Statistics
Normal Distribution Calculator
Easily calculate normal distribution probabilities and percentiles online. Visualize the distribution and understand probability with this interactive tool.
Input Parameters
Result
Calculated Result:
P(X < > between and ) =
Percentile for P(X < x) = is:
Enter parameters and calculate to see the result.
Visualization
Understanding Normal Distribution
The normal distribution, also known as the Gaussian distribution or bell curve, is a continuous probability distribution that is symmetric about the mean. It shows that data near the mean are more frequent in occurrence than data far from the mean.
- Mean (\( \mu \)): The average value of the distribution. It determines the center of the bell curve.
- Standard Deviation (\( \sigma \)): A measure of the spread or dispersion of the distribution. A larger standard deviation means a wider curve.
- Probability: The likelihood of a random variable falling within a certain range.
- Percentile: The value below which a given percentage of observations in a group of observations falls. For example, the 90th percentile is the value below which 90% of the observations may be found.
This calculator helps you find probabilities for different ranges under a normal distribution curve and also calculate percentile values. Use it to explore and understand normal distribution concepts.
Learn more about normal distribution on Wikipedia.
Frequently Asked Questions
What is the Normal Distribution Calculator?
The Normal Distribution Calculator is an online Statistics calculator. You enter your values, and it returns the answer with the steps shown so you can follow along.
How accurate is the Normal Distribution Calculator?
The solver uses a math engine that avoids the floating-point rounding errors you get from most hardware calculators. For typical homework and professional calculations, the results will match what you would get by hand.
Can I use the Normal Distribution Calculator for professional Statistics projects?
Yes. The math behind it is standard Statistics, so the results are reliable for professional use. That said, always double-check that your inputs are in the right format before relying on the output.
Why use the Normal Distribution Calculator instead of calculating by hand?
Manual calculation is slow and error-prone, especially with multiple steps. This tool does the arithmetic for you and shows each step, so you can catch mistakes before they carry forward.
How do I format my inputs for the Normal Distribution Calculator?
Type your numbers into the input fields. Leave out units and symbols unless a field specifically asks for them. The solver handles the rest.