How to Grade on a Curve: Formulas and Methods

How to grade on a curve is a question that usually arises when an exam or test doesn’t go as planned. Imagine that you’re a teacher. You grab a cup of tea, sit down at your desk, and prepare to grade the easiest test of the term. But once you’ve finished, to your surprise, you have a sea of Fs in front of you. What went wrong?

Don’t doubt your students straight away — there is a tiny chance that absolutely nobody studied for it, but maybe the test was just way harder than you thought. Don’t worry, you can still save most of your students — not by adding missing points, but by using statistics to ensure a fair assessment.

In this article, we will be talking about the...

• Most popular methods teachers use when deciding how to curve grades;
• Formula for curving grades that can magically transform a fail into a pass;
• Statistics behind the bell curve and standard deviation; and
• Definitive answer to the big question: “Is the bar exam graded on a curve?”

Before we move on to formulas and statistics, let’s establish what curving grades actually means. Essentially, it’s about putting absolute results in relative terms.

Usually, a 95% is always considered an A, but sometimes, you want to treat that 95% as 100%, so that students at the bottom can still pass. This way, you’re not basing their knowledge on a textbook, but rather on the collective performance of the group.

There are multiple ways to achieve this, and the approach depends on your specific objective. Read on to discover what each of those methods entails.

When an educator decides how to curve exam grades, they usually use one of four methods. Let’s break them down.

1. The linear method

This is the easiest and most popular method. Imagine that your highest-scoring student scored 88%, while some other students failed quite spectacularly; however, you want to help them improve in some way. You can choose to treat that 88% as the perfect score, automatically bumping everyone else by 12 percentage points.

Here’s the math:

$\rm{New\ score} = \rm{Raw\ score} + (100 - \rm{Max\ score})$

In this system, everyone gets the same “gift”. It will make some Cs become Bs, but it won’t change the distribution — if you got 20%, a 12-point bump won’t make you pass.

2. Ratios

This method is based on the same idea of using your highest-scoring student as a reference, but instead of just adding points, you will redefine the maximum score. For example, if the maximum score was 100 and the highest score was 80, the students would not be graded out of 100, but out of 80.

$\rm{New\ score} = \frac{\rm{\footnotesize Raw\ score}}{\rm{\footnotesize Highest\ score}} \times 100$

If someone scored a 60, they would’ve originally got a D-, but with this new system, they will get a C: $\frac{60}{80} \times 100 = 75$.

However, bear in mind that this method won’t change much if anyone got a 99, for instance. The difference is not big enough to change the grades of the other students.

3. Square root

How do you curve grades when the class average is catastrophically low? The square root method boosts lower scores more than it does higher scores.

The formula is quite simple:

$\rm{New\ score} = 10 \times \sqrt{\rm{Raw\ score}}$

Let’s examine an example to gain a thorough understanding of how to curve test grades using this method.

See? The students at the very bottom get a lifeline, while those who already aced it get nothing. The gap between the highest and lowest scores is compressed, which is desirable, especially for the most challenging tests, such as organic chemistry.

If you want to play around with these numbers yourself, try our grade curve calculator, which does this math instantly.

4. Bell curve

This method is what most people think of when wondering how to curve test grades — and it’s horrifyingly statistical. In most cases, you won’t have to resort to this, but it’s good to understand how it works.

The bell curve forces all the grades of the group into the bell curve shape. The teacher needs to calculate both the class average and the spread of scores (standard deviation). Then, for instance, they can mandate that the...

• Top 10% get As;
• Next 20% get Bs;
• Middle 40% get Cs; and
• Bottom 30% receive Ds or Fs.

You don’t want to do this if everyone passed your test. It doesn’t matter if the bottom students scored 89% — if they are in the bottom percentile, they get the low grade.

If you are a teacher looking to apply a curve, or a student trying to predict your final score, here is a quick guide on how to curve exam grades manually:

• Identify the goal: Are you fixing a bad test or just adjusting the average? The square root method will be perfect for the former, while the latter might require the linear adjustment method.
• Find the anchor: If using a linear scale, find the gap between the highest score and 100.
• Apply the math: Add that gap to every score.
• Check the failures: Did the curve help the bottom students pass? If not, consider the square root method.

Ultimately, knowing how to grade on a curve empowers you to understand the fairness of the system you are in. It turns a mysterious letter grade into a transparent number, allowing you to focus on what really matters: learning the material (and maybe thanking the math gods for that square root function).