Areas Under the Normal Curve

Calculate probabilities and find values for any normal distribution. Enter raw scores, z-scores, or probabilities.

Mean (μ)

Standard Deviation (σ)

Raw Score (X)

Z-Score

Probability ()

Enter a probability to find symmetric bounds around the mean.

Probability Between

or enter bounds manually below

Raw Score (X₁)

Z-Score (z₁)

Raw Score (X₂)

Z-Score (z₂)

Probability Between

P(X₁ < X < X₂)

Raw Score

Z-Score

z = (X - μ) / σ

Converts a raw score to standard units, measuring how many standard deviations away from the mean.

X = μ + (z × σ)

Converts a z-score back to raw score units using the mean and standard deviation.

±1σ

≈ 68.27%

±2σ

≈ 95.45%

±3σ

≈ 99.73%