Chebyshev's Theorem Calculator
Apply Chebyshev's inequality to find the minimum share of any dataset within k standard deviations.
It holds for every distribution, which is why it is weak
Chebyshev guarantees 75% within two standard deviations for literally any dataset, however skewed. A normal distribution actually holds 95.4%. The theorem's value is that it never fails — reach for it when normality cannot be assumed, and for the empirical rule when it can.
Significance is not the same as importance
With a large enough sample almost any difference becomes statistically significant, because significance measures how confident you can be that a difference exists at all — not how big it is or whether it matters. Effect size answers the second question, and the two should always be read together.
The formula
At least 1 − 1/k² of any distribution lies within k standard deviations
Every result on this page comes from this formula. Nothing is rounded until the final display, so figures match a spreadsheet to the cent.
How to use the Chebyshev's Theorem Calculator
- Fill in each field with your own figures — the defaults are only there as an example.
- The result updates as you type, so there is no button to press.
- Check the breakdown under the main result for the supporting numbers.
- Use the copy button to take the result with you, or share the link to reload the same inputs.
Chebyshev's Theorem Calculator — frequently asked questions
Is this chebyshev's theorem calculator free to use?
Yes. Every calculator on the site is free, needs no sign-up, and runs entirely in your browser, so your figures never leave your device.
How accurate is the result?
The maths is exact for the formula shown on the page. Accuracy in the real world depends on your inputs and on assumptions the formula cannot see, so treat the output as a well-grounded estimate rather than a quote.
Can I use it on my phone?
Yes. The page is responsive, weighs a few kilobytes and works offline once loaded, so it behaves the same on a phone as on a desktop.
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About this calculator
Written and reviewed by The Samsung Calculator editorial team. Every calculator is written against a published formula, reviewed against at least one independent reference implementation, and dated when it changes.
Last reviewed September 14, 2026 · Calculation runs client-side · No data collected · Report an error