Normal Distribution Calculator
Result
Normal Distribution Calculator — free online calculator.
Formula
- Normal Distribution Calculator calculates its result from Mean (μ), Standard Deviation (σ), Value (x). It uses the formula z = (x−μ)/σ · PDF = exp(−z²/2) / (σ√(2π)) · CDF = Φ(z). Change any input to recalculate the result instantly.
- The main inputs are Mean, Standard Deviation, Value. Enter them in the units and format shown in the calculator.
- Keep comparable quantities in compatible units whenever the formula combines or compares them.
- Changing any input above recalculates the result with the same calculation engine used by this page.
Example: Normal Distribution
- Mean: 0 μ
- Standard Deviation: 1 σ
- Value: 1.5 x
Z = (x−mean)/standard deviation. Normal PDF evaluated at x; left and right tails from a standard normal CDF approximation; central symmetric probability from |z|.
Sample result: Calculating…
Frequently asked questions
What does the Normal Distribution calculate?
Normal Distribution Calculator — free online calculator.
Which values should I enter?
Enter Mean, Standard Deviation, Value using the units and format shown beside each field.
What formula does this calculator use?
The calculator uses the following relationship: z = (x−μ)/σ · PDF = exp(−z²/2) / (σ√(2π)) · CDF = Φ(z).
Why might my result differ from another source?
Results can differ when another source uses different units, rounding rules, conventions or assumptions. Compare the inputs and definitions before comparing results.
Does the result update automatically?
Yes. Changing an input updates the result using the same calculation engine shown on this page.