10 June 2026
TMUA.co.uk team
TMUA Score Conversion: Raw Marks to the 1.0-9.0 Scale
The TMUA reports a score from 1.0 to 9.0, but nobody hands you the table that turns raw marks into that number. It does not exist publicly. The conversion is recalculated for every sitting. What you can know: how the mechanism works, where the common scores cluster, and roughly what a competitive score costs in raw marks.
Table of contents
- The mechanics: raw marks to scaled score
- Why the conversion moves between sittings
- Percentile intuition: where scores actually cluster
- What a 6.5 costs in raw marks
- What this means for your practice targets
- Frequently asked questions
Intro
Every October, the same forum thread appears within hours of results: "I got X, is that good?" The honest answer requires three pieces of context that the score report does not include: the shape of that year's distribution, the raw marks behind the scaled number, and what the universities you care about actually treat as competitive. This post covers all three, and is honest about which parts are published fact and which are calibrated estimate.
The mechanics: raw marks to scaled score
The raw scoring is simple. Two papers, 20 multiple-choice questions each, one mark per question, no negative marking, no calculator, 75 minutes per paper. Paper 1 covers applications of mathematical knowledge; Paper 2 covers mathematical reasoning and logic. Your maximum raw total is 40.
Those raw marks are then converted onto the 1.0 to 9.0 reporting scale. The conversion is not a fixed lookup table and it is not a simple percentage. It is a statistical adjustment designed so that a given scaled score represents a comparable level of performance across different sittings, even though the papers themselves differ in difficulty. A 6.5 earned on a brutal paper and a 6.5 earned on a gentler paper are meant to mean the same thing.
The practical consequence: the number of raw marks behind any scaled score changes from year to year, and the exam board does not publish the mapping. Anyone showing you a precise official raw-to-score table for a recent sitting is showing you something that does not exist.
Why the conversion moves between sittings
Two papers are never equally hard. If 13 raw marks always mapped to the same scaled score, candidates sitting an unusually hard paper would be systematically punished and admissions tutors comparing across years would be comparing noise.
So the conversion flexes. On a harder paper, fewer raw marks buy the same scaled score. On an easier paper, more are needed. This is also why drilling for a specific raw-mark target is slightly the wrong mental model. You are not racing a fixed mark threshold; you are racing the rest of the cohort on that day's paper. The 2024 format change made this concrete: the wordier, more applied style changed how raw marks distributed across the cohort, and the conversion absorbed it. If your practice material predates that shift, the new format post explains why your raw scores on old papers may flatter you.
Percentile intuition: where scores actually cluster
The published headline from the October 2025 sitting: the most common score was 4.5. That single fact recalibrates most students' expectations, because the 1.0 to 9.0 scale invites people to read it like a mark out of nine. It is not. The distribution is bottom-heavy.
From the 2025 distribution data our free score converter is built on:
| Scaled score | Approximate 2025 percentile |
|---|---|
| 3.8 | 50th (median) |
| 4.5 | ~66th, and the most common single score |
| 5.0 | ~76th |
| 6.0 | ~88th |
| 6.5 | ~92nd |
| 7.0 | ~94th |
| 8.0 | ~96th-97th |
Read that table slowly. A 5.0, which feels mediocre on a nine-point scale, beat roughly three quarters of the October 2025 cohort. A 6.5 put you around the top 8%. And this is a cohort that self-selects: almost everyone sitting the TMUA is a strong A-level mathematician aiming at Cambridge, Imperial, LSE, UCL, Warwick or Durham. Mid-table in this field is not mid-table nationally.
The competitive bands follow from the percentiles. For Cambridge and Imperial, roughly 6.0 to 6.5 and above is broadly competitive. Neither publishes a cutoff, and a lower score does not auto-reject you, but the percentile maths explains why those numbers keep being quoted. How each university actually uses the number, screen versus holistic read versus interview input, is covered in What TMUA Score Do You Need for Cambridge, Imperial and LSE?
What a 6.5 costs in raw marks
Here is the honest version, clearly labelled.
Published fact: nothing. No official raw-to-scale table exists for recent sittings.
Our estimate: by back-mapping the 2025 percentile distribution onto raw performance, our calibration puts a 6.5 at roughly 13 out of 20 per paper, with 11 out of 20 already landing around the middle of the scale. The full estimated table, with percentile context per grade, is in our free TMUA score chart.
Two implications worth internalising. First, you can get seven questions wrong per paper and still hold a top-8% score. The TMUA is not an accuracy exam; it is a triage exam. Second, the gap between the median candidate and a competitive one is only about two to three extra correct answers per paper. That is a closable gap, and it is mostly closed through technique rather than new content, a point we expand in Is the TMUA Hard? The route from one to the other is the 16-week plan.
What this means for your practice targets
Stop tracking raw marks in isolation. A 14/20 on a gentle practice set and a 14/20 on a hard one are different results, and neither tells you a scaled score by itself. Better targets:
- Track percentile-anchored estimates, not marks. The score converter maps marks from specific past sittings onto the current scale so your practice numbers mean something.
- Mock under real conversion logic. The six auto-marked mocks in TMUA Pro report calibrated 1.0 to 9.0 estimates rather than raw percentages, so your trajectory is measured in the unit universities actually see. Pro is £299 and carries a 6.5+ score guarantee, which only makes commercial sense because the raw-mark gap behind it is genuinely closable.
- Answer everything. No negative marking means a blank is the only guaranteed zero on the paper.
Related reading
- Is the TMUA Hard? An Honest Difficulty Breakdown
- The New TMUA Format: Why Pre-2024 Past Papers Mislead You
- 10 TMUA Mistakes That Cost Marks Under Time Pressure
Closing
TMUA score conversion is deliberately opaque at the level students most want it to be precise: the raw-mark table. But the parts that matter for decision-making are knowable. The scale is percentile-shaped, not mark-shaped. The most common score in October 2025 was 4.5. A 6.5 sat around the top 8% and, on our calibration, costs roughly 13 correct answers per paper. Aim at the percentile, practise the triage, and let the conversion take care of itself.
Frequently asked questions
How is the TMUA scored? Each paper has 20 multiple-choice questions worth one mark each, with no negative marking. Raw marks are converted onto a 1.0 to 9.0 scale. The conversion is adjusted per sitting to account for paper difficulty, and the official raw-to-scale table is not published.
What is the average TMUA score? The most common score in the October 2025 sitting was 4.5. The median sits a little lower; in the 2025 distribution data our converter is built on, the 50th percentile lands around 3.8.
What TMUA score do Cambridge and Imperial want? Neither publishes a hard cutoff. Broadly, 6.0 to 6.5 and above is competitive for Cambridge and Imperial. In the 2025 distribution a 6.5 sat around the top 8% of candidates.
How many raw marks is a 6.5? Not officially published. On our calibration, built by back-mapping the 2025 percentile distribution, 6.5 corresponds to roughly 13 out of 20 per paper. Treat that as an estimate; the true mapping shifts with each sitting's difficulty.
Is there negative marking on the TMUA? No. A wrong answer scores the same as a blank, so you should answer every question. There is never a reason to leave a TMUA question unanswered.
Percentile figures are from the October 2025 distribution data used by our score converter. Raw-mark equivalences are our calibrated estimates, not official conversions. Last updated 2026-06-10.