Empirical Rule Calculator

Find the 68-95-99.7 ranges of a normal distribution.

68% range (±1σ) 85 to 115

95% range (±2σ) 70 to 130

99.7% range (±3σ) 55 to 145

Formula: mean ± 1σ, ± 2σ, ± 3σ

Step-by-step with your numbers:

1. Values used:

2. Mean = 100

3. Standard deviation = 15

5. 68% range (±1σ) = 85 to 115

6. 95% range (±2σ) = 70 to 130

7. 99.7% range (±3σ) = 55 to 145

Did we solve your problem today?

In a normal distribution, ~68%, 95% and 99.7% of data lie within 1, 2 and 3 standard deviations.

The math behind it

68% within mean ± 1σ; 95% within ± 2σ; 99.7% within ± 3σ.

μ 100, σ 15 → 68% in 85–115.

Only normal data?

Yes — the rule assumes an approximately normal distribution.