Normal Distribution Percentile Calculator
Calculate percentile rank, z-score, and cutoff values using a normal distribution with your own mean and standard deviation.
Find where a value sits in the distribution (its percentile rank).
What this normal distribution percentile calculator does
This tool helps you work with a bell-curve (normal distribution) quickly and accurately. You can convert a raw value to a percentile, convert a percentile back to a value, or calculate the probability of falling within a range.
It is useful for test scores, process control, quality metrics, finance assumptions, and any dataset that can be reasonably modeled as normal.
Core concepts in plain English
1) Mean and standard deviation
- Mean (μ) is the center of the distribution.
- Standard deviation (σ) measures how spread out values are.
2) Z-score
A z-score tells you how far a value is from the mean in standard deviation units.
3) Percentile
Percentile means the percentage of values at or below a given value. If a score is at the 84th percentile, it is higher than about 84% of observations.
How to use each mode
Percentile from value (X → Percentile)
Enter your mean, standard deviation, and value. The calculator returns:
- z-score
- cumulative probability P(X ≤ x)
- percentile rank
Value from percentile (Percentile → X)
Enter a percentile (such as 95). The calculator finds the corresponding z-score and raw value. This is ideal for cutoff scores and thresholds.
Probability between two values
Enter lower and upper bounds. The calculator computes the probability and percent of values expected in that interval.
Example applications
- Education: Convert SAT-like scores to percentile standing.
- Hiring assessments: Set a top-20% cutoff score.
- Operations: Estimate defect probability outside tolerance bands.
- Finance: Approximate tail risks under normal assumptions.
Important interpretation notes
- Results are only as good as the assumption of normality.
- Very skewed or heavy-tailed data may need other distributions.
- For percentiles extremely close to 0 or 100, cutoff values can be very large in magnitude.
Quick FAQ
Is percentile the same as percentage?
No. Percentage is a proportion out of 100; percentile is relative rank in a distribution.
What if my standard deviation is zero?
A normal distribution requires a positive standard deviation. The calculator will reject zero or negative values.
Can I use decimals?
Yes, all inputs support decimal values.