Wolfram Language. (2007). BinLists. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_binlists, author="Wolfram Research", title="{BinLists}", year="2023", howpublished="\url{}", note=[Accessed: 05-March-2024 ]}


@online{reference.wolfram_2024_binlists, organization={Wolfram Research}, title={BinLists}, year={2023}, url={}, note=[Accessed: 05-March-2024 ]}