Adonis Tools

Area Under the Curve & Empirical Rule Calculator

Set a sigma level to see the proportion of area captured under a standard normal distribution, and the proportion remaining in each tail.

Normal Distribution Instrument

1.00σ

Area between ±σ Tail regions

68.269% Area between ±σ

15.866% Right tail (X > σ)

15.866% Left tail (X < −σ)

Methodology

Computed from the standard normal cumulative distribution function (Abramowitz & Stegun erf approximation). Values match the familiar 68.27% / 95.45% / 99.73% rule at 1σ, 2σ, and 3σ.

Area between ±σ = Φ(σ) − Φ(−σ)
Each tail = 1 − Φ(σ)

For educational purposes only. Not intended for regulated quality, safety, or compliance decisions.