Below is an explanation of how final grades are calculated using the uniform mark scale (UMS). You may also find the following information sheets useful in understanding how your results have been reached.
Many AS/A Level, and GCSE qualifications are unitary or modular. Each exam paper tests candidates' knowledge of an individual unit in the syllabus.
After they have sat the exam, the script is marked by an examiner, according to a set of strict criteria. The examiner then calculates the raw mark. The difficulty of an exam paper may vary from year to year. In order to ensure fairness and consistency across years and within subjects, an Awarding Meeting takes place. In this meeting a group of experienced senior examiners looks at a sample of papers from that year and compares them to previous papers and statistics using their professional judgement to decide what the grade thresholds should be (see example below).
The raw marks for the unit have already been established, but they don't mean very much on their own. They have to be converted to a uniform mark scale (or score), known as UMS. The weighting of units may vary so UMS unifies the marks to make them compatible and comparable. UMS gives a fixed scale with common boundaries that are unchanged year-on-year.
Sally and Peter both sat an A Level Accounting unit, but in different years. There are four, equally weighted units needed to achieve the qualification. Both papers are marked out of 80 and both students score 61. But, as Sally's exam included more complex questions than Peter's, the grade boundary for achieving an 'a' is set at 61. Peter's exam was relatively straightforward and the 'a' boundary is set at 64. Therefore for this unit, Sally achieves an 'a' and Peter achieves a 'b'. Their marks are converted to UMS (out of a maximum of 80) as shown below.

Peter therefore has 61 raw marks with the 'a' boundary for his unit set at 64. When this is converted into UMS, he has 60 uniform marks. Sally also has 61 raw marks with the 'a' boundary for her unit set at 61. When this is converted into UMS, she has 64 uniform marks.
The grade of the overall qualification is calculated by adding together the uniform marks achieved in the individual units. This gives candidates a final uniform mark which is compared against the overall UMS grade boundaries.
For unitised qualifications, both the unit uniform marks and grades, and the final uniform mark and grade are given on the statement of results.

Access teacher and student resources information for A Levels (from 2008).