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Number of Standard Deviations Above/Below Mean Calculator

How many SDs is a value from the population mean?

Calculates the number of standard deviations (z-score) that a value X is from the mean, and the raw score from a given z-score. Useful in quality control (±3σ) and grading on a curve.

Priya Venkatesan By Priya Venkatesan
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

z = (X−μ)/σ; X = μ + z·σ

In depth

Calculates the number of standard deviations (z-score) that a value X is from the mean, and the raw score from a given z-score. Useful in quality control (±3σ) and grading on a curve.