The top-box (also referred to as top-two-box or top-three-box scores) is a calculation method for scale questions. It is the sum of percentages for the highest point(s), or most favorable point(s), on a satisfaction, intent or awareness scale. This calculation method is used as an alternative for the mean score for the scale. The idea behind this method is that you only take those responses that are expressing a strong attitude such as "extremely satisfied".
Count the number of respondents that selected the highest, or most favorable, response and divide this count by the total number of responses.
You have conducted a customer satisfaction research with a 5 point scale questions. The responses can be categorizes as follows:
120 out of 1000 (12%) have answered with Very satisfied
340 out of 1000 (34%) have answered with Satisfied
250 out of 1000 (25%) have answered with Neutral
190 out of 1000 (19%) have answered with Dissatisfied
100 out of 1000 (10%) have answered with Very dissatisfied
The top-two-box score is the combination of the two highest categories. So you add up the number of respondents that have chosen either Very satisfied or Satisfied, in this case 460 respondents out of the total number of 1000 (=46%).
A higher top-box score means that a larger part of your respondents is (very) positive in their answer.