ESAT Grade Boundaries and Score Conversion 2026

The ESAT is scored on a scale of 1.0 to 9.0 for each module. Students’ raw scores out of 27 for the module are converted to the scale score using a complex statistical model.

Applicants to Cambridge and Imperial will naturally want to know what the ESAT grade boundaries are and how score conversion works. How many raw marks do you need to achieve your target score?

In this guide, we explain how scoring works and what the score conversion process is for the ESAT. We also examine the official results data on ESAT score distributions, as well as what score you need for a competitive Cambridge or Imperial application.  

How does ESAT scoring work?

The ESAT is scored on a scale of 1.0 to 9.0 (where 1.0 is lowest and 9.0 is highest), with separate scores issued for every module you take. This differs from the way the TMUA is scored, where students receive one overall scale score for the test as a whole.

The test consists of five modules, each with 27 multiple-choice questions. Students only take three of these modules; this is determined by the course you are applying for. For instance, applicants for Engineering at Cambridge are required to take Mathematics, Mathematics 2, and Physics. (Indeed, these three modules are by far the most popular combination, with 72% of all ESAT-takers sitting these three in 2024-25.)

Every question is worth one mark, with no penalty for wrong answers. Students therefore get a raw score out of 27 for every module; this is then scaled to give the final score of 1-9. Students never see their raw score, only the scale score.

ESAT Score Scaling

According to the ESAT’s official annual report, the scaling process is conducted using the Rasch item response theory (IRT) model.

To explain why this is used, we need to understand that, in a given test sitting, not every person who sits an ESAT module is asked the exact same questions as another candidate who sits the same module. The examiners write more than 27 questions for each module and different candidates receive a different set of questions when they come to sit the test.

Although the examiners try to make the questions a similar level of difficulty, naturally some questions are slightly easier or harder than others. It would be unfair, therefore, for candidate A, who happened to get an easier set of questions, to be rewarded with a higher mark than candidate B, who got a harder set of questions.

The Rasch IRT model is used to analyse how difficult each set of questions is and therefore to determine the ability of a candidate based on their answers. Once the October sitting is over, all candidates can be placed on the same ability scale regardless of which questions they were asked.

The model places candidates on a scale from -3.0 to +3.0, which is then mapped to the final scale score between 1.0 and 9.0.

The examiners fix the 50^th percentile of the score distribution in the October sitting at 4.5 and the 90^th percentile at 7.0. Any candidates who sit the ESAT in the January sitting are mapped onto the same scale based on the data from October.

ESAT Score Conversion

UAT-UK, which administers the ESAT, does not publish any official ESAT score conversion tables. This is because the scaling system accounts for the relative difficulty of individual questions, making straightforward conversion impossible. In other words, a difficult question will be worth more in the scaling process than an easy question, so it is not possible to say that x number of correct answers equals y number of points.

However, the predecessors of the ESAT, the NSAA and ENGAA, did operate on a straightforward score conversion basis and did produce conversion tables.

Here are the tables for these tests for the last year they were used, 2023.

Each module in the NSAA and ENGAA contained 20 questions, whereas the ESAT modules contain 27 each. For that reason, we have added a column showing what the equivalent raw score out of 27 would be for reference.

NSAA Conversion Table – Section 1 2023

Raw Score /20	/27 equivalent	Maths Scaled	Physics Scaled	Chemistry Scaled	Biology Scaled
0	0	1	1	1	1
1	1	1	1	1	1
2	3	1	1	1	1
3	4	1	1	1	1
4	5	1.5	1	1	1
5	7	2	1.1	1	1.2
6	8	2.4	1.8	1.5	2.1
7	9	2.8	2.5	2.1	2.9
8	11	3.1	3.1	2.7	3.6
9	12	3.5	3.7	3.2	4.3
10	14	3.8	4.3	3.8	5
11	15	4.2	4.8	4.3	5.6
12	16	4.5	5.4	4.9	6.3
13	18	4.9	6	5.4	6.9
14	19	5.3	6.7	6	7.6
15	20	5.7	7.4	6.6	8.4
16	22	6.2	8.1	7.3	9
17	23	6.7	9	8.1	9
18	24	7.5	9	9	9
19	26	8.6	9	9	9
20	27	9	9	9	9

The conversion varied by module, with a perfect 20/20 needed to score 9.0 in Maths vs only 16/20 (equivalent to 22/27) needed to score 9 in Biology.

The score required for 7.0 or above similarly ranged from 14/20 to 18/20, equivalent to 19/27 to 24/27.

For a 4.5, this was between 10/20 and 12/20 (14/27 and 16/27).

ENGAA Conversion Table – 2023

Raw Score /20	/27 Equivalent	Maths and Physics Scaled	Advanced Maths and Physics Scaled	Section 2 Scaled
0	0	1	1	1
1	1	1	1	1
2	3	1	1	1
3	4	1	1.6	1.3
4	5	1.2	2.5	2
5	7	1.9	3.2	2.6
6	8	2.4	3.8	3.1
7	9	2.9	4.3	3.6
8	11	3.4	4.9	4.1
9	12	3.9	5.4	4.5
10	14	4.3	5.9	4.9
11	15	4.8	6.4	5.3
12	16	5.3	6.9	5.8
13	18	5.7	7.5	6.2
14	19	6.3	8	6.7
15	20	6.8	8.7	7.2
16	22	7.4	9	7.7
17	23	8.2	9	8.4
18	24	9	9	9
19	26	9	9	9
20	27	9	9	9

In the ENGAA, the conversion also varied by module. Between 16/20 and 18/20 (equivalent to 22/27 and 24/27) were needed to score 9.0 in 2023.

For a scale score of 7.0 or more, you needed between 13/20 and 16/20 (equivalent to 18/27 to 22/27).

And for a score of 4.5 or more, you needed between 8/20 and 11/20 (equivalent to 11/27 to 15/27).

Implications for ESAT Score Conversion

Can we draw any conclusions from this data about how ESAT score conversion might work in 2026? As noted above, simple score conversion is not used in the ESAT. However, if the NSAA and ENGAA are anything to go by, a rough rule of thumb might be that between 11/27 and 16/27 will be needed for a score of 4.5, between 18/27 and 24/27 for a 7.0, and between 22/27 and 27/27 for a 9.0.

This will vary by module, by the difficulty of the questions you receive, and from year to year.

ESAT Grade Boundaries

There are no official grade boundaries for the ESAT. This is for a reason we’ve noted already in this guide: a given raw score does not equate straightforwardly to a scale score. Instead, UAT-UK use a complex scaling model called the Rasch IRT model to produce the scale scores for every module, based on the relative difficulty of the questions each candidate answered in the version of the module they took.

However, there were grade boundaries for the two predecessor tests to the ESAT, the NSAA and ENGAA. We present these below for the final time these tests were used, in 2023, for reference.

The tables shows the raw score needed to achieve each scale score in 0.5 increments for the different modules of each test. Note that the modules for these tests contained 20 questions each, whereas every ESAT module contains 27 questions.

NSAA Grade Boundaries – Section 1 2023

Scale score	Maths raw score /20	Physics raw score /20	Chemistry raw score /20	Biology raw score /20
1	0	0	0	0
1.5	4	6	6	6
2	5	7	7	6
2.5	7	7	8	7
3	8	8	9	8
3.5	9	9	10	8
4	11	10	11	9
4.5	12	11	12	10
5	14	12	13	10
5.5	15	13	14	11
6	16	13	14	12
6.5	17	14	15	13
7	18	15	16	14
7.5	18	16	17	14
8	19	16	17	15
8.5	19	17	18	16
9	20	17	18	16

ENGAA Grade Boundaries – 2023

Scale score	Maths and Physics raw score /20	Advanced Maths and Physics raw score /20	Section 2 raw score /20
1	0	0	0
1.5	5	3	4
2	6	4	4
2.5	7	4	5
3	8	5	6
3.5	9	6	7
4	10	7	8
4.5	11	8	9
5	12	9	11
5.5	13	10	12
6	14	11	13
6.5	15	12	14
7	16	13	15
7.5	17	13	16
8	17	14	17
8.5	18	15	18
9	18	16	18

Implications for ESAT Grade Boundaries

Although these tests were the ESAT’s predecessors, they were different tests, which were scored in a different way. We should therefore exercise a lot of caution about applying their grade boundaries to the ESAT.

As noted above, the ESAT does not have grade boundaries in the traditional sense, as each candidate’s score is scaled differently according to the difficulty of questions they answered.

Nonetheless, the information presented above may be useful in giving a very rough idea of what kind of score is needed to achieve each scale score.

If you’re aiming for a 9.0, for instance, you may only be able to afford to drop a couple of marks per module at most. You may need 65-90% to score a 7.0 in the ESAT, and 55-80% to score a 6.0 (roughly the average score of accepted Cambridge applicants, as we’ll see later). For a 5.0 (roughly the average score of accepted Imperial applicants – again, more on that later), you may need 45-70%.

All these scores are estimates, and will vary by module, by the difficulty of questions you received in your test version, and from year to year.

You may also be interested in our guide on grade boundaries in the TMUA, another UAT-UK test.

ESAT Score Distribution

The following charts show the ESAT score distribution for every module, for both the October and January test sittings.

2025-26

These charts are based on the official ESAT results data for the 2025-26 application cycle.

Mathematics 1

We can see that there is a fairly conventional bell curve distribution for the Mathematics 1 module, albeit slightly bunched towards the lower ends of the scoring range. The most common scores were 4 and 4.5, with more than 15% of candidates achieving each of these scores. 3 and 3.5, at 12-13% were slightly more common than 5, at just over 10%.

Only a fraction of a percent of candidates scored 1.0, the lowest score. Meanwhile, only 1.4% of candidates scored 9.0, the highest score. This was the lowest percentage to achieve a 9.0 of all ESAT modules.

The 50^th percentile score was 4.1 and the 90^th percentile 6.2.

Biology

The score distribution for the Biology module was notably more flat than Mathematics 1, with no individual score being achieved by more than 11% of candidates. Particularly noteworthy is the fact that 7% of candidates scored 1.0 in Biology.

The most common scores were 4.5 and 5.0, with 10.9% and 10.8% of candidates achieving these scores respectively. 2.6% of candidates scored 9.0.

The 50^th percentile score in Biology was approximately 4.2, and the 90^th percentile 6.6.

Chemistry

The most common score in the Chemistry module was 4.0, achieved by 14% of candidates, followed by 4.5, 3.0, and 5.5.

3% of students scored 9.0 in Chemistry, the highest of any module.

The 50^th percentile score was approximately 5.2 and the 90^th percentile 6.8.

Physics

The most common scores in the Physics module were 3.5 and 4.5, with 13% of candidates achieving each of those scores. A fairly high 3.7% scored only 1.0, while only 1.7% scored 9.0 – second lowest behind Mathematics 1.

The 50^th percentile score was approximately 3.9, and the 90^th percentile 6.3. These are among the lowest of any ESAT module, indicating that many candidates found Physics difficult.

Mathematics 2

14.8% of candidates scored 4.0 in Mathematics 2, the most common score, followed by 3.5 (13.3%) and 5 (12.5%). 2.1% of candidates scored 1.0 and 2.3% of candidates 9.0.

The 50^th percentile score was approximately 3.9 and the 90^th percentile score was 6.2. Along with Physics, these are the lowest for any ESAT module, suggesting that many candidates found Mathematics 2 difficult.

2024-25

The following table shows the ESAT score distributions for 2024-25, split by the October and January sittings.

Module	Sitting	Number of students	Mean	Percentile 25	Percentile 50	Percentile 75	Percentile 90
Maths 1	All	11,919	4.46	3.3	4.2	5.4	6.7
Maths 1	Oct	9,141	4.59	3.4	4.5	5.7	7
Maths 1	Jan	2,778	4.03	3.1	4	5	5.9
Biology	All	1,429	4.71	3.6	4.5	5.9	7
Biology	Oct	1,428	4.72	3.6	4.5	5.9	7
Biology	Jan	1	NA	NA	NA	NA	NA
Chemistry	All	2,821	4.62	3.4	4.5	5.7	6.8
Chemistry	Oct	2,570	4.7	3.4	4.5	5.8	7
Chemistry	Jan	251	3.8	2.6	3.7	4.7	5.8
Physics	All	9,237	4.5	3.4	4.4	5.6	6.8
Physics	Oct	6,853	4.65	3.4	4.5	5.6	7
Physics	Jan	2,384	4.08	3	3.9	4.9	6
Maths 2	All	10,040	4.52	3.4	4.5	5.5	6.8
Maths 2	Oct	7,303	4.66	3.6	4.5	5.6	7
Maths 2	Jan	2,737	4.15	3.2	4.2	5	6

The 50^th percentile scores were between 4.2 and 4.5 for all modules, with the mean slightly higher. The 75^th percentile score was between 5.4 and 5.7, and the 90^th percentile score between 6.7 and 6.8

To get an ESAT score in the top 25%, therefore, you generally needed a score in the middle 5s, and to score in the top 10%, in the mid-to-high 6s.

Scores for applicants in the October sitting were markedly higher, and fixed according to the system we outlined earlier – 50^th percentile = 4.5, 90th percentile = 7.0.

The reason the January scores are lower is because Cambridge applicants, who are likely to be among the strongest students, all sit the ESAT in the October sitting. When the non-Cambridge applicants are placed on the same scale, they tend to do slightly worse, thereby dragging the average scores down.

What is a good ESAT score?

A good ESAT score is one that gets you accepted onto the course of your choice, and this depends on the course and university you are applying to. We shall see that the scores of accepted students vary depending on whether you are applying to Cambridge or Imperial, and what subject you’re applying for.

Generally speaking, you will need an ESAT score of around 5.5 in a module to be confident of being in the top 25% of all test-takers, and a score around 6.7 for the top 10%.

These figures apply to the application cycle as a whole; if you are applying to Cambridge (and therefore taking the more competitive October sitting), the top 10% is fixed at 7.0 for each module.

Average ESAT score

In 2025-26, the 50^th percentile scores for each ESAT module were between 3.9 and 4.2:

Module	50th Percentile
Mathematics 1	4.1
Biology	4.2
Chemistry	4.2
Physics	3.9
Mathematics 2	3.9

Note that the 50^th percentile is fixed at 4.5 for the October sitting; the figures above apply to both the October and January sittings as a whole.

In 2024-25, these were the 50^th percentile and mean scores for each ESAT module, divided by test sitting:

Module	Sitting	Mean	Percentile 50
Maths 1	All	4.46	4.2
Maths 1	Oct	4.59	4.5
Maths 1	Jan	4.03	4
Biology	All	4.71	4.5
Biology	Oct	4.72	4.5
Biology	Jan	NA	NA
Chemistry	All	4.62	4.5
Chemistry	Oct	4.7	4.5
Chemistry	Jan	3.8	3.7
Physics	All	4.5	4.4
Physics	Oct	4.65	4.5
Physics	Jan	4.08	3.9
Maths 2	All	4.52	4.5
Maths 2	Oct	4.66	4.5
Maths 2	Jan	4.15	4.2

The average ESAT score is higher in October than January for the reasons explained above.

The mean score was 4.6-4.7 in October, 3.8-4.2 in January, and 4.5-4.6 overall. This varies by module.

The 50^th percentile score is fixed at 4.5 for the October sitting, and was 3.7-4.2 in the January sitting and 4.2-4.5 overall.

Good score for Cambridge

According to the latest official Cambridge admissions data, the average ESAT score of accepted applicants in 2025 was around 6.1, though this varied by module:

Module	Applicant	Offer holder	Accepted
Maths 1	4.67	5.62	5.69
Biology	4.75	5.92	6.07
Chemistry	4.81	5.93	6.05
Physics	4.77	6.24	6.29
Maths 2	4.80	6.13	6.18
Average	4.76	5.97	6.06

Accepted Cambridge applicants did best in Physics, scoring 6.3 on average, and worst in Maths 1, scoring 5.7 on average.

The overall average for all Cambridge applicants was 4.76, slightly better than the 50^th percentile score of 4.5 for the October sitting. Nonetheless, we can see that the higher your ESAT score, the more likely you are to be accepted by Cambridge.

Good score for Imperial

Imperial releases data on the ESAT scores of applicants who receive and do not receive offers. For 2026, this was as follows. (Note that the scores are aggregate scores across all three modules a student takes; we have added in the average score per module for reference.)

Department	Unsuccessful – not interviewed	Unsuccessful – interviewed	Offered
Aeronautics	8.2	15.5	17.5
Chemical Engineering	5.9	14.2	14.2
Civil and Environmental Engineering	3		12.9
Design Engineering	7.3	11.4	8.9
Electrical and Electronic Engineering	11.2	11.8	16.6
Mechanical Engineering	10	15.3	15.8
Physics	10.4		17.5
Weighted average	9.1	14.0	15.7
Per module weighted average	3.0	4.7	5.2

When producing our average scores for the different applicant types, we have weighted the average by the number of applicants each department receives.

The average ESAT score of offered applicants at Imperial was 15.7 in total, or 5.2 per module, while for unsuccessful applicants who weren’t interviewed, it was just 9.1 in total, or 3.0 per module. Applicants who were interviewed but did not receive an offer scored an average of 14.0 in total, or 4.7 per module.

On average, successful applicants to Imperial score about 0.9 points per module lower than successful applicants to Cambridge, underscoring that Cambridge is more selective.

The departments at Imperial which require the highest ESAT scores are Aeronautics and Physics, where accepted applicants score 17.5 in total across their three modules on average. Design Engineering has by far the lowest average ESAT scores of accepted applicants, at just 8.9 in total.

You can learn more about the acceptance rates of different departments at Imperial in our dedicated guide.

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Sources

ESAT Explanation of Results, 2025-26

ESAT Technical Report 2024-25

Cambridge admissions statistics, 2025

Imperial ESAT and TMUA statistics