📐 Chebyshev’s Theorem Calculator
Find the minimum percentage of any data set that must fall within k standard deviations of the mean, no matter the distribution’s shape.
What Chebyshev’s theorem tells you
Chebyshev’s theorem is a general rule that applies to any data set, regardless of its shape, including skewed or unusual distributions. It guarantees that at least 1 – 1/k² of the data will fall within k standard deviations of the mean, for any k greater than 1.
How this calculator works
Enter how many standard deviations (k) you want to check. The calculator applies the formula 1 – 1/k² to find the guaranteed minimum share of data within that range. If you also enter a mean and standard deviation, it shows the actual numeric interval those k standard deviations correspond to.
Because Chebyshev’s theorem makes no assumption about the shape of the distribution, its bound is more conservative than the Empirical Rule, which only applies to roughly bell-shaped (normal) data. Use this tool for general statistics education and planning.