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.
Common searches this calculator answers include “normal distribution calculator”, “normal curve calculator”, “bell curve calculator”, “bell curve probability”, “area under normal curve”.
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.
Tips for accurate results
- Enter the standard deviation, not the variance; the variance is the square of the standard deviation.
- Use the sample mean and standard deviation when you are estimating from data.
- The probability between two values equals the difference of the two cumulative probabilities.
Common mistakes
- Entering the variance where the standard deviation is required.
- Assuming the data are normal without checking; skewed data make these probabilities misleading.
- Reading a probability as a percentage without multiplying by 100.
Frequently asked questions
What is the normal distribution probability calculator used for?
Find the probability between two values for a normal distribution. It helps with questions such as “normal distribution calculator”, “normal curve calculator”, “bell curve calculator”.
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 the normal distribution probability 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 normal distribution probability 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.