Normal Distribution Calculator
Working with bell-curve probabilities? Enter the mean, standard deviation and your value, choose below, above or between, and get the probability instantly — with the Z-score steps shown so students can check their working and understand the math.
How to use
- Enter the mean and standard deviation.
- Choose the mode and enter the X value(s).
- Steps will be shown for Z-score = (X − μ) / σ.
Note: Probability is calculated from standard normal table (Z-table) values. Empirical rule: about 68% of the data lies within μ ± 1σ, about 95% within ± 2σ, and about 99.7% within ± 3σ.
Tips
- Use the between mode when you need the probability of a range, not a single point.
- The tool shows the Z-score steps, so students can verify their manual working.
- Results assume a true normal distribution — check your data is roughly bell-shaped first.
- A probability of 0.95 above a value is the same as 0.05 below it; flip the mode to sanity-check.
Frequently Asked Questions (FAQ)
What does the normal distribution calculator compute?
The Z-score and the probability below, above or between your value, given the mean and standard deviation. It shows the steps behind the result, not just the final number.
What inputs does the normal distribution calculator need?
The mean (mu), the standard deviation (sigma), your X value — or two values for the between mode — and which probability you want: below, above or between.
What formula does it use?
Z equals (X minus mu) divided by sigma, with probabilities from standard normal Z-table values. As a sanity check, about 68 percent of data lies within mu plus or minus 1 sigma, 95 percent within 2 sigma and 99.7 percent within 3 sigma.
What does the result assume?
A true normal distribution. Check that your data is roughly bell-shaped first, and use the between mode when you need the probability of a range rather than a single point.