Use the calculator below to find cutoff values in a few common ways. The Normal Cutoff tab computes the raw-score cutoff (a quantile) for a given percentile assuming a normal distribution.

Cutoff Value Calculator

Proportional Adjustment
Normal Cutoff
Z Critical Value

Enter any 3 values to calculate the missing variable (proportional adjustment; p and r are proportions, not percentile ranks).

Related Calculators

Cutoff Value Formula

In statistics, a cutoff value for a given percentile is typically a quantile of the underlying distribution. For a normal distribution, the percentile cutoff is computed from the inverse normal CDF. (The “Proportional Adjustment” tab uses a separate scaling relationship that is not a general quantile formula.)

\begin{aligned}
\text{Normal cutoff:}\quad CV &= \mu + z_p\sigma,\quad z_p=\Phi^{-1}(p)\\
\text{Proportional adjustment:}\quad CV &= \frac{T\cdot p}{1-r}
\end{aligned}

Variables:

  • CV is the cutoff value (threshold) in the same units as the scores/values
  • p is a percentile written as a decimal between 0 and 1 (normal cutoff)
  • μ is the population mean (normal cutoff)
  • σ is the population standard deviation (normal cutoff)
  • zp is the z-score at percentile p, i.e., zp = Φ−1(p) (normal cutoff)
  • T is a reference total value (proportional adjustment tab)
  • r is an expected rejection/loss fraction as a decimal between 0 and 1 (proportional adjustment tab)

To calculate a normal-distribution cutoff, convert the percentile p to a z-score (zp) and compute CV = μ + zpσ. To perform the proportional adjustment, compute CV = (T·p)/(1−r).

What is a Cutoff Value?

A cutoff value is a predetermined threshold used to divide results into categories (for example, “pass” vs “fail,” or “normal” vs “abnormal”). In many statistical settings, a cutoff tied to a percentile is a quantile of a dataset or an assumed distribution (such as the normal distribution). In applied settings (such as medical tests), the cutoff may also be chosen to balance criteria like sensitivity and specificity, not just a percentile.

How to Calculate Cutoff Value?

The following steps outline common ways to calculate a cutoff value.

  1. Decide what “cutoff” means for your problem (percentile cutoff from a distribution, hypothesis-test critical value, or a simple proportional adjustment).
  2. If using a normal percentile cutoff, determine the mean (μ) and standard deviation (σ).
  3. Write the percentile as a decimal p (for example, 0.75 for the 75th percentile).
  4. Compute zp = Φ−1(p), then compute the cutoff CV = μ + zpσ.
  5. If you need a z critical value for hypothesis testing, choose α and the tail type, then compute z using the Z Critical Value tab.
  6. Verify your result with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge (this example matches the Proportional Adjustment tab):

reference total (T) = 80

target proportion (p) = 0.75

rejection/loss rate (r) = 0.2

adjusted cutoff value (CV) = (80 · 0.75) / (1 − 0.2) = 75