Math

Normal Distribution Calculator

Find a normal cumulative probability, upper tail, or inverse quantile with a supplied mean and deviation.

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Result

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How to use Normal Distribution Calculator

Standardize a value by z=(x−mean)/SD. Incomplete-gamma arithmetic evaluates normal tails; bisection finds bounded inverse probabilities.

Enter distribution mean, population standard deviation, value or quantile probability.
Check the model, units, and supported limits before calculating.
Run the tool, inspect the result, then copy or download it.

Positive standard deviation. Quantile probabilities 1e-12–1−1e-12. The chosen normal model is an assumption; extreme tails can underflow to zero.
Runs locally. Numeric inputs are bounded; floating-point output is approximate and rounded to 12 significant digits. Unsupported or non-finite calculations produce an error.

How does Normal Distribution Calculator calculate its result?

Standardize a value by z=(x−mean)/SD. Incomplete-gamma arithmetic evaluates normal tails; bisection finds bounded inverse probabilities.

What assumptions and boundaries apply?

Positive standard deviation. Quantile probabilities 1e-12–1−1e-12. The chosen normal model is an assumption; extreme tails can underflow to zero.