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Item Difficulty Index Calculator

Work out item difficulty index instantly with clear inputs, formula shown and shareable results.

About Item Difficulty Index Calculator

Item difficulty is confusingly named: it is the proportion answering correctly, so a high p means an easy item. 78 of 120 gives p = 0.65. For a four-option multiple choice item the optimal difficulty is midway between chance and certainty, at 0.625, because that maximises the item's ability to discriminate.

Formulas

Difficulty index

p = correct responses / total candidates

Optimal difficulty

p = (1 + 1/options) / 2

Worked example

With the default values below, Item Difficulty Index Calculator returns Item Difficulty (p Value) of 0.6500. Change any input above and every figure here is recalculated in your browser.

Inputs used

Candidates answering correctlyminimum 0
78
Total candidatesminimum 1
120
Answer options in the itemminimum 2
4

Results

Item Difficulty (p Value)
0.6500
Interpretation
Moderate - near the optimal range
Optimal Difficulty For This Item Type
0.625
Difficulty Corrected For Guessing
0.5333

Step by step

  1. 1Values used
  2. 2Difficulty index
  3. 3Optimal difficulty
  4. 4Item Difficulty (p Value)= 0.6500
  5. 5Interpretation= Moderate - near the optimal range
  6. 6Optimal Difficulty For This Item Type= 0.625
  7. 7Difficulty Corrected For Guessing= 0.5333

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why is 0.5 not always optimal?

Because guessing raises the floor. With four options the effective floor is 0.25, so the midpoint of the usable range is 0.625.

Should very easy items be removed?

Not always. A few easy items early in a test build confidence, but they contribute almost nothing to discriminating between candidates.

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