# How Many A's Do I Need to Raise My GPA?

TR Smith is a product designer and former teacher who uses math in her work every day.

Your grade point average or GPA is what universities and scholarship committees want to know when you're in high school applying to colleges for the first time. And once you're in college, it's what graduate school programs and summer internship programs want to know. As long as you're in school and earning grades, you'll always be marked by your GPA.

GPA is nothing more than the average grade you received in your courses weighted by the number of credit hours for each class. It's the total number of grade points earned divided by the number of credits attempted. The basic GPA system assigns points to the grades A, B, C, D, and F as follows,

A = 4, B = 3, C = 2, D = 1, F = 0

For instance, suppose during one semester you take a 3-credit English literature class, a 5-credit chemistry class, and a 4-credit history class, for a total of 12 credits. If you get an A in English, a C in chemistry, and a B in history, then your GPA for that semester is

(3*4 + 5*2 + 3*4)/12 = 2.83

GPAs can be calculated semester-by-semester, year-by-year, or cumulatively. Most academic programs and scholarships want to know your cumulative GPA, so it is natural to ask "How many credits of A do I need to raise my GPA to a certain level?" With a little algebra, you can quickly figure out what grades and how many credits you need to raise your GPA to 3, 3.5, 3.8 or any other target number.

## How to Solve the GPA Equation

Let G be your current cumulative GPA, K be the number of credits you've taken, T be your target GPA, and X be the unknown number of credits of "A" you need to earn in order to raise your current GPA to the target level. To find X, you solve the equation

T = (G*K + 4*X)/(K + X)

This equation may look complicated, but basically it is a weighted average expression. In the numerator we have the current grade point average times the number of credits, G*K; this product is your current number of grade points. To this we add 4*X, the weight for a grade of "A" times the number of new credits X. The denominator is K + X, the number of credits already earned plus the number of new credits. Now let's solve this equation for X.

T = (G*K + 4*X)/(K + X)
T*(K + X) = G*K + 4*X
T*K + T*X = G*K + 4*X
T*X - 4*X = G*K - T*K
4*X - T*X = T*K - G*K
X*(4 - T) = K*(T - G)
X = K*(T - G)/(4 - T)

In words, X is the number of credits you've earned so far (K) times the difference between your target GPA and current GPA (T - G), all divided by the difference between 4 and your target GPA (4 - T). If X turns out not to be an integer, round it up to the nearest whole number. Let's use technique to solve some example problems in raising GPAs.

## Example 1

Violette has a GPA of 3.122 and 56 university credit hours under her belt. To be eligible for a stipend scholarship next year, she needs to raise her GPA to at least 3.35. How many credits worth of classes does she need to take and earn an "A" in so that her cumulative GPA will meet the threshold next year?

In this example we have G = 3.122, T = 3.35, and K = 56. If we plug these values into the GPA raising equation, we get

X = 56*(3.35 - 3.122)/(4 - 3.35)
= 56*0.228/0.65
= 19.643

Rounding this up to the next integer gives us X = 20. Therefore she needs to take 20 more credit hours and pass all of them with a grade of "A" in order to be eligible for the scholarship. If she does this, her new GPA will be

T = (3.122*56 + 4*20)/(56 + 20)
= 3.353

At colleges that award + / - grades, they may use the following grade point system:

pts.
pts.
A+
4.33
C+
2.33
A
4
C
2
A-
3.67
C-
1.67
B+
3.33
D+
1.33
B
3
D
1
B-
2.67
D-
0.67

## Example 2

Brad's current cumulative GPA is 1.863, and to date he has taken 47 credit hours. If he doesn't work to raise his GPA to 2.5, his parents are going to stop paying his tuition and he'll have to pay for college himself. How many credits of "A" does Brad need to earn so that he can maintain his parents' generosity?

For this new example we have G = 1.863, T = 2.5, and K = 47, so we can calculate the number of credits of "A" he needs:

X = 47*(2.5 - 1.863)/(4 - 2.5)
= 47*0.637/1.5
= 19.96

Rounding up gives us X = 20. In other words, Brad needs to take 20 more credits worth of class and pass all of them with a grade of "A" in order to raise his GPA to 2.5

What if Brad doesn't think he can make all A's in the next 20 course hours, but he does think he can make all B's? How many credits of "B" does he need to raise his GPA to 2.5? To solve this related problem, we use the same equation as above, but replace the 4 with a 3. This gives us

X = K*(T - G)/(3 - T)
= 47*(2.5 - 1.863)/(3 - 2.5)
= 47*0.637/0.5
= 59.88

Rounding up gives us X = 60. Thus, Brad would need to pass 60 credits worth of courses with a grade of "B." Making a grade of "B" in 60 credits worth of classes is probably much more work than making a grade of "A" in 20 credits worth of classes. If he does this, is new GPA will be

T = (1.863*47 + 4*20)/(47 + 20)
= 2.5009

## Example 3

How many A's do I need to get if my current GPA is 3.3 and I need to raise my cumulative GPA to 3.7? If the number of credits I have taken so far is Z, how many more credits of "A" do I need to get? The answer to this question will be in terms of Z.

As before, let X be unknown number of new credits with a grade of "A." Since the current GPA is 3.3, the current number of grade points is 3.3Z. If the target GPA is 3.7, then we get the equation

3.7 = [3.3Z + 4X] / [Z + X]

Solving for X in terms of Z gives us

X = (4/3)Z

In other words, the number of new credits I need to take is 4/3 of what I've currently taken so far, or in other terms, I need to take 133% more credits worth of classes and pass them all with an A. For example, suppose I've taken 30 credits so far and have a cumulative GPA of 3.3. Since (4/3)*(30) = 40, I need to take 40 more credits and get all A's if in order to raise my GPA to 3.7.

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• Dil Vil 3 years ago from India

Interesting hub, thank you for the good share.

• paxwill 3 years ago from France

Great explanation of a question that gets asked A LOT. With the current trend grade inflation in higher education, it would be rare to see anyone with a GPA of 1.863 these days. I think it would take an effort to get grades that low!

• Maggie 3 years ago

Good information. As a college English instructor, I know how students often worry about this and often can't figure it out. My school uses the stupid +/- grading system; we call it a third of a letter grade.

When it was just A-B-C-D-F, you'd get a certain number of students in your office every semester asking how they could go from B to A, C to B, etc. Now with these silly third-grades, you get three times as many grade grubbers trying to go from B- to B, B+ to A-, etc. The finer the scale, the more agitation it causes.

I wish they'd use a simple A-C-F system. A if you learned it, C if you kind of learned it, and F if you didn't learn it. I worked at a college that let students take electives on a pass/fail basis. The pass/fail students never argued about grades.

• Maggie 3 years ago

To address Paxwill's comment, grade inflation is rampant. If other schools in the same tier as your school do it, then your school has to do it too.