Charts & Visual Data
Normal Distribution Bell Curve Formula: Exact Gaussian PDF Ordinate & Sigma Grid
Generate smooth XY Scatter Bell Curve coordinates for any mean mu and standard deviation sigma using the universal closed-form Gaussian density formula (1 / (sigma * SQRT(2*PI()))) * EXP(-0.5 * z^2).
Plot smooth Gaussian curves across [mu - 4*sigma, mu + 4*sigma] in any spreadsheet!
To plot a smooth Normal Bell Curve over a histogram or Six Sigma capability chart, create an evenly spaced X-grid spanning mu - 4*sigma to mu + 4*sigma (e.g., 81 steps of 0.1*sigma) and compute the exact probability density ordinate f(x) = (1 / (sigma * SQRT(2 * PI()))) * EXP(-0.5 * ((x - mu) / sigma)^2)!
Writing the closed-form exponential with EXP, SQRT, and PI() runs identically in every spreadsheet engine without version-specific statistical add-ins, peaking at f(mu) = 0.398942 / sigma and reaching inflection points at x = mu +- sigma (60.65% of peak height).
| Grid Coordinate x (mu = 100, sigma = 15) | Standard Score z | Gaussian Density f(x) | Relative Peak Height |
|---|---|---|---|
| x = 100 (Mean Apex) | 0.0000 | 0.026596 | 100.00% |
| x = 115 (+1 Sigma Inflection) | +1.0000 | 0.016131 | 60.65% (= e^-0.5) |
| x = 130 (+2 Sigma Tail) | +2.0000 | 0.003599 | 13.53% (= e^-2) |
Closed-Form Gaussian Bell Curve Density Ordinate f(x)
Evaluates exact normal probability density at x (B2) for mean mu (B3) and standard deviation sigma (B4 > 0).
=IF(B4 <= 0, "Sigma Must Be Positive", ROUND((1 / (B4 * SQRT(2 * PI()))) * EXP(-0.5 * ((B2 - B3) / B4) ^ 2), 6))Standardized Z-Score Distance from Mean
Computes signed standard deviations (x - mu) / sigma.
=IF(B4 <= 0, 0, ROUND((B2 - B3) / B4, 4))Try the example
Use the original values or change them to test your understanding.