How to use the normal distribution probability calculator
Find the probability between two values for a normal distribution. Enter mean, standard deviation, lower value, upper value in the fields above; the p(x < b), p(a < x < b), p(x > b) are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- mu — Mean
- s — Standard deviation
- a — Lower value
- b — Upper value
Worked example
With mean = 100, standard deviation = 15, lower value = 85, upper value = 115, the calculator gives p(x < b) ≈ 0.8413447; p(a < x < b) ≈ 0.6826895; p(x > b) ≈ 0.1586553.
Frequently asked questions
What is the formula for the normal distribution probability calculation?
P(X < b) = ncdf((b-mu) / s). P(a < X < b) = ncdf((b-mu) / s)-ncdf((a-mu) / s). P(X > b) = 1-[P(X < b)]. Here mu is mean, s is standard deviation, a is lower value, b is upper value.
What inputs do I need for the normal distribution probability calculator?
You need mean, standard deviation, lower value, upper value. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.