A normal distribution calculator finds probabilities for values from a normal (bell-shaped) distribution. Enter the mean, standard deviation and a value or range, and it calculates the probability, z-score or percentile. It’s a core tool for statistics classes, test score analysis and quality control.
The z-score tells you how many standard deviations a value is from the mean: z = (x − μ) ÷ σ. For example, if test scores have a mean of 75 and a standard deviation of 8, a score of 87 has z = 1.5. The probability of scoring below 87 is about 0.933, meaning that score is around the 93rd percentile.
The empirical rule gives quick estimates: about 68 percent of values fall within one standard deviation of the mean, about 95 percent within two and about 99.7 percent within three. So for the test above, about 95 percent of scores fall between 59 and 91.
Tips: check whether your data is roughly normal before using these calculations; skewed data needs other methods. For “between” probabilities, subtract the two cumulative probabilities. For sample means, use the standard error (σ ÷ √n) instead of σ. The inverse normal function finds a value for a given percentile, like the score needed to be in the top 10 percent.
Tips for getting accurate results from the Normal Distribution Calculator: double-check that every input uses the right units, enter numbers without commas or symbols, and run the calculation a second time with a quick estimate in your head to confirm the answer looks reasonable.
How to use the Normal Distribution Calculator on Minedit: enter your values in the fields, press calculate, and review the step-by-step breakdown under the result. If something looks off, change one input at a time to see how it affects the answer, which is also a great way to learn the math behind it.
Learn more on Wikipedia’s normal distribution article. Find t value, Poisson and point estimate calculators on Minedit.