Normal Distribution Calculator

Your details

Left/right tail gives the area on one side of a single value. Between/outside uses two bounds. Inverse solves for the x-value that gives a target probability.
The center of the distribution.
The spread of the distribution. Must be greater than 0.
The raw value to locate on the normal curve.
Probability1sigma to 2sigma from mean
90.8789%

The probability for the selected mode.

z-score1.3333
P(X < x)90.8789%
P(X > x)9.1211%
Density f(x)0.010934
Percentile90.88
P(mu-1sig < X < mu+1sig)68.2689%
1.333390.9% below · z-score

x is 1.33 standard deviations above the mean (z = 1.3333).

  • 90.88% of the distribution falls below x; 9.12% falls above it.
  • The z-score is unitless, letting you compare values across different normal distributions on a common scale.
  • Under the empirical rule: ~68% within 1sigma, ~95.45% within 2sigma, ~99.73% within 3sigma.

Next stepSwitch to "Between two values" to find the probability of a range instead of a tail.

 = Powered by OnlyCalculators