Normal Distribution Calculator
Calculate z-score, probability density, cumulative probability, and right-tail probability for a normal distribution using a value, mean, and standard deviation.
Formulae used:
z = (x − μ) / σ
PDF = (1 / (σ√(2π))) · e^(-(1/2)z²)
| Metric | Value |
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Privacy: calculations run locally in your browser. No inputs are stored or transmitted.
How it works
This tool standardizes the value with a z-score, then estimates the normal CDF using a numerical approximation of the error function.
Examples
- x = 85, μ = 70, σ = 10 → z = 1.5
- Left-tail probability is P(X ≤ x)
- Right-tail probability is P(X > x)
When to use this tool
This tool is designed for quick, practical tasks such as everyday calculations, data formatting, or simple conversions. It is best used when you need fast results without installing software or using complex tools.
When to use
- Quick checks or one-time calculations
- Validating or converting data before using it elsewhere
- Simple tasks that do not require advanced software
When not to use
- Critical financial, legal, or medical decisions
- Large-scale or automated processing
- Situations requiring guaranteed precision beyond basic validation
Always review results before using them in important contexts.
About this tool
This tool helps you perform quick utility operations directly in your browser. It runs entirely in your browser without sending data to a server.
You can use this tool when handling simple tasks without installing additional software. The results should be interpreted as a processed output based on your input data.
FAQ
- What does this normal distribution calculator compute?
It computes z-score, probability density (PDF), cumulative probability to the left of x (CDF), and right-tail probability for a normal distribution.
- What is z-score?
A z-score tells you how many standard deviations a value is above or below the mean.
- What happens if standard deviation is 0?
The calculation is undefined because a normal distribution requires a positive standard deviation.
- Are calculations stored?
No. Everything runs locally in your browser.