Grade Curve Calculator

Q: How do I curve grades?

Curving grades depends on the method used: For the linear rescaling , you add a fixed number of points for all students so that the best score is always 100%. For the ratios method , you multiply all results by a fixed number so that the best score is 100%. The ratios of other scores remain constant. For the Bell curve algorithm , you adjust the scores to follow a normal distribution with a given mean value and standard deviation. For a square root method , you take the square root of the initial scores and multiply them by an additional factor. This way, lower scores get a bigger boost than higher grades.

Q: What does graded on a curve mean?

Graded on a curve or applying a curve to grades means to adjust test results from absolute values to scores relative to other students . It is a typical procedure if you want the highest score to be 100% or to ensure that most grades fall in the middle range (e.g., from B to D) even for a difficult exam.

Q: How do I apply a curve to grades?

It depends on the method used: Linear rescaling — Add the same points for every student; Ratios — Multiply each score by the same number; Bell curve — Define a new mean and standard deviation so that the grades would follow the normal distribution; or Square root — Take the square root of each score, and multiply by a fixed factor. Typically, you want to apply the rescaling method to get 100% as the best score. Other grades would follow the specific curve, depending on the chosen option.

Creators

Wojciech Sas, PhD

Wojciech SasPhD, Institute of Physics in Zagreb

Wojciech, PhD, is a physicist at the Institute of Physics in Zagreb, investigating materials under extreme conditions such as low temperatures and high pressures. He specializes in experimental work, including participation in Large-scale User Facilities such as synchrotrons. Wojciech uses his experience and knowledge to create calculators in physics, math, and statistics categories. In his free time, he likes swimming, playing board games, and looking for meteors while stargazing. See full profile

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Reviewers

Steven Wooding

Steven Wooding is a physicist by training with a degree from the University of Surrey specializing in nuclear physics. He loves data analysis and computer programming. He has worked on exciting projects such as environmentally aware radar, using genetic algorithms to tune radar, and building the UK vaccine queue calculator. Steve is now the Editorial Quality Assurance Coordinator here at Omni Calculator, making sure every calculator meets the standards our users expect. In his spare time, he enjoys cycling, photography, wildlife watching, and long walks. See full profile

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Welcome to Omni’s grade curve calculator — an amazing tool that helps you curve the grades according to your needs. Keep on reading to learn how to curve grades and how to apply different formulas for grade curving.

Whether you want to use linear scaling, ratios, the Bell curve, or the square root method, our calculator will show you the result in no time. Let’s explore our curving grades calculator in more detail!

🔎 If you want to dig deeper into the philosophy of relative assessments, you can check the additional information by reading a dedicated page: What Does It Mean to Grade on a Curve?

What is a grade curve?

Grading on a curve is a method that adjusts students’ scores from absolute values to a relative measure. It helps evaluate everyone’s performance, regardless of the test’s difficulty. For example, it’s reasonable to apply if you want to treat the best result as 100%.

There are several distinct ways to apply a grade curve, where the most popular ones are:

Linear rescaling method;
Ratios method;
Bell curve method; and
Square root method.

If you are asking yourself, “How do curved grades work?”, then read the following sections of the article or go directly to use the grade curve calculator.

🙋 Estimate your test score with our test grade calculator — a quick and precise tool for checking the grades.

How do I curve grades?

Curving grades depends on the method used:

For the linear rescaling, you add a fixed number of points for all students so that the best score is always 100%.
For the ratios method, you multiply all results by a fixed number so that the best score is 100%. The ratios of other scores remain constant.
For the Bell curve algorithm, you adjust the scores to follow a normal distribution with a given mean value and standard deviation.
For a square root method, you take the square root of the initial scores and multiply them by an additional factor. This way, lower scores get a bigger boost than higher grades.

How to use the Bell curve grade calculator

Let’s have a look and see how Omni’s grade curve calculator works for the Bell curve method. Let’s assume we have the following list of scores: 80, 80, 75, 60, 60, 55, 50, 50, 40, 25.

Begin by evaluating the mean value and the standard deviation of the scores. The mean value is μ₀ = 57.5, and the standard deviation is σ₀ = 16.77.
Define the new distribution parameters. Let’s say we want a new mean to be μ = 75 with a standard deviation of σ = 12.
Calculate the z-score for each grade. Check our Z-score calculator if you don’t remember the formulas by heart. Remember to use the mean and standard deviation of the original grades, μ₀, and σ₀. The z-scores are: 1.3417, 1.3417, 1.0435, 0.14908, 0.14908, -0.14908, -0.4472, -0.4472, -1.0435, -1.938.
Convert the resulting z-scores to new grades using the new mean and standard deviation:

new grade = μ + z-score × σ
The list of new grades is the following: 91.1, 91.1, 87.5, 76.8, 76.8, 73.2, 69.6, 69.6, 62.5, 51.7.

If you want to learn the formulas for curving grades with different methods, check the dedicated page on how to grade on a curve.

🙋 Still unsure about using a Bell curve method? No worries — we explore the topic in detail at How does grading on a Bell curve work?

How do curved grades work? Pros and cons

The key advantages of using the curved grades:

It adjusts students’ performance by including the test’s difficulty.
It helps obtain a positive grade for results below the class average.
The best performers remain best after curving the grades, usually getting the full score.

The most notable disadvantages of curved grades:

It helps boost weak grades more than strong scores.
It may create unnecessary competition and tension among students.
The method of grade curving is always an arbitrary choice.

🔎 We have dedicated pages that explore the topic even further:

FAQs

What does graded on a curve mean?

Graded on a curve or applying a curve to grades means to adjust test results from absolute values to scores relative to other students. It is a typical procedure if you want the highest score to be 100% or to ensure that most grades fall in the middle range (e.g., from B to D) even for a difficult exam.

How do I apply a curve to grades?

It depends on the method used:

Linear rescaling — Add the same points for every student;
Ratios — Multiply each score by the same number;
Bell curve — Define a new mean and standard deviation so that the grades would follow the normal distribution; or
Square root — Take the square root of each score, and multiply by a fixed factor.

Typically, you want to apply the rescaling method to get 100% as the best score. Other grades would follow the specific curve, depending on the chosen option.

How do I apply linear rescaling for grades: 80, 70, 90, 55, 60, and 85?

The linear rescaling method adds a fixed value to each score. Typically, we want the best grade to equal 100. Here is the explanation for grades 80, 70, 90, 55, 60, and 80:

Find the best score in the list — it’s 90;
Evaluate the difference between 100 and the best score: 100 − 90 = 10.
Add this difference to each original result.
The final grades are: 90, 80, 100, 65, 70, 90.