K12 Grades is a free website that helps students figure out their current standing in class and what is needed to improve or maintain their grades during a school year.

How to use the grade calculator

At the bottom there are two optional fields.

After you have filled the form out press the “Compute” button to get your results.

#### The Problem

For students that have grades without pluses and minuses (A+, B-, etc.) it is easy to calculate a grade percentage.

For example:

Table 1:
A90
B80
C70
D60
F

Students that use pluses and minuses will need to determine minimum percentages like the example in table 2.

Table 2:
A+?
A?
A-?
B+?
B?
B-?
C+?
C?
C-?
D+?
D?
D-?
F

#### My Solution

You can think of the grading scale with pluses and minuses as having three ranges: B+, B, B- for example. Because of this the minimum percentage for a B- under the new grading scale should be the same as the minimum percentage for a B under the original grading scale.

Table 3:
A+?
A?
A-90
B+?
B?
B-80
C+?
C?
C-70
D+?
D?
D-60
F

The other minimum percentages are based on a grade-point conversion scale:

Table 4:
A+?
A4
A-3.7
B+3.3
B3
B-2.7
C+2.3
C2
C-1.7
D+1.3
D1
D-0.7
F

Unfortunately, there is a problem between tables 1,2,3 and table 4. The first three look at minimum values and the fourth is concerned with middle values. In order to use the new scale you need to look at middle, and not minimum, percentages.

Table 5:
A+
A95
A-?
B+?
B85
B-?
C+?
C75
C-?
D+?
D65
D-?
F

In order to fill in the other percentages we need to assume that the relative spacing of the grades on the grade-point conversion scale should dictate the relative spacing of the grades’ middle percentages on my grading scale. I’ll start with the C+. Since a C+ is worth 2.3 grade points, and 2.3 is 30 percent of the way from a C (2.0) to an B (3.0), I want to know what number is 30 percent of the way from an 75 to a 85. That number, of course, is 78. So, that should be the middle percentage for a C+.

Table 6:
A+98
A95
A-92
B+88
B85
B-82
C+78
C75
C-72
D+68
D65
D-62
F

Now that we have the middle values all we need to do to figure out the corresponding ranges is to figure out the midpoints that lie between consecutive numbers:

Table 7:
A+9896.5
A9593.5
A-9290
B+8886.5
B8583.5
B-8280
C+7876.5
C7573.5
C-7270
D+6866.5
D6563.5
D-62
F

There a couple of things left to figure out. What should the threshold between D– and F be? We will make it 60.

Second, should a student whose percentage is equal to a threshold percentage get the letter grade just below or above? We are going with the letter grade just above. So, these thresholds are actually the minimum percentages for the grades just above them. That means that I can completely fill in the “minimum percentage” table I started with, but couldn’t get very far with at the time (table 3):

Table 8:
A+96.5
A93.5
A-90
B+86.5
B83.5
B-80
C+76.5
C73.5
C-70
D+66.5
D63.5
D-60
F

Most grading systems max out at A; there is no A+. One way of handling this is to enlarge the intervals associated with each of the eleven remaining passing grades (A down to D–). Another option is to proportionally enlarge the intervals associated with A and A–, so that 90 remains the minimum value for A–, with 95 being the new minimum value for A. This, however, would make the unavailability of the A+ grade result in a disproportionately high percentage required in order to get an A. I think that would make A’s harder to get than they should be. A third option, and the one used on this website, is just to absorb the values associated with A+ into the range for A. So, the minimum value for an A would remain 93.5, and anything above that (up to 100, or higher, for that matter) would still be an A:

Table 9:
A93.5
A-90
B+86.5
B83.5
B-80
C+76.5
C73.5
C-70
D+66.5
D63.5
D-60
F

So those are the minimum percentages used on the K12 Grades Calculator.

Table 10:
A93.50 and above
A-90.00–93.49
B+86.50–89.99
B83.50–86.49
B-80.00–83.49
C+76.50–79.99
C73.50–76.49
C-70.00–73.49
D+66.50–69.99
D63.50–66.49
D-60.00–63.49
F59.99 and below

1. The ranges for the plus/minus grades (such as B+ and B–) are 3.5 percentage points wide, but the ranges for the flat grades (such as B) are only 3 percentage points wide. Isn’t that weird?

Yes, considered by itself. But it reflects the fact that the grade points aren’t themselves evenly spaced: there’s a difference of 0.3 between some pairs of consecutive grade points (e.g., 3.0 and 3.3), but a difference of 0.4 between some others (e.g., 3.3 and 3.7). If the grade points were more evenly spaced (e.g., 3.00, 3.33, 3.67, etc.), then the mathematical technique used above (the one used to fill in table 6) would yield more equally sized percentage-point ranges for the letter grades.

2. Does that mean there’s something fishy about the fact that pluses and minuses are worth only 0.3 instead of 0.33?

No—the grades available in a grading system don’t need to be equally spaced along whatever numerical scales (e.g., grade points or percentages) they can be correlated with.

3. So why not just say that a B is anything between 83.33 and 86.67? Those numbers seem more intuitive, as thresholds, than 83.5 and 86.5.