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Deviation Score (Hensachi) Calculator

Calculate a deviation score from a score, mean and standard deviation. Paste a set of scores to get the mean, standard deviation, every deviation score and a top-percentile estimate at once.

Last updated: 2026/10/16 Calculator Feedback & bug reports
Enter values
Enter to show an estimated rank
Deviation score -- Enter score, mean and standard deviation.
-- Top percentile
-- Estimated rank

How to Use

1

Choose a mode

Use "Single" to get just your own deviation score, or "Batch" to compute everyone from a set of scores.

2

Enter values

For Single, enter score, mean and standard deviation. For Batch, paste scores separated by line breaks or commas.

3

Check the results

The deviation score, top percentile and rank estimate update in real time. You can copy the results.

What is a deviation score?

A deviation score (hensachi) shows where a score sits within a group. The mean is set to 50, and the score moves by 10 for every one standard deviation away from the mean. The formula is "deviation score = 50 + 10 × (score − mean) ÷ standard deviation". It reveals relative standing that raw scores alone cannot, making it easy to compare across tests of different difficulty.

Features

  • Real-time calculationThe deviation score is computed instantly as you type, with no waiting.
  • Batch from a score setJust paste scores to auto-calculate the mean, standard deviation and every deviation score.
  • Percentile & rank estimateEstimates the top percentile from the normal distribution, and a rank from the group size.
  • Privacy protectedAll processing happens in your browser. Your scores are never sent to any server.

Use Cases

  • Check your own deviation score on mock or regular exams
  • Compute deviation scores for a whole class or team at once
  • Gauge your position toward a target school or goal line
  • Relative comparison of survey or rating scores
  • Review the calculation steps when studying statistics

FAQ

What is the formula for the deviation score?
It is "deviation score = 50 + 10 × (your score − mean) ÷ standard deviation". Equal to the mean gives 50; one standard deviation above the mean gives 60.
What if I do not know the standard deviation?
Use "Batch" mode and paste everyone's scores. The mean, standard deviation and each deviation score are calculated automatically, so you do not need the standard deviation in advance.
Should I use population SD or sample SD?
For a standard deviation score over a whole group (such as a test), use population SD. For statistical estimation of a population from a sample, choose sample SD (n−1).
How is the "top percentile" calculated?
Assuming scores follow a normal distribution, it is derived from the cumulative standard normal distribution. It is an estimate that holds when the distribution is close to normal.
Are my entered scores saved or transmitted?
No. All calculations run entirely in your browser, and your scores are never sent to or stored on any server.
Can a deviation score be negative or above 100?
In theory, yes. For extreme scores more than about five standard deviations from the mean, a deviation score below 0 or above 100 can occur.

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