Z-score calculator
Find how many standard deviations a value is from the mean. Use the second mode to calculate areas under the standard normal curve.
Your numbers stay in this browser. No account or upload to the server is needed.
How to use it
- Choose value standardisation or normal distribution areas.
- Enter your data and select “Calculate”. Standard deviation must be greater than zero.
- Review the formula or shaded interval. Use normal probabilities only when the normal model is justified.
Method and worked example
Z = (x − μ) / σ. A positive result is above the mean, a negative result below it, and zero is the mean itself.
Standardisation does not establish normality. The area mode applies only to the standard normal distribution with mean 0 and standard deviation 1.
Density φ(z) = exp(−z²/2) / √(2π). Areas use numerical Simpson integration with a step no larger than 0.005. Input bounds range from −10 to 10.
Tail areas are integrated directly to 12 to reduce cancellation near 1. Results are approximate and rounded for display.
Example: x=85, μ=70, σ=10 gives Z=(85−70)/10=1.5. Under the standard normal model, the interval from −1.96 to 1.96 has probability approximately 0.950004.