Find the 68%, 95%, and 99.7% intervals around a mean using the empirical rule.
| −1σ | – |
| +1σ | – |
| −2σ | – |
| +2σ | – |
| −3σ | – |
| +3σ | – |
Use this calculator when a roughly bell-shaped distribution can be summarised by a mean μ and a standard deviation σ. The empirical rule (68–95–99.7) sketches the intervals that hold about 68%, 95%, and 99.7% of the values on a normal curve.
The formulas are: μ ± σ, μ ± 2σ, and μ ± 3σ. Enter μ and σ in the same units. For IQ-style numbers, μ = 100 and σ = 15 give about 85–115 (68%), 70–130 (95%), and 55–145 (99.7%).
This is a normal-shape sketch, not a confidence interval for a mean and not a guarantee for skewed data. σ must be positive.
Mean (μ): Centre of the distribution.
Standard deviation (σ): Spread; must be positive.
−1σ / +1σ: Interval covering about 68% of values.
−2σ / +2σ: Interval covering about 95% of values.
−3σ / +3σ: Interval covering about 99.7% of values.
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