The calculation uses:
- relative difficulty weightings
- statistic values
- the eligible student cohort
- participation rates.
On this page
Relative difficulty weightings
After NCEA marking is complete, ÐÇ¿Õ´«Ã½ calculates relative difficulty weightings for each Level 3 or higher standard, standard version, and assessed result.
This calculation includes Not Achieved, Achieved, Merit and Excellence results for students enrolled in secondary school during the current academic year. If a student is enrolled in both secondary and tertiary study, results from both enrolments are included.
First, we calculate result distribution midpoints for each standard, standard version, and assessed result. These are based on data published in the National Standard Attainment data files.
Next, we apply subject and cohort adjustments using the method described in:
- New Zealand Science Review
This process produces an adjusted percentile for each standard, standard version, and assessed result. The adjusted percentile is used as the relative difficulty weighting in the ATAR calculation.
Relative difficulty weighting are calculated each year using the results available when the initial ATAR calculation is completed.
Most unit standards only have Not Achieved and Achieved results. For calculation purposes, Merit and Excellence difficulty values may still appear in the calculation tables, even though those results are not available for those standards.
Calculation method
Statistic values
ÐÇ¿Õ´«Ã½ calculates a statistic value for each student using their best 90 assessed credits. For each credit we:
- multiply it by its adjusted percentile
- add the results together
- divide the total by 90.
Statistic values range from 0 to 1.
Identifying a student’s best 90 credits
To identify a student’s best 90 credits, ÐÇ¿Õ´«Ã½ ranks results in the following order:
- standards in University Entrance (UE) approved subjects
- achievement standards in non-UE approved subjects
- unit standards.
This means:
- results from UE-approved subjects are considered before results from non-UE approved subjects
- results from non-UE approved subjects are considered before unit standards.
List of standards in UE-approved subjects
ÐÇ¿Õ´«Ã½ then works through the ranked list of standards from highest to lowest relative difficulty weighting. Credits are added to the calculation until the student’s best 90 credits have been identified.
A maximum of 24 credits from any one subject can be included. Credits above this limit are not included.
If the student has a result for a combination, the credits and weighting are added to their ATAR calculation and subject total. If not, ÐÇ¿Õ´«Ã½ moves to the next combination in the list.
This process continues until the student’s best 90 credits have been identified, using a pro rata calculation where needed.
Once we’ve identified a student’s best 90 credits and their relative difficulty weightings, we can calculate the student’s statistic value.
Students with fewer than 90 credits
If a student has between 60 and 89 assessed credits, their statistic value is still divided by 90.
This usually results in a lower statistic value.
Students with fewer than 60 assessed credits are not eligible for an ATAR score.
Duplicate and repeated standards
When a student has more than one result for the same standard, we apply the following rules:
Same standard and version in the same year
If a student has multiple assessed entries for the same standard and version in the same academic year, ÐÇ¿Õ´«Ã½ uses the result with the highest grade and excludes the others.
Same standard with different versions in the same year
If a student has multiple assessed entries for different versions of the same standard in the same academic year, ÐÇ¿Õ´«Ã½ uses version with the best result and excludes the others.
If the grades are the same, ÐÇ¿Õ´«Ã½ uses the version with the higher relative difficulty weighting.
Same standard across different years
If a student has multiple assessed entries for the same standard in different academic years, ÐÇ¿Õ´«Ã½ uses the most recent result and excludes the others.
This happens even if an earlier result had a higher relative difficulty weighting.
Cohort and participation rates
The participation rate helps determine how many students are allocated to each ATAR score.
ÐÇ¿Õ´«Ã½ calculates participation rates using:
- Statistics New Zealand population estimates
- the number of students (by age at June) who have 60 or more assessed Level 3 or higher credits in the year the ATAR is calculated.
The participation rate is calculated by dividing the total New Zealand candidature by the weighted Statistics New Zealand population.
Example
In 2025, New Zealand's total candidature was 46,017, the weighted Statistics New Zealand population was 72,054, and the participation rate was 63.86%.
New Zealand and all Australian states use a cubic function to describe the relationship between the participation rates and ATAR scores.
This relationship is described by the Harrison and Hyndman one-parameter model:
- Rob J Hydman
For participation rates between 25% and 75%, the calculation uses the formula shown below.
Calculation method
How ATAR scores are allocated
The Harrison and Hyndman model calculates how many students should be allocated to each ATAR score.
At the top of the ATAR range, this is 0.05 percent of the eligible cohort.
The number of students allocated to each score decreases towards the lower end of the range. This reflects differences between New Zealand and Australian jurisdictions, such as:
- retention rates
- school leaving age
- acceleration patterns
To allocate learners to ATAR scores, ÐÇ¿Õ´«Ã½:
- sorts student statistic values from highest to lowest
- applies the Harrison and Hyndman model
- assigns students to ATAR score bands.
Updated ATAR calculations
Students who become eligible after the initial January calculation may be added to the ATAR population later. If these students have a low statistic value, larger numbers of students can be grouped the lower end of the ATAR range.
These students are assigned the minimum ATAR value established in the January calculation.