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.