2016-2025 TMUA DATA
TMUA score conversion, curves and calculator
Enter both papers’ raw marks: official per-paper tables for 2016-2023, MioMath Model curves for 2024-2025, historical curves.
Register and view my scoresImportant: UAT-UK no longer publishes a raw-to-scaled table for 2024 or 2025. The current-format curves here come from the MioMath Model; they do not represent official scores.
October 2026 is not converted yet: the official curve has not been published. Once results are out (expected mid-November), we will publish a conversion table that tracks the actual score distribution.
The Rasch formula in the official UAT-UK technical report prints its denominator as
1 − exp(θ − b); it should be1 + exp(θ − b). The typo changes none of its conclusions.
TMUA Score Calculator · 2016–2025
Calculator: convert correct answers to a TMUA score
Choose a year and enter the number correct for Paper 1 and Paper 2.
Enter your raw marks
Each paper has 20 questions. Enter counts, not scores.
October 2026 is not converted here: the official curve has not been published. Once results are out, we will publish a table that tracks the actual score distribution.
2025 score conversion
Complete both raw marks to see your score
- Paper 1
- —
- Paper 2
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Target score reference
Not universal cutoffs- 6.5
- 30/40
- 7.0
- 31/40
- 8.0
- 35/40
- 33/40
See where you stand in a computer-based mock test.
Start mock testView the complete 2025 Overall conversion table
| Raw | Overall | Raw | Overall |
|---|---|---|---|
| 0/40 | 1.01.0 | 21/40 | 4.74.0-5.0 |
| 1/40 | 1.01.0 | 22/40 | 4.94.5-5.5 |
| 2/40 | 1.01.0 | 23/40 | 5.14.5-5.5 |
| 3/40 | 1.01.0 | 24/40 | 5.35.0-6.0 |
| 4/40 | 1.01.0 | 25/40 | 5.55.0-6.0 |
| 5/40 | 1.01.0-1.5 | 26/40 | 5.85.5-6.0 |
| 6/40 | 1.21.0-1.5 | 27/40 | 6.05.5-6.5 |
| 7/40 | 1.61.0-2.0 | 28/40 | 6.25.5-6.5 |
| 8/40 | 1.91.0-2.5 | 29/40 | 6.46.0-7.0 |
| 9/40 | 2.11.5-2.5 | 30/40 | 6.76.0-7.0 |
| 10/40 | 2.42.0-3.0 | 31/40 | 7.06.5-7.5 |
| 11/40 | 2.62.0-3.0 | 32/40 | 7.26.5-8.0 |
| 12/40 | 2.92.5-3.5 | 33/40 | 7.67.0-8.0 |
| 13/40 | 3.12.5-3.5 | 34/40 | 7.97.5-8.5 |
| 14/40 | 3.33.0-3.5 | 35/40 | 8.38.0-9.0 |
| 15/40 | 3.53.0-4.0 | 36/40 | 8.78.0-9.0 |
| 16/40 | 3.73.0-4.0 | 37/40 | 9.09.0 |
| 17/40 | 3.93.5-4.5 | 38/40 | 9.09.0 |
| 18/40 | 4.13.5-4.5 | 39/40 | 9.09.0 |
| 19/40 | 4.34.0-5.0 | 40/40 | 9.09.0 |
| 20/40 | 4.54.0-5.0 | ||
2016-2023 use official legacy conversion tables; the 2024-2025 MioMath Model is an IRT-Constrained Score Reconstruction Model built on UAT-UK’s official psychometric framework and historical candidate score distributions, with consistency validated against verified real-world results.
2016–2025 TMUA
Historical conversion curves and score distributions
Switch between raw-to-scaled conversion curves and candidate score distributions.
2016–2023 Official legacy raw-to-Overall tables; the archived official page confirms the materials grouped as Practice Papers were the 2016 test papers.
2024–2025 · MioMath Model An IRT-Constrained Score Reconstruction Model built on UAT-UK’s official psychometric framework and historical candidate score distributions, with consistency validated against verified real-world results; use the calculator above for ranges.
What to know about the table and the curves
- 1The same 25 correct answers do not always score the same. A sitting uses several forms, issued to different regions at different times, of differing difficulty, equated onto one scale afterwards — so no single raw-to-score table fits everyone. Within one form the opposite holds: the same number correct gives the same score, and which questions you got right is irrelevant.
- 2This chart reads difficulty, not a formula. It shows where that year’s paper difficulty sits, so results compare across years and sittings. It is not a conversion formula and does not replace the official table — UAT-UK has published none since 2024; the 2024–2025 curves come from the MioMath Model.
Official TMUA results and percentiles
TMUA reports a 1.0-9.0 scaled score. A percentile describes your position within a candidate cohort; it is not a university admissions cutoff, and each course uses results in its own context.
| Cycle | Candidates | Mean | Median | 75th percentile | 90th percentile | Source |
|---|---|---|---|---|---|---|
| 2025-26 | 16,092 | 4.28 | 4.1 | 5.3 | 6.7 | UAT-UK PDF |
| 2024-25 | 13,855 | 4.20 | 4.0 | 5.2 | 6.5 | UAT-UK PDF |
Figures come from the corresponding UAT-UK technical report; each row combines the October and following January sittings. Per-score distributions are in the Distribution view above.
TMUA candidate benchmarks
The UAT-UK technical reports publish 2024-25 results by area of residence (UK / EU / Other) and by nationality (top five non-British nationalities); from 2025-26 they publish area of residence only. Every figure below is transcribed from the official reports.
2024-25 cycle · by residence and nationality
Official figures cover UK / EU / Other by residence and the top five non-British nationalities. Chinese candidates are shown separately by nationality; the "Other" residence row includes Chinese and every other non-UK/EU candidate.
| Group | Basis | Candidates | Mean | P50 | P75 | P90 |
|---|---|---|---|---|---|---|
| UK | Residence | 7,715 | 3.86 | 3.8 | 4.8 | 5.8 |
| EU | Residence | 664 | 3.78 | 3.6 | 4.8 | 5.9 |
| Other | Residence | 5,472 | 4.74 | 4.6 | 5.9 | 7.5 |
| Chinese | Nationality | 2,554 | 5.42 | 5.4 | 6.7 | 8.4 |
| Indian | Nationality | 779 | 3.63 | 3.5 | 4.7 | 5.7 |
| Singaporean | Nationality | 316 | 4.78 | 4.7 | 5.8 | 6.9 |
| Hong Kong | Nationality | 296 | 5.06 | 5.0 | 6.3 | 7.6 |
| Malaysian | Nationality | 231 | 3.80 | 3.8 | 4.7 | 5.7 |
| All candidates | 13,855 | 4.20 | 4.0 | 5.2 | 6.5 |
Enter a score between 1.0 and 9.0 to compare.
2025-26 cycle · by area of residence
No by-nationality split exists for this cycle. "Other" (outside the UK/EU) aggregates every other nationality, including Chinese and Indian candidates.
| Group | Basis | Candidates | Mean | P50 | P75 | P90 |
|---|---|---|---|---|---|---|
| UK | Residence | 8,643 | 3.98 | 3.9 | 4.9 | 6.0 |
| EU | Residence | 716 | 3.94 | 3.7 | 4.9 | 6.4 |
| Other | Residence | 6,733 | 4.71 | 4.5 | 5.8 | 7.5 |
| All candidates | 16,092 | 4.28 | 4.1 | 5.3 | 6.7 |
Sources: TMUA Technical Report 2024-25 · TMUA Technical Report 2025-26. Counts and quantiles are as published; percentile comparisons for each group interpolate the official quantiles and are approximate.
Official tables and the MioMath Model
| Years | Status | Use |
|---|---|---|
| 2016-2023 | Published paper conversion tables | Use for that exact year and paper |
| 2024–2025 | MioMath Model | Use to view score ranges |
2024-2026 TMUA
4 conclusions a TMUA candidate should read first
Read the full article: TMUA scoring decoded- 1
No “raw marks = score” table you see online is official
Since the move to computer-based testing in 2024, UAT-UK publishes scores and distributions but no raw-to-scaled table — the table itself was discontinued that year, and no conversion table circulating online comes from UAT-UK. The legacy tables do not carry over either: in the official 2019-2021 tables 28/40 was 7.0, while the MioMath Model puts 7.0 at about 31 correct for 2025. The distribution moved with it — in 2019-2023, 26-32% of candidates scored 6.5 or more each year; since 2024 only about 12-13% score 6.3 or more. So estimating yourself from an old year’s question count will overstate where you stand.
- 2
“January is easier” — no. January and October are scored on the same ruler
UAT-UK fixes the October 50th-percentile candidate (θ = −0.0639) at 4.5 and the 90th percentile (θ = 1.4634) at 7.0, draws the line score = 4.6046 + 1.6369 × θ, and uses the same constants for both sittings, capped at 1.0-9.0. January’s median of 3.3-3.6 reflects a weaker January cohort, not a friendlier ruler. So the only reason to sit in January is a second attempt with more preparation — not an easier board.
- 3
The 0.5 between 6.5 and 7.0 is smaller than one sitting’s own measurement error
Across both sittings the top-10% line is only 6.5-6.7 (October alone starts at 7.0), while a single sitting carries about ±1.3 of measurement error — the same person’s two sittings can differ by a full point. So a 6.5 has not dropped out of the top band and 6.5 against 7.0 is not a tier apart; and if you are weighing a retake, judge it on that noise — a 0.5 gap buys another draw, not a higher level.
- 4
Which questions you miss does not matter — every question is worth the same
On the same form, the same number correct always gives the same score, and a hard final question carries exactly the weight of an easy one. Reports of “same raw mark, different score” come from different forms. So do not grind a hard question to the point where you have no time to check the ones you can already answer — spend the time where a correct answer is most likely. In the official statistics, 23% of 2024-25 candidates left at least one question answered in 10 seconds or less or never reached it (16% in 2025-26), and that is usually where marks go.
Official figures come from UAT-UK and Cambridge Assessment publications; 2024-2025 raw conversions come from the MioMath Model.
Official sources: TMUA Technical Report 2024-25·TMUA Technical Report 2025-26·Explanation of Results 2024-25·Explanation of Results 2025-26·Explanation of Results 2023·UAT-UK
MioMath research: TMUA Scoring Decoded (MioMath research report)