Math & Science100% Free Tool

Free Normal Distribution Probability Calculator (Bell Curve Area) Online

Calculate probability density function (PDF) and cumulative area under the Gaussian bell curve between any lower and upper bounds. — 100% free online utility, zero sign-up, zero paywalls, and private client-side processing.

100% Client-Side0ms Latency
Algebraic & Polynomial Solverax² + bx + c = 0
Roots of Equationx₁ = 3.000, x₂ = 2.000
Discriminant (Δ)1
Parabola Vertex(2.50, -0.25)
Axis of Symmetryx = 2.50

How It Works

1

Enter Mean (μ) & Standard Deviation (σ)

Define distribution center and dispersion.

2

Set Integration Bounds

Input lower bound a and upper bound b.

3

Review Area Probability

Computes P(a ≤ X ≤ b) using numerical error function approximations.

Frequently Asked Questions

In any normal distribution: 68.27% of values fall within 1 standard deviation, 95.45% within 2, and 99.73% within 3.

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