Normal distribution probability
Enter your numbers — the results update instantly.
P(a < X < b)68.27 %
P(X < a)15.87 %
P(X > b)15.87 %
Worked example
Given: Mean μ = 0; σ = 1; Lower bound a = -1; Upper bound b = 1
Result: P(a < X < b) = 68.27 %; P(X < a) = 15.87 %; P(X > b) = 15.87 %
How it is calculated
1. Enter the values you know. 2. The calculator converts them to base units and applies the formula. 3. The result is shown in the unit you choose.
Frequently asked questions
How do I calculate it?
Given: Mean μ = 0; σ = 1; Lower bound a = -1; Upper bound b = 1. Result: P(a < X < b) = 68.27 %; P(X < a) = 15.87 %; P(X > b) = 15.87 %.
Is the calculator free and private?
Yes. It is free, needs no sign-up and runs in your browser — the numbers you type stay on your device.