Scaled Test Score Calculator & Formula

A scaled test score calculator converts a raw score (number of correct answers) into a scaled score on a consistent grading scale, typically 100–200 or 200–800, so that scores from different test versions are comparable. You enter the raw score, the total number of questions, and the scoring scale’s minimum and maximum values (or a conversion table if you have one), and the calculator applies the standard linear transformation to give you the scaled score. This is the same formula used by many standardized exams to adjust for slight differences in difficulty across test forms.

Formula

The calculator uses a simple linear conversion:

Scaled Score = Scale Minimum + (Scale Maximum − Scale Minimum) × (Raw Score ÷ Total Questions)

Where:

• Raw Score = number of correctly answered questions (integer, 0 to total)
• Total Questions = total number of questions on the test
• Scale Minimum = lowest possible scaled score (e.g., 100 on a 100–200 scale)
• Scale Maximum = highest possible scaled score (e.g., 200 on a 100–200 scale)

This assumes a perfectly linear relationship between raw and scaled scores, which is the simplest and most common approach. Real exams often use more complex equating methods, but the linear model is a good approximation for practice tests and informal score predictions.

Worked Example

Using the default values from the calculator:

• Raw score = 35
• Total questions = 50
• Scale minimum = 100
• Scale maximum = 200

Step 1: Compute the raw percentage: 35 ÷ 50 = 0.7 (70%).

Step 2: Multiply by the scale range: 0.7 × (200 − 100) = 0.7 × 100 = 70.

Step 3: Add the scale minimum: 70 + 100 = 170.

So the scaled score is 170 on a 100–200 scale, and the percentage correct is 70%.

When to Use a Scaled Score Calculator

Use this calculator when you have a raw score and want to estimate a scaled score on a uniform scale. Common situations include:

• Practice tests for exams that report scaled scores (e.g., many professional licensing exams).
• Converting a percentage to a different grading scale (e.g., 0–100 to 0–4 for GPA).
• Comparing scores from different test versions that use the same raw-to-scaled conversion.

It is also useful for teachers who want to normalize grades across different test difficulties. However, always check whether the official test uses a linear conversion or a more complex equating method (like item response theory).

How to Read the Result

The scaled score tells you where you fall on the chosen scale, not how many questions you got right. For example, a scaled score of 170 on a 100–200 scale means you performed at 70% of the maximum possible score, but it does not directly tell you your percentile rank. Percentile rank depends on how other test-takers performed, which is not part of this calculation.

If the scale is 200–800 (like the old SAT), the formula works the same way: a raw score of 35 out of 50 would give 200 + (800 − 200) × 0.7 = 620. That is a reasonable estimate, but real SAT scoring used a more sophisticated equating process.

Common Mistakes and Misconceptions

• Mixing up raw and scaled scores: The raw score is always the number correct, not the percentage. If you enter a percentage, you will get a different (and wrong) result.
• Assuming a linear scale is official: Many exams use non-linear equating. This calculator gives an approximation, not an official score.
• Ignoring the scale range: Always check the minimum and maximum of the scale you are converting to. A 100–200 scale is different from a 200–800 scale.
• Rounding too early: Keep the raw percentage as a decimal (e.g., 0.7) until the final step to avoid rounding errors.

Limitations of the Linear Formula

The linear conversion assumes that each additional correct answer adds the same amount to the scaled score. In reality, standardized tests often adjust for question difficulty: a correct answer on a hard question may add more to the scaled score than a correct answer on an easy one. This is why official score conversion tables are not simple straight lines. If you have the official conversion table, use it instead of the linear formula.

Another limitation is that the formula does not account for guessing penalties (if any) or unanswered questions. If your test subtracts points for wrong answers, your raw score should be calculated as correct − (wrong × penalty) before using this calculator.

Frequently Asked Questions

What is the difference between raw score and scaled score?

A raw score is simply the number of questions you answered correctly. A scaled score is a conversion of that raw score to a standard scale, so that scores from different test versions can be compared fairly. For example, two different test forms may have different difficulty levels; scaling adjusts for that.

Can I use this calculator for the SAT or GRE?

You can use it to get a rough estimate, but neither the SAT nor the GRE uses a simple linear conversion. They use equating methods that account for question difficulty. For official practice, use the conversion tables provided by the test maker.

How do I convert a scaled score back to a raw score?

Rearrange the formula: Raw Score = (Scaled Score − Scale Minimum) ÷ (Scale Maximum − Scale Minimum) × Total Questions. For example, a scaled score of 170 on a 100–200 scale with 50 questions gives (170 − 100) ÷ (200 − 100) × 50 = 35.

What if my test has a different scale, like 1–36?

Just enter 1 as the minimum and 36 as the maximum. The formula works the same way. For instance, a raw score of 30 out of 40 on a 1–36 scale gives 1 + (36 − 1) × (30/40) = 27.25, which you would round to 27.

Does this calculator work for AP tests or IB exams?

AP tests use a 1–5 scale, so you can enter 1 and 5. IB exams use a 1–7 scale. However, both use complex grade boundaries that vary by subject and year, so the linear result is only a rough estimate. Always refer to official grade descriptors.

Why is my official scaled score different from what this calculator gives?

Because official scaled scores are derived from equating procedures that consider question difficulty, test-taker performance, and sometimes a penalty for guessing. The linear formula is a simplification. If you have the official conversion table, use that instead.

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in raw | Raw score | - | 35 | 0
in total | Total questions | - | 50 | 0
in min | Scale minimum | - | 100 | 0
in max | Scale maximum | - | 200 | 0
out scaled | Scaled score | - | min + (max - min) * (raw / total) | 0
out pct | Percentage correct | % | (raw / total) * 100 | 1