Normal Distribution Calculator
Normal Distribution with explicit assumptions and reproducible inputs.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Assumes a normal population with known μ and positive σ. Density is not a point probability. Numerical results are approximate. Extremely small probabilities can underflow to zero. No personal, clinical or financial decision rule is inferred.
Example Calculation
- Value x: 0
- Mean μ: 0
- Population standard deviation σ: 1
For the standard normal distribution at x=0, each tail has probability 0.5.
Frequently asked questions
How do I use this calculator?
Enter value x, mean μ, population standard deviation σ. The result updates automatically. Use Reset to restore the example values.
What method does it use?
z=(x−μ)/σ; report Φ(z), its upper tail, and normal density.. Assumes a normal population with known μ and positive σ. Density is not a point probability. Numerical results are approximate. Extremely small probabilities can underflow to zero. No personal, clinical or financial decision rule is inferred.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.