Normal Distribution Calculator

Calculate PDF, CDF and probabilities for any normal distribution.

Distribution Parameters

Set μ, σ, and select probability mode

Probability Mode

Mean (μ)

Standard Deviation (σ)

X₂ (upper bound)

Enter your values above and tap Calculate Probability to see the result.

Probability Density Probability

Z-Score

Enter distribution parameters above and tap Calculate.

Step-by-step Solution

Normal Curve Visualization

Z-Table Reference

Z = 1.00

0.8413

Z = 1.645

0.9500 (90%)

Z = 1.96

0.9750 (95%)

Z = 2.576

0.9950 (99%)

Z-Score Formula

Z = (X - μ) / σ

X = Observed value
μ = Population mean
σ = Population standard deviation

Related Calculators

Pro Tips

Results update as you type — change any field to see the effect immediately.

Check that every value uses the same unit before comparing results.

Use the copy button to paste the normal distribution figures into a note or spreadsheet.

Nothing is sent to a server, so you can use this with private figures.