What this calculator does
Empirical rule (68-95-99.7) works out the share of normal data expected within 1, 2 and 3 standard deviations of the mean. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
Formula≈68% within ±1σ, ≈95% within ±2σ, ≈99.7% within ±3σ, for approximately normal data
The inputs explained
| Field | What to enter |
|---|---|
| Mean | A number. Starts at 100. |
| Standard deviation | A number. Starts at 15. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with mean
Every other input is held at the calculator’s starting values while mean varies. Select any row to load that scenario into the calculator.
How the answer changes with mean
| Mean | 68% of values fall within | 95% of values fall within | 99.7% of values fall within |
|---|---|---|---|
| 50 | 35.000 to 65.000 | 20.000 to 80.000 | 5.000 to 95.000 |
| 75 | 60.000 to 90.000 | 45.000 to 105.000 | 30.000 to 120.000 |
| 100 | 85.000 to 115.000 | 70.000 to 130.000 | 55.000 to 145.000 |
| 150 | 135.000 to 165.000 | 120.000 to 180.000 | 105.000 to 195.000 |
| 200 | 185.000 to 215.000 | 170.000 to 230.000 | 155.000 to 245.000 |
| 300 | 285.000 to 315.000 | 270.000 to 330.000 | 255.000 to 345.000 |