What Is an invNorm Calculator?
An invNorm calculator finds the value (or z-score) that corresponds to a given cumulative probability under the normal distribution — the inverse of the normal cumulative distribution function. Where a normal probability calculator answers "what is the probability below this value?", invNorm answers "what value has this probability below it?". It is essential for finding percentiles, critical values, and cutoffs in statistics.
How to Use the Calculator
- Enter the cumulative probability (area to the left), between 0 and 1.
- Optionally enter the mean and standard deviation (defaults: 0 and 1 for the standard normal).
- Calculate — see the corresponding value or z-score.
What invNorm Returns
For the standard normal distribution, invNorm(p) gives the z-score with probability p to its left. For a general normal distribution, the value is:
x = mean + z × standard deviation, where z = invNorm(p).
Common invNorm Values
| Cumulative Probability | z-score (invNorm) |
|---|---|
| 0.90 | 1.282 |
| 0.95 | 1.645 |
| 0.975 | 1.960 |
| 0.99 | 2.326 |
Where invNorm Is Used
- Critical values: finding cutoffs for confidence intervals and hypothesis tests.
- Percentiles: converting a percentile into a data value.
- Quality control: setting thresholds based on probability.
- Standardized testing: mapping percentiles to scores.
invNorm vs normalcdf
These two functions are inverses. normalcdf takes a value and returns a probability (area), while invNorm takes a probability and returns the value. Use normalcdf to find "how likely," and invNorm to find "what value" for a target probability.
Frequently Asked Questions
What does invNorm do?
invNorm finds the value or z-score that has a given cumulative probability to its left under the normal distribution — the inverse of the normal CDF.
How do you find a z-score from a probability?
Enter the cumulative probability into invNorm. For example, invNorm(0.95) ≈ 1.645, the z-score with 95% of the area to its left.
What is the z-score for the 95th percentile?
The 95th percentile corresponds to a z-score of about 1.645 in the standard normal distribution.
What is the difference between invNorm and normalcdf?
normalcdf converts a value into a probability, while invNorm converts a probability back into a value. They are inverse operations.
Is this invNorm calculator free?
Yes — it is completely free, requires no signup, and finds values for any probability.