Gaussian Normal Bell Curve f(x) = (1 / σ√2π)·e^(−(x−μ)²/2σ²)

Normalized probability density function with total area equal to 1, peak at x = μ, and inflection points at x = μ ± σ.

Expressions & Parameters

Primary Function f₁(x)

Comparison Curve f₂(x)

Plot Tangent Line at x₀ Shade Integral [a, b]

Live Parameter Sliders (a, b, c)

a1.00

b1.00

c0.00

Interactive Coordinate Plane (Drag to Pan · Wheel to Zoom)

(0.000, 0.000)

Pre-Computed Analytical Curve Reference

Primary Equationy = exp(-(x - c)^2 / (2*a^2)) / (a*sqrt(2*pi))

Symbolic Derivative dy/dxexp(-(x - c)^2/(2*a^2))*-2*(x - c)/(2*a^2)/(a*sqrt(2*pi))

Canonical Viewportx ∈ [-5, 5], y ∈ [-0.1, 0.55]

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Machine Learning & Biology

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Mathematical Reference & Frequently Asked Questions

How can I modify the parameters of Gaussian Normal Bell Curve f(x) = (1 / σ√2π)·e^(−(x−μ)²/2σ²)?

Drag sliders a, b, and c in the expression sidebar or edit the formula directly to observe real-time shifts in amplitude, frequency, roots, and extrema.