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How CAT Turns Raw Marks Into a Scaled Score and a Percentile

The IIMs’ own equating formula and P = (N − r)/N, step by step, with a simulator — and a check that the official top-percentile counts are consistent with the formula.

By ProSyllabus Admin
Updated 2 days agoCAT · Scoring · Percentile
#cat normalisation#cat scaled score#cat percentile calculation#how is cat percentile calculated#cat raw score to percentile#cat 2026 percentile formula
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Must-have cheatsheet · CAT 2026Every important point, on 7 pagesfor CATQuant formulas unit by unit, DILR set types, VARC methods and the scoring maths — what the 2023–2025 papers asked.Quant formulasDILR methodsVARC methods15 traps7-page PDFInstant download1 hr to read all of itSee what's inside →
Source: The CAT 2026 Information Bulletin and Eligibility document dated 26.07.2026, the Press Release of 26.07.2026 and the Media Releases of 15.09.2026 and 22.09.2026. and 2 more
How CAT Turns Raw Marks Into a Scaled Score and a Percentile

Checked 29 September 2026. From the CAT 2025 and CAT 2024 Scoring and Equating and Scaled Score Calculation documents and the CAT 2023–2025 result releases. The CAT 2026 scoring document has not been published; the method has been the same in 2024 and 2025.

CAT is sat in three sessions with three different papers, so your raw marks are never compared directly with anyone else’s. The published calculation first equates each session’s scores to a common scale, caps each section at 100, adds the three sections, and turns the result into a percentile using your rank among everyone who appeared. The IIMs also state that scores are “further normalised across different sections” by percentile equivalence, a step they do not describe in enough detail to reproduce (Step 3 below). The method is published — the CAT 2024 and CAT 2025 documents are identical in substance — but almost every “CAT percentile calculator” online skips it. This guide walks through the official formula, lets you run it, and checks it against the numbers the IIMs actually announced.

2.58 lakh
appeared in CAT 2025
12
scored 100 percentile in CAT 2025
100
ceiling on each sectional scaled score
2 decimals
percentiles are rounded to

CAT 2025 result release (24.12.2025) and Scaled Score Calculation.

Where other pages get this wrong

A CAT percentile is P = (N − r)/N × 100, where r is your rank on the scaled score and tied candidates share a rank.

Commonly published instead: “Percentile is the share of candidates who scored at or below you.”

The CAT 2025 Scaled Score Calculation document defines N as everyone who appeared across the three sessions and r as your rank by scaled score, with identical scores given identical ranks (two tied at the top are both rank 1; the next is rank 3). So N − r counts everyone who scored below you plus everyone tied with you except yourself. Against “at or below you”, the formula always leaves out exactly one candidate — you — so the two differ by 1/N. That is tiny, but it is the definition the check further down relies on.

Step 1: your raw score in each section

Question typeCorrectWrongNot attempted
MCQ+3−10
Non-MCQ (type the answer)+300

CAT 2026 FAQ, Exam Q10, Q11 and Q15. The raw score of a section is negative when the −1 marks from wrong MCQs exceed the +3 marks earned from correct answers.

The raw score is calculated per section: VARC, DILR and QA each get their own. Two objections were accepted in CAT 2023 — one VARC answer key was corrected and one DILR question was given two correct options — which is a reminder that the raw score is only final after the answer-key review.

Step 2: equating the three sessions

For every section, the CAT Centre computes two numbers for each session and the same two numbers for all sessions combined. The first is G = mean + standard deviation of the raw scores, a marker for a good-but-typical performance. The second is the mean raw score of the top 0.1%, a marker for the very top. The formula then maps your session’s scale onto the combined scale so that those two markers line up.

TermMeaning
RYour raw score in the section
Mi, SiMean and standard deviation of raw scores in that section in your session (i = 1, 2 or 3)
GiMi + Si
M, S, GThe same for all three sessions combined; G = M + S
Ai0.1Mean raw score of the top 0.1% of candidates in that section in your session
A0.1Mean raw score of the top 0.1% in that section across all sessions
Scaled score(R − Gi) × (A0.1 − G) / (Ai0.1 − Gi) + G; above 100 is rounded down to 100

CAT 2025 Scaled Score Calculation (the CAT 2024 document states the same steps). The documents illustrate with QA and say the same method applies to VARC and DILR.

Read the formula as “how far above your session’s typical mark were you, measured in units of your session’s spread to the top?” — then re-expressed on the combined scale. The official note says the aim is to “adjust for location and scale differences of score distributions across different forms”. Whether a given raw score moves up or down depends on both anchors of your session (Gi and the top-0.1% mean) against the combined ones — a simple “hard session” or “easy session” label does not decide it, and the formula does. A candidate exactly at their session’s Gi gets exactly the combined G.

Input (made-up example, not CAT data)Result
Your session: mean 10, SD 8, top-0.1% mean 60Gi = 18
All sessions: mean 11, SD 8.5, top-0.1% mean 62G = 19.5
Stretch factor (62 − 19.5) / (60 − 18)1.012
Raw score 30 → (30 − 18) × 1.012 + 19.5scaled 31.64

Our worked example with invented inputs, to show the arithmetic. The IIMs do not publish any session’s mean, SD or top-0.1% average.

Session-equating simulator (the official formula)

The IIMs do not publish the session means, standard deviations or top-0.1% averages, so nobody outside the CAT Centre can compute a real scaled score. Use this to see how the formula behaves: change your session’s mean, spread or top average and watch how the same raw score moves up or down. The pre-filled numbers are made-up examples, not CAT data.

Your session, one section

All three sessions together, same section

Formula from the CAT 2025 (and 2024) Scaled Score Calculation document: scaled = (R − Gi) × (A0.1 − G) / (Ai0.1 − Gi) + G, where Gi = Mi + Si for your session and G = M + S for all sessions combined. Any scaled score above 100 is rounded down to 100.

Step 3: cap, then add the sections

If the formula gives more than 100 in a section, the scaled score is rounded down to 100. The overall scaled score is simply the sum of the three sectional scaled scores. The CAT 2025 Scoring and Equating note adds one sentence the calculation document does not expand on: after normalising across forms, “the scores shall be further normalised across different sections”, using “percentile equivalence”. The published step-by-step calculation describes only the session equating and the sum, so we cannot tell you how that cross-section step is applied — both statements are official, and we print both rather than guess.

Step 4: from scaled score to percentile

StepWhat happens
1N = all candidates who appeared, across all three sessions
2Rank everyone by scaled score (per section, and overall); equal scores share a rank — two candidates tied at the top are both rank 1 and the next is rank 3
3P = (N − r)/N × 100
4Round to two decimals: P ≥ 99.995 shows as 100; 99.985 ≤ P < 99.995 shows as 99.99; and so on

CAT 2025 Scaled Score Calculation, Percentile Score Calculation, Steps 1–4. The same steps give the overall percentile and each sectional percentile.

Because percentile comes from rank, it depends on how many people appeared. The rounding rule is also why “100 percentile” is not one person: at 2.58 lakh candidates, every rank from 1 to 12 rounds to 100.

A consistency check: the official top-percentile counts

Every result release lists how many candidates scored 100, 99.99 and 99.98 percentile. If the formula above is really what the IIMs use, those counts should be exactly the ranks that round to each value, given the number who appeared. We ran that check. Using the rounded appeared figures as approximations for N, all nine counts match. Because the exact N and the tie pattern are not published, this is supporting evidence, not an exact verification.

CycleAppeared (release)Official 100 / 99.99 / 99.98Ranks that round to each (our arithmetic)
CAT 2023~2.88 lakh14 / 29 / 291–14 / 15–43 / 44–72 → 14 / 29 / 29
CAT 20242.93 lakh14 / 29 / 301–14 / 15–43 / 44–73 → 14 / 29 / 30
CAT 20252.58 lakh12 / 26 / 261–12 / 13–38 / 39–64 → 12 / 26 / 26

Our arithmetic with N = 2,88,000, 2,93,000 and 2,58,000. Example for 2025: 100 needs P ≥ 99.995, i.e. r ≤ 0.00005 × 2,58,000 = 12.9, so ranks 1 to 12. The exact N is not published and can move a boundary within the rounding: for example, the 99.99 band in 2024 has 30 ranks rather than 29 once N reaches 2,93,334. Ties across a boundary would also change the counts.

Candidates who appeared in CAT
CAT 2023~2.88 lakh
CAT 20242.93 lakh
CAT 20252.58 lakh

CAT 2023, 2024 and 2025 result media releases. Registered eligible candidates: ~3.28, 3.29 and 2.95 lakh.

CycleRegistered eligibleAppeared100 pct99.9999.98
CAT 2023~3.28 lakh~2.88 lakh142929
CAT 20243.29 lakh2.93 lakh142930
CAT 20252.95 lakh2.58 lakh122626

What a percentile means in candidates

Turn the formula round and a percentile gives an approximate rank: r ≈ N × (1 − P/100); the number strictly ahead of you is r − 1. Because the displayed percentile is rounded to two decimals, it really stands for a range of ranks (at 2.58 lakh, a displayed 99.99 is any rank from 13 to 38) — the calculator below shows that range. The table gives central estimates for the last two fields. It is arithmetic, not an official rank list, and the 2026 field is unknown until the result — but it shows why the same percentile means a different number of people each year.

PercentileApproximate rank at 2.58 lakh (2025 field)Approximate rank at 2.93 lakh (2024 field)
99.992629
99.9258293
99.51,2901,465
992,5802,930
985,1605,860
977,7408,790
9512,90014,650
9025,80029,300
8538,70043,950
8051,60058,600
7564,50073,250
7077,40087,900

Our arithmetic: approximate rank r ≈ N × (1 − P/100), with N = 2,58,000 (CAT 2025) and 2,93,000 (CAT 2024), rounded. A displayed percentile covers a range of ranks, not one.

Percentile and rank, both ways

Enter how many candidates appeared and either a rank or a percentile. The first line uses the official formula; the second shows which ranks round to the percentile you typed.

Official formula (CAT 2025 Scaled Score Calculation): P = (N − r)/N × 100, rounded to two decimals; tied scaled scores share a rank. N defaults to 2,58,000, our rounding of the "2.58 lakh" who appeared in CAT 2025. The 2026 N is unknown until the result.

What is not published — and why every marks-to-percentile table is an estimate

The IIMs publish the method, not the inputs. There is no official table that says “this many marks gives this percentile”: the session means, standard deviations and top-0.1% averages stay inside the CAT Centre, and the percentile depends on the whole field. Third-party marks-vs-percentile tables are estimates assembled from sources such as candidates’ response sheets or scorecards, score-calculator submissions and previous-year trends; the method varies by publisher. Such tables can be useful for a rough target, but they are estimates on scaled scores from a previous year, and a table “out of 204” also assumes a 68-question paper, which the IIMs have not announced.

What you can use with confidence: your raw score is +3/−1 on MCQs and +3/0 on typed answers; session differences are adjusted by the equating; each section is capped at 100 scaled; and your percentile is your rank among everyone who appeared, rounded to two decimals. For an estimate of rank from a percentile, the CAT rank predictor in this series does the same arithmetic in more detail.

How is the CAT percentile calculated?

P = (N − r)/N × 100, where N is the number who appeared and r your rank on the scaled score; tied candidates share a rank and P is rounded to two decimals.

What is the CAT normalisation formula?

Scaled = (R − Gi) × (A0.1 − G)/(Ai0.1 − Gi) + G, where G is mean plus SD and A0.1 the top-0.1% mean, for your session (i) and for all sessions.

Can a scaled score be more than 100?

No. Any sectional scaled score above 100 is rounded down to 100.

Is the overall scaled score the sum of the sections?

Yes, according to the Scaled Score Calculation document.

Does a harder session hurt me?

The equating is designed to adjust for differences in the location and spread of each session’s scores; whether a particular raw score moves up or down depends on the formula’s anchors, not on a hard or easy label.

Is there an official marks-to-percentile table for CAT?

No. The IIMs publish the method only; marks-vs-percentile tables are coaching estimates.

How many candidates got 100 percentile in CAT 2025?

12, of whom 10 were male and 2 female; 3 were engineers and 9 non-engineers.

How many candidates appeared in CAT 2025?

2.58 lakh, of 2.95 lakh registered eligible candidates.

What does 99 percentile mean in candidates?

A rank of roughly 2,580 in a field of 2.58 lakh — our arithmetic, not an official rank; a rounded percentile covers a range of ranks.

Why do 12 people share 100 percentile?

Percentiles are rounded to two decimals, so every rank up to 0.005% of the field shows as 100.

Is the CAT 2026 scoring method published?

Not yet; the 2024 and 2025 documents describe the same method.

Can my sectional raw score be negative?

Yes, if the −1 marks from wrong MCQs exceed the +3 marks from correct answers; IIM Calcutta, for example, requires a non-negative raw score in every section.

This chapter is part of the CAT Board ExaminationExplore every chapter — summary, notes, extra questions & MCQ quizzes
Page 1 free
Must-have cheatsheet · CAT 2026Every important point, on 7 pagesfor CATQuant formulas unit by unit, DILR set types, VARC methods and the scoring maths — what the 2023–2025 papers asked.Quant formulasDILR methodsVARC methods15 traps7-page PDFInstant download1 hr to read all of itSee what's inside →
Source: The CAT 2026 Information Bulletin and Eligibility document dated 26.07.2026, the Press Release of 26.07.2026 and the Media Releases of 15.09.2026 and 22.09.2026. and 2 more

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