Standard normal distribution, middle 95%
The area between z = −1.96 and z = 1.96 is 0.9500, the basis of 95% confidence intervals.
Bell Curve Examples
Each graph below is what this bell curve maker draws from the example's numbers, unedited. Open one in the tool to see its inputs and change anything.
68-95-99.7 rule for IQ scores
Mean 100, SD 15: the bands show 34.1%, 13.6%, 2.1% and 0.1% of scores, with z-scores under the axis.
Exam grades with a failing cut-off
Mean 72, SD 12: the share of students below 60 is P(X < 60) = 0.1587, with lines at the D, C, B and A boundaries.
Two bell curves on one graph
Control (mean 50, SD 5) and treatment (mean 62, SD 7) overlaid, with Cohen's d.
99% confidence interval with t
x̄ = 5.95, s = 2.68, n = 20: t* = 2.8609 with 19 degrees of freedom gives the interval [4.2355, 7.6645].
Left-tailed z test
α = 0.05: the rejection region is z < −1.645; z = −1.75 falls in it, p = 0.0401, so H₀ is rejected.
How to Make a Bell Curve
Three steps, no formulas to type
The curve is drawn from the normal density function, so the shape, the height of the peak and every shaded area are exact for your numbers.
1
Enter what you know
A mean and standard deviation, a list of raw data, your confidence interval results or a hypothesis test. You can also paste the whole problem into the AI tab and it fills in the numbers.
2
Shade the area you need
Left, right, between or outside two values, in x or z units. The probability appears at once, and Show steps writes out the z-scores and the arithmetic.
3
Download the graph
Save a 4K PNG at 300 DPI for slides and documents, or an SVG whose text you can still edit in PowerPoint, Illustrator or Inkscape. Both are free, with no watermark.
One Bell Curve Maker, Three Workflows
Students · Researchers · Teachers
Whether you are working through a statistics problem set, preparing a figure for a paper, or making a handout for class, the same tool draws the curve and does the math.
Statistics Students
From intro stats to inference
Enter the numbers from your problem and see the curve, the shaded area and its probability, with each step written out so you can check your own working.
- z-scores, probabilities, confidence intervals and hypothesis tests
- Show steps lays out the formula with your numbers
- Paste a whole problem with parts a), b), c) and AI sets up one chart per part
Researchers
Figures you can defend
Every curve is computed from the density function, so the y-axis, the critical values and the shaded areas hold up when a reviewer checks them. Download an SVG to restyle it with the rest of your figures.
- Editable SVG with real text, not outlines
- 4K PNG at 300 DPI for posters and print
- t distributions with any degrees of freedom
Teachers
Prep less, teach more
Make the 68-95-99.7 picture, a grade distribution or a rejection region for tomorrow's lesson in a minute, in color or grayscale for the photocopier.
- 68-95-99.7 bands with z-scores under the axis
- Two curves on one graph for comparing groups
- Grayscale palette for printed handouts
What This Bell Curve Maker Does
Exact math, clean graphs
Everything is calculated in your browser from the formulas in your textbook, then drawn as a clean, labeled graph.
Exact
Drawn From the Formula
Not an AI picture of a curve
The curve is plotted point by point from the normal density, so the peak of N(74, 6²) sits at 0.0665 on the y-axis and a shaded area is exactly the probability printed next to it.
Probability
Any Area, With Its Probability
Left, right, between, outside
Shade below, above, between or outside one or two values, typed as x values or as z-scores. The tool works out Φ(z) and the area to four decimal places.
Inference
Confidence Intervals and Hypothesis Tests
z and t, one or two tails
Draw a confidence interval for a mean or a proportion, or the rejection region of a z or t test. Add your test statistic to get the p-value and the decision.
Data
From Raw Data or Two Groups
Histogram plus fitted curve
Paste raw values to get the mean, the sample standard deviation and a normal curve over the histogram, or overlay two curves to compare groups with Cohen's d.
AI
Paste the Whole Problem
AI reads the numbers, code does the math
Paste a word problem and AI fills in the inputs, one chart per part. It only copies numbers from your text; the probabilities are still computed by the tool. 2 credits per run.
Export
Steps, Then a Clean Download
4K PNG and editable SVG
Open Show steps to see the z-scores and the arithmetic, then download a 4K PNG at 300 DPI or an editable SVG. Drawing and downloading are free, with no watermark.
What Students and Teachers Tell Us
Feedback we've received from people who use the bell curve maker for homework, teaching and reports. They asked us not to publish their names.
I
Intro statistics student
I paste the whole homework problem into the AI tab and get one graph per part, a), b) and c). The shaded areas finally match the answers in my textbook.
H
High school statistics teacher
I build every normal-curve slide for class here now. I type the mean and SD, shade the area, and download a clean PNG with no watermark.
Drawing is free; credits are for AI
Making and downloading bell curves costs nothing. Credits are used when AI reads a pasted problem, and by the AI tools elsewhere on Vizcept.
Student or teacher? Apply for an education discount
Bell Curve Maker FAQ
FAQ
A bell curve maker draws the graph of a normal (Gaussian) distribution from its mean and standard deviation and shades the area you ask for. This one also works out the probability of that area, confidence intervals and hypothesis tests, and shows the steps.
Drawing the curve, shading areas, the steps and the PNG and SVG downloads are free, and the downloads carry no watermark; that part runs in your browser and never uses credits. Reading a pasted problem with AI uses 2 credits per run, because each run calls a language model. New accounts get 5 credits plus daily check-in credits, and plans and credit packs are on the pricing page. Desmos and GeoGebra can also draw a normal curve for free, but you type the function and the shading yourself and they do not write out the steps.
Enter the mean and standard deviation, choose Left, Right, Between or Outside under Shade the area, and type the cut-off values. The tool converts each value to a z-score with z = (x − μ) ÷ σ, finds Φ(z), and shows the area as a probability, for example P(X < 60) = 0.1587 for a mean of 72 and an SD of 12.
Enter the class mean and standard deviation, for example 72 and 12. To show the share of students who failed, shade Left of 60. To mark the grade boundaries, type one per line under Vertical lines, such as 60 D, 70 C, 80 B and 90 A. To fit the curve to actual scores instead, paste them in the Data tab.
Yes. Turn on 68-95-99.7 rule bands and the curve is split at μ ± 1σ, 2σ and 3σ, with 34.1%, 13.6%, 2.1% and 0.1% written in each band. Turn on z-scores under the axis to label the bands −3 to 3 as well.
Yes. In the CI tab, enter x̄, s or σ, n and the confidence level (or p̂ and n for a proportion) to get the standard error, the critical value, the margin of error and the interval on the sampling distribution. In the Test tab, choose z or t, the tail and α to shade the rejection region; add your test statistic to get the p-value and the decision.
Yes. Paste the values in the Data tab, one per line or separated by spaces, commas or semicolons; decimal commas such as 5,6 are read too. The tool calculates the mean and the sample standard deviation (n − 1), draws the fitted normal curve over a histogram of your data, and lets you shade areas as usual.
Yes. Turn on Add a second curve and enter its mean and standard deviation, plus a name for each curve. Both are drawn on the same axes in different colors, with a legend and Cohen's d in the results.
Yes. Paste the problem in the AI tab, in English, Spanish or another language, and it fills in the inputs, one chart for each part such as a), b) and c). AI only copies the numbers in your text; every probability, z-score, interval and p-value is then calculated by the tool, so the answers do not depend on the AI doing arithmetic. It uses 2 credits per run.
It matches normalcdf on a TI-84, NORM.DIST in Excel and pnorm in R. A printed z-table rounds z to two decimals, so the fourth decimal of a probability can differ slightly; the tool shows the exact z it used in Show steps.
PNG at 3840 pixels wide (4K) and 300 DPI, for slides, documents and posters, and SVG with editable text for PowerPoint, Illustrator, Inkscape or Figma. Both downloads are free and have no watermark.
Yes. The curves are computed from the density function, so the axes, areas and critical values are exact. Download the SVG to match your other figures' fonts and colors, or the 4K PNG to insert as is.
R, Python and Excel give the same numbers, but you write code or set up a chart series to draw and shade the curve. Here you type the values and get the labeled graph, the probability and the steps at once.
Make Your Bell Curve Now
Exact curve, shaded area and probability, calculated in your browser. Download a 4K PNG or an editable SVG for free.
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