What is my semester grade?
Enter your two quarter grades and your final exam grade to get your semester grade. Leave the exam empty and enter a goal to see the grade you need.
- Semester grade
- 89%
With quarter grades of 88% and 92% and 85% on the final exam, the semester grade is 89%.
Semester grade: 89%. With quarter grades of 88% and 92% and 85% on the final exam, the semester grade is 89%.
How to calculate
Computes a semester grade as the weighted average of two quarter grades and a final exam (40%, 40% and 20% by default), or the final exam or quarter grade needed for a target semester grade.
Example with the default inputs (Quarter 1 grade 88%, Quarter 2 grade 92%, Final exam grade 85%, Quarter 1 weight 40%, Quarter 2 weight 40%, Final exam weight 20%): With quarter grades of 88% and 92% and 85% on the final exam, the semester grade is 89%.
Formula: semester = (w1 × Q1 + w2 × Q2 + wE × exam) ÷ (w1 + w2 + wE); solved for any one grade from the other three.
- The semester grade is a weighted average of two quarter grades and one final exam. The weights are divided by their total, so they need not add up to 100.
- The default weights are 40%, 40% and 20%, the split many US high schools use. Check your school’s split and change the weights to match.
- Grades are percentages from 0 to 1,000 (above 100 allows extra credit). A needed grade above 100% means the goal is out of reach without extra credit.
- Every step is exact on the numbers as typed; grades are rounded to two decimal places only for display.
Worked examples
Each example is checked against the calculator on every build.
- Quarter 1 grade 88%, Quarter 2 grade 92%, Final exam grade 85%, Quarter 1 weight 40%, Quarter 2 weight 40%, Final exam weight 20% gives Semester grade 89%.Source: Akron Public Schools grade calculator (1st quarter 40%, 2nd quarter 40%, exam 20%), https://homeaccess.akron.k12.oh.us/finalgrade/
- Quarter 1 grade 88%, Quarter 2 grade 92%, Semester grade 90%, Quarter 1 weight 40%, Quarter 2 weight 40%, Final exam weight 20% gives Final exam grade 90%.Source: (90 × 100 − 40 × 88 − 40 × 92) ÷ 20 = 1,800 ÷ 20 = 90 (weights from the Akron Public Schools grade calculator, https://homeaccess.akron.k12.oh.us/finalgrade/)
- Quarter 1 grade 70%, Quarter 2 grade 72%, Semester grade 80%, Quarter 1 weight 40%, Quarter 2 weight 40%, Final exam weight 20% gives Final exam grade 116%.
- Quarter 1 grade 80%, Final exam grade 70%, Semester grade 85%, Quarter 1 weight 40%, Quarter 2 weight 40%, Final exam weight 20% gives Quarter 2 grade 97.5%.
- Quarter 1 grade 88%, Quarter 2 grade 92%, Final exam grade 85%, Quarter 1 weight 2%, Quarter 2 weight 2%, Final exam weight 1% gives Semester grade 89%.
- Quarter 1 grade 90%, Quarter 2 grade 80%, Final exam grade 75%, Quarter 1 weight 45%, Quarter 2 weight 45%, Final exam weight 10% gives Semester grade 84%.
How it works
The semester grade is the weighted average of the first quarter grade Q1, the second quarter grade Q2, and the final exam grade E, with weights w1, w2 and wE:
semester = (w1 × Q1 + w2 × Q2 + wE × E) ÷ (w1 + w2 + wE)
The weights start at 40%, 40% and 20%. They are divided by their total, so they do not have to add up to 100: weights of 2, 2 and 1 give the same answer as 40, 40 and 20.
Fill in the weights and any three of Q1, Q2, E and the semester grade; the calculator finds the fourth. Rearranged, with W = w1 + w2 + wE:
- E = (semester × W − w1 × Q1 − w2 × Q2) ÷ wE
- Q1 = (semester × W − w2 × Q2 − wE × E) ÷ w1
- Q2 = (semester × W − w1 × Q1 − wE × E) ÷ w2
Rules
- Grades are percentages from 0 to 1,000 (above 100 allows for extra credit). Weights are from 0 to 100 each.
- If all three weights are 0 there is no semester grade: "The three weights add up to 0. Give at least one part a weight above 0."
- A part with weight 0 cannot be solved for, because it does not change the semester grade: "The final exam has a weight of 0, so it does not change the semester grade." (or the quarter 1 grade, or the quarter 2 grade).
- If the part you solve for would need a grade below 0%, there is no answer: "Even 0% on the final exam gives a semester grade above this one." (or the quarter 1 grade, or the quarter 2 grade).
- A needed grade above 100% is shown: it means the goal needs extra credit. Above 1,000% there is no answer.
Exact arithmetic and display
Each number is read exactly as its decimal (87.5 is 875/10), and the sums and the division are exact fractions. Every grade is shown as a percent rounded half up from that exact value to at most two decimal places, without trailing zeros (88.005 shows as 88.01%; 89 shows as 89%).
Worked examples by hand
Quarters of 88% and 92%, 85% on the final, 40/40/20. 40 × 88 = 3,520; 40 × 92 = 3,680; 20 × 85 = 1,700. Sum: 8,900. Semester grade: 8,900 ÷ 100 = 89%.
The exam grade needed for 90%, after 88% and 92% (40/40/20): E = (90 × 100 − 3,520 − 3,680) ÷ 20 = 1,800 ÷ 20 = 90%.
A goal that needs extra credit. Quarters of 70% and 72%, goal 80% (40/40/20): E = (8,000 − 2,800 − 2,880) ÷ 20 = 2,320 ÷ 20 = 116%.
The quarter 2 grade needed for 85%, with 80% in quarter 1 and 70% on the exam (40/40/20): Q2 = (8,500 − 3,200 − 1,400) ÷ 40 = 3,900 ÷ 40 = 97.5%.
Weights of 2, 2 and 1. (2 × 88 + 2 × 92 + 1 × 85) ÷ 5 = 445 ÷ 5 = 89%, the same as 40/40/20.
A 45/45/10 split. (45 × 90 + 45 × 80 + 10 × 75) ÷ 100 = 8,400 ÷ 100 = 84%.
Other questions people ask
How do I calculate my semester grade?
Multiply each grade by its weight, add the results, and divide by the total weight. With quarters of 88% and 92% at 40% each and an 85% final exam at 20%: (40 × 88 + 40 × 92 + 20 × 85) ÷ 100 = 8,900 ÷ 100 = 89%.
What do I need on my final exam to get the semester grade I want?
Enter both quarter grades and your goal as the semester grade, and leave the final exam empty. The exam grade you need is (goal × total weight − the weighted quarter grades) ÷ exam weight. For a 90% goal after 88% and 92%: (9,000 − 3,520 − 3,680) ÷ 20 = 90%.
How much is a semester final exam worth?
It depends on the school. A common split is 40% for each quarter and 20% for the exam, which is what Akron Public Schools uses for classes with one final exam. Your syllabus or school handbook gives your split; enter it under Weights.
Do the weights have to add up to 100?
No. The calculator divides by the total of the weights, so 40, 40 and 20 give the same result as 2, 2 and 1. A part with weight 0 does not count at all.
What does it mean if I need more than 100% on the final?
The goal is out of reach unless the exam has extra credit. With quarters of 70% and 72% at 40% each, an 80% semester would need (8,000 − 2,800 − 2,880) ÷ 20 = 116% on a 20% exam. Try a lower goal to see what is possible.
Can I find the grade I need in a quarter instead?
Yes. Leave that quarter empty and fill in the other quarter, the exam and your goal. For an 85% semester with 80% in quarter 1 and 70% on the exam (40/40/20), quarter 2 needs (8,500 − 3,200 − 1,400) ÷ 40 = 97.5%.