Normal Distribution Probability Calculator

About this calculator

This calculator finds P(a < X < b) = Φ((b − μ)/σ) − Φ((a − μ)/σ), where Φ is the standard normal cumulative distribution function, μ is the mean and σ is the standard deviation — it converts your two bounds into z-scores and looks up the area under the bell curve between them.

Statisticians, quality-control engineers and students use it whenever a real-world quantity is roughly normally distributed — exam scores, manufacturing tolerances, measurement error — to answer questions like "what fraction of parts fall within spec?" or "what percentage of students scored between a B and an A," without needing z-tables or calculus by hand.