Converted grade
g′ = g ÷ M × M′
Grade scale converter
Convert a grade proportionally from one grading scale to another (out of 20, 10, 100, 40…) and see the matching percentage.
Proportional rescale, not an official equivalence between national grading systems.
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How does this tool work?
A paper marked out of 40, a quiz out of 25, a test out of 10: before averaging or comparing results, every grade has to be on the same scale. This converter does that cross-multiplication. Enter the grade, the original maximum and the target maximum, and it shows the converted grade and the matching percentage. It helps students placing a mark, parents reading a report card and teachers lining up assessments of different lengths.
The conversion keeps the proportion: the grade is divided by its original maximum, giving the share of points earned, then multiplied by the new maximum. 14 out of 20 is 70% of the points, so 7 out of 10 or 70 out of 100. The percentage shown is that same share times 100.
This method assumes two linear scales that start at 0 and where the highest number is the best grade. It ignores pass marks, which differ between systems, as well as letter scales and inverted scales. That is why the result is an arithmetic conversion, not an official equivalence between countries or institutions.
Convert a grade
Enter the grade
Type the grade as it appears on the paper, decimals included.
Set both scales
The original scale is the maximum possible on the assessment; the new scale is the one you want to express it on.
Read the converted grade
The grade on the new scale and the percentage appear at once. Round it the way your school does.
Conversion formulas
The same share of points, expressed on two different scales.
Percentage
p = g ÷ M × 100
- g
- grade on the original scale
- M
- original maximum
- M′
- new maximum
- g′
- converted grade
Use cases
Preparing an average
Before entering grades into a weighted average calculator, bring them all to the same scale.
Reading a grade on an unusual scale
21 out of 25 is easier to judge once shown as 84% or 16.8 out of 20.
Marking with a points-based rubric
A teacher scoring a test out of 37 points gets each student’s grade on the class scale directly.
Placing a result earned abroad
The conversion gives a first order of magnitude, to be completed with the host institution’s official table.
Examples
From 20 to 100
14 ÷ 20 = 0.7, times 100. Out of 10, the same grade is 7.
Input
14 out of 20 to a scale of 100Result
70 / 100 (70%)Lining up a paper marked out of 40
34 ÷ 40 = 0.85, then 0.85 × 20 = 17. The grade can now go into an average out of 20.
Input
34 out of 40 to a scale of 20Result
17 / 20 (85%)Why proportion falls short between systems
At Italian universities, 18 out of 30 is the lowest passing grade, while 12 out of 20 is comfortably above the pass mark of 10 in France. Same proportion, different meaning.
Input
18 out of 30 to a scale of 20Result
12 / 20 (60%)Tips and best practices
- Keep decimals through intermediate steps and round only at the end, so errors do not pile up in an average.
- For an inverted scale such as German grades from 1 (best) to 6, cross-multiplication does not work: a dedicated formula or table is needed.
- US letter grades are not proportional: on the standard NCES table, 75 out of 100 is a C, worth 2 points out of 4, not 3.
- For a study-abroad file in Europe, ask for your institution’s ECTS grade distribution table: it is the tool designed to compare grades across countries.
Sources and references
- European Commission, ECTS Users' Guide 2015 (opens in a new tab), Publications Office of the European Union, 2015Page in English
- National Center for Education Statistics, How is Grade Point Average Calculated? (opens in a new tab), U.S. Department of EducationPage in English
Frequently asked questions
How do I convert a grade out of 20 to a grade out of 10?
Divide by 2: 13 out of 20 becomes 6.5 out of 10. In general, divide by the old maximum and multiply by the new one.
How do I turn a grade out of 40 into a percentage?
Divide by 40 and multiply by 100: 29 out of 40 is 72.5%.
Is this conversion officially recognized?
No. It is a mathematical proportion. Equivalences between national systems are set by institutions or credential evaluation bodies, which take pass marks and the actual distribution of grades into account.
How do European universities compare grades?
The European Commission’s ECTS Users’ Guide recommends grade distribution tables: a grade is compared by its rank among students in the same field rather than by its raw value.
Can I convert a grade into a US GPA?
Not by proportion: GPA is built on letter grades turned into points. 15 out of 20 gives 3 out of 4 by proportion, while a US institution may rate it differently. Only the receiving institution’s table counts.
What if my grade is above the maximum (bonus points)?
The tool needs a grade no higher than the original maximum. If a bonus takes the grade past it, convert the capped grade or raise the original maximum according to the rule your teacher set.
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