The formula
target grade = grade ÷ source maximum × target maximum
Where it comes from
Every linear scale converts by simple proportion: work out what share of the maximum the grade represents and apply that same share to the maximum of the target scale. A 7 out of 10 is 70 %, which on the 100 scale is 70 points and on the 5 scale is 3.5.
How to work it out by hand
- Divide the grade by the maximum of its scale
- The result is the proportion achieved
- Multiply that proportion by the maximum of the target scale
What is worth knowing
The linear conversion has an important limit: the pass mark is not in the same place everywhere. It is 5 out of 10 in Spain and Argentina, 60 out of 100 in Mexico, 3.0 out of 5.0 in Colombia and 4.0 out of 7.0 in Chile. 60 % passes in Mexico and fails in Spain, so a numerical equivalence is not the same academic judgement.