Paste a list of numbers and choose how to group them into bins. You instantly get a histogram, a frequency distribution table with relative and cumulative frequencies, and summary statistics, ready to download as PNG or CSV.
Last updated:
Bins
Chart
Frequency table
Advertisement
Advertisement
How to use the Histogram Maker
Paste your numbers separated by commas, spaces, tabs or new lines (a spreadsheet column works).
Choose the bins: keep Auto, enter a number of bins, or set an exact bin width and start value.
Pick the y-axis (frequency, relative frequency or density) and options like the normal curve or count labels.
Add a title and axis label, and choose a bar color.
Download PNG for the chart and Download CSV for the frequency table.
How a histogram is built
Find the range: maximum − minimum.
Choose the number of bins k (or a bin width). Bin width = range ÷ k, usually rounded up to a clean number.
Set the bin edges: start at or just below the minimum and add the width repeatedly until the maximum is covered.
Count how many values fall in each bin. A bin [a, b) includes a but not b; the last bin includes its upper edge.
Draw touching bars whose heights are the counts (or relative frequencies).
Example with the sample commute data (n = 40, minimum 12, maximum 95). Sturges' rule gives k = ⌈log₂ 40⌉ + 1 = 7 bins; 83 ÷ 7 ≈ 11.9. The tool then picks the clean width (1, 2, 2.5 or 5 × a power of ten) whose bin count is closest to 7: a width of 10 gives the bins 10–20, 20–30, … 90–100. Choose Number of bins with rounding switched off to get exactly 7 bins of width 11.86.
Bin rules compared
Rule
Formula
Best for
Sturges
k = ⌈log₂ n⌉ + 1
Small, roughly symmetric data sets (n under about 200)
Square root
k = ⌈√n⌉
Quick default used by many spreadsheet tools
Freedman–Diaconis
width = 2 × IQR ÷ ∛n
Skewed data or data with outliers (uses the IQR, which ignores extremes)
Scott
width = 3.49 × s ÷ ∛n
Larger, roughly normal data sets
Too few bins hide the shape; too many make the chart noisy with gaps. If two rules disagree, look at both: real features like two peaks (a bimodal distribution) should appear in either.
Reading the shape
Symmetric, bell-shaped: mean ≈ median; the normal curve fits well.
Right-skewed (long tail to the right, like incomes or commute times): mean > median.
Left-skewed: mean < median.
Bimodal: two peaks, often two groups mixed together.
Isolated bars far from the rest: possible outliers; check them with the Box Plot Maker.
Frequently asked questions
How many bins should a histogram have?
There is no single right answer. Sturges' rule uses k = ⌈log₂(n)⌉ + 1 bins and works well for small, roughly normal data. The square-root rule uses k = ⌈√n⌉. The Freedman–Diaconis rule sets the bin width to 2 × IQR / ∛n and handles skewed data and outliers better. Try a few and pick the one that shows the shape clearly.
How do I calculate the bin width?
Bin width = (maximum − minimum) ÷ number of bins. For example, data from 12 to 87 with 5 bins gives a width of 75 ÷ 5 = 15, so the bins are 12–27, 27–42, 42–57, 57–72 and 72–87. Rounding the width up to a clean number such as 5, 10 or 20 makes the chart easier to read.
Which bin does a value on the boundary go into?
Bins include their lower edge and exclude their upper edge, written [a, b). A value of exactly 20 with bins 10–20 and 20–30 is counted in 20–30. The last bin also includes its upper edge so the maximum is always counted.
What is the difference between frequency, relative frequency and density?
Frequency is the count of values in each bin. Relative frequency is that count divided by the total, shown as a percentage, so all bars add up to 100%. Density is relative frequency divided by the bin width, so the total area of the bars equals 1, which is what the normal curve is compared against.
What is the difference between a histogram and a bar chart?
A histogram shows the distribution of one numeric variable: the bars touch because the bins cover a continuous range. A bar chart compares separate categories, so its bars usually have gaps and can be reordered.
What does the normal curve show?
It is the bell curve with the same mean and standard deviation as your data, scaled to the histogram. If the bars follow it closely the data is roughly normally distributed; skew, multiple peaks or heavy tails show up as clear departures.
Is my data uploaded?
No. The histogram is calculated and drawn in your browser. Your data is only stored in your browser's local storage so it is still there next time.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.