Science & Engineering

Empirical Rule Calculator (68-95-99.7)

Applies the 68-95-99.7 rule to a normal distribution from your mean and standard deviation. Enter a value and it also returns the z-score and which standard-deviation band that value lands in.

How to use

Enter the distribution mean and standard deviation.
Optionally enter a data value.

Mean (μ)

Std deviation (σ)

Test value (x) — optional

Try

z-score of x

z = 2.000

68 — 95 — 99.7 rule · ±1σ, ±2σ, ±3σ

Percentile

97.72%

Within ±|z| range

95.45%

±1σ band (68%)

85 — 115

±2σ band (95%)

70 — 130

For study and estimation. Verify against authoritative data before relying on a result.

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Reference ranges

Within	% of data	Range
1 SD	68%	mean ± 1σ
2 SD	95%	mean ± 2σ
3 SD	99.7%	mean ± 3σ

Common questions

What is the 68-95-99.7 rule?

For a normal distribution, about 68 percent of values fall within one standard deviation of the mean, 95 percent within two, and 99.7 percent within three.

Does it work for non-normal data?

Not reliably. The rule assumes a roughly bell-shaped distribution, so skewed data needs different tools.