Calculate an item’s difficulty index from observed counts or normalized average score, reverse-solve targets, and review clearly labeled classification and uncertainty. Chance correction is optional.

The index p is the proportion correct: higher means easier. Classification cutoffs here are illustrative (<0.30 difficult, 0.30–0.70 moderate, >0.70 easy), not universal standards.

Chance correction

Assumes every incorrect response is a wrong answer and equal-probability guessing; do not use for omitted responses.

Related Calculators

Difficulty Index Formula

The following formula is used to calculate an item’s difficulty index (often denoted p, the proportion correct).

DI = (K) / (N)

Variables:

  • DI (or p) is the item difficulty index (proportion correct), from 0 to 1 (higher = easier item).
  • K is the number of examinees who answered the item correctly (dichotomous scoring).
  • N is the total number of examinees who responded to the item.
  • For polytomous items, a common normalized form is p = (average item score) ÷ (maximum points) so the result is still on a 0–1 scale.

To calculate the difficulty index for a dichotomous item, divide the number correct by the total responses. For polytomous items, divide the average item score by the maximum possible points.

What is a Difficulty Index?

In educational and psychological measurement, the difficulty index (often called the item p-value) summarizes how easy or hard a test item was for a group of examinees. It is typically the proportion of examinees who answered correctly (for right/wrong items), so values closer to 1 indicate an easier item and values closer to 0 indicate a harder item.

How to Calculate Difficulty Index?

The following steps outline how to calculate the Difficulty Index.

  1. Enter the total number of responses (N).
  2. For dichotomous items, enter the number correct (K). For polytomous items, switch modes and enter the average item score and the maximum points.
  3. Compute DI (p) using DI = K ÷ N (dichotomous) or p = average score ÷ max points (polytomous).
  4. Interpret the result: higher p means an easier item. The calculator uses illustrative categories: p < 0.30 difficult, 0.30 ≤ p ≤ 0.70 moderate, and p > 0.70 easy. Cutoffs vary by assessment purpose and are not universal standards.
  5. Observed whole-count mode provides an approximate 95% Wilson interval and binomial standard error under independent comparable binary-response assumptions. Optional chance correction assumes equally likely guesses and no omitted responses. Reverse or normalized-score modes do not infer a binomial interval; this calculator does not compute item discrimination or distractor performance.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Total Responses (N) = 100

Number Correct (K) = 42

Difficulty Index (DI = p) = 42 ÷ 100 = 0.42 (42%), which would be classified as Moderate using this calculator’s illustrative thresholds of 0.30 and 0.70.