Every CAT Quant Formula You Need for 2026: The Complete Master List Organised by Topic

Every CAT Quant Formula You Need for 2026: The Complete Master List Organised by Topic

You do not need 200 formulas to score well in CAT Quant. You need 50-60 core CAT quant formulas that cover every topic the exam tests, and you need to know when to apply each one. The problem most aspirants face is not a lack of formulas but a lack of organisation. Formulas are scattered across 15 different PDFs, 10 YouTube playlists, and a notebook with illegible handwriting from three months ago.

This is the master list of all formulas for CAT 2026 Quant, organised by topic. Bookmark it, screenshot it, or copy it into your own revision sheet. Every formula here has appeared in CAT papers within the last 5 years. If a formula is not on this list, you probably do not need it for CAT.

CAT Quant Formulas: Number Systems

Number systems carry 4-6 questions per CAT paper. The formulas below cover divisibility, remainders, HCF/LCM, and factorial properties. These are the most frequently tested CAT quant formulas in this topic area, and each one has appeared in at least 2 of the last 5 CAT papers.

Formula	What It Does
HCF(a,b) x LCM(a,b) = a x b	Relates HCF and LCM for two numbers
n! has floor(n/p) + floor(n/p^2) + ... trailing zeros of prime p	Count trailing zeros or highest power of p in n!
Euler's totient: phi(n) = n x (1-1/p1)(1-1/p2)...	Count of numbers less than n coprime to n
Number of factors of n = (a1+1)(a2+1)... where n = p1^a1 x p2^a2...	Total factor count from prime factorisation
Sum of factors = (p1^(a1+1)-1)/(p1-1) x (p2^(a2+1)-1)/(p2-1) x ...	Sum of all divisors
Remainder of a^n / d: use cyclicity of last digit or Fermat's little theorem	Remainder problems with large exponents

CAT Quant Formulas: Algebra

Algebra questions in CAT test equations, inequalities, functions, and logarithms. The formulas below are the ones that save time on CAT day. Quadratic equations and logarithm properties together account for about 60% of all CAT algebra questions based on analysis of recent papers.

Formula	What It Does
ax^2 + bx + c = 0: x = (-b +/- sqrt(b^2-4ac)) / 2a	Quadratic formula
Sum of roots = -b/a, Product of roots = c/a	Vieta's formulas for quadratics
log(ab) = log(a) + log(b), log(a/b) = log(a) - log(b)	Logarithm product and quotient rules
log_a(b) = log(b)/log(a) = 1/log_b(a)	Change of base formula
AM >= GM >= HM (for positive numbers)	Arithmetic mean, geometric mean, harmonic mean inequality
|a+b| <= |a| + |b| and |a-b| >= ||a| - |b||	Triangle inequality for absolute values

CAT Quant Formulas: Geometry and Mensuration

Geometry has the highest formula density in the CAT quant formulas list. Triangles, circles, and quadrilaterals each carry their own set of formulas. The ones below are tested most frequently. Memorise the triangle area formulas first; they appear in some form in every single CAT paper.

Formula	What It Does
Area of triangle = (1/2) x base x height	Basic triangle area
Heron's: Area = sqrt(s(s-a)(s-b)(s-c)), s = (a+b+c)/2	Triangle area from three sides
Area of equilateral triangle = (sqrt(3)/4) x a^2	Equilateral triangle with side a
Circumradius R = abc / 4A, Inradius r = A/s	Circumscribed and inscribed circle radii
Area of circle = pi x r^2, Circumference = 2 x pi x r	Circle basics
Arc length = (theta/360) x 2pi x r, Sector area = (theta/360) x pi x r^2	Arc and sector from central angle
Similar triangles: sides proportional, areas in ratio of squares of sides	Similar triangle properties
Pythagoras: a^2 + b^2 = c^2 (right triangle)	Right triangle side relationship

• Common Pythagorean triples for CAT: (3,4,5), (5,12,13), (7,24,25), (8,15,17)
• 30-60-90 triangle sides ratio: 1 : sqrt(3) : 2
• 45-45-90 triangle sides ratio: 1 : 1 : sqrt(2)

CAT Quant Formulas: Arithmetic

Arithmetic topics (time-speed-distance, profit/loss, percentages, averages, mixtures, time-work) together account for 8-10 questions per CAT paper. These all formulas for CAT arithmetic section are among the most frequently tested and among the easiest to apply once memorised.

Topic	Formula
Speed-Distance-Time	Distance = Speed x Time, Average speed = 2ab/(a+b) for equal distances
Relative Speed	Same direction: |s1-s2|, Opposite: s1+s2
Profit/Loss	Profit% = (SP-CP)/CP x 100, Loss% = (CP-SP)/CP x 100
Markup	SP = MP x (1 - Discount%), MP = CP x (1 + Markup%)
Simple Interest	SI = P x R x T / 100
Compound Interest	A = P(1 + R/100)^T
Percentages	%change = (New-Old)/Old x 100, Successive: a+b+ab/100
Averages	Avg = Sum/Count, Weighted avg = (w1.x1 + w2.x2)/(w1+w2)
Mixtures	Alligation: (C2-Cavg)/(Cavg-C1) = n1/n2
Time-Work	If A does in x days, B in y days, together: 1/x + 1/y = 1/T

CAT Quant Formulas: Modern Math

Modern math covers permutations, combinations, probability, and arithmetic/geometric progressions. These topics carry 3-5 questions per CAT paper. The formulas below are the core set you need for all formulas for CAT modern math questions. Progressions formulas are particularly useful because they appear in both direct and disguised forms across multiple question types.

Topic	Formula
Permutations	nPr = n! / (n-r)!
Combinations	nCr = n! / (r! x (n-r)!)
Probability	P(A) = Favourable / Total, P(A or B) = P(A) + P(B) - P(A and B)
Conditional	P(A|B) = P(A and B) / P(B)
AP: nth term	a_n = a + (n-1)d
AP: Sum	S_n = n/2 x (2a + (n-1)d) = n/2 x (first + last)
GP: nth term	a_n = a x r^(n-1)
GP: Sum (finite)	S_n = a(r^n - 1)/(r - 1) when r != 1
GP: Sum (infinite)	S = a/(1-r) when |r| < 1

How to Use This CAT Quant Formulas List

A master list is useful only if you convert it into active knowledge. Reading this page once does not make these formulas available during the exam. Here is a revision method that works, based on how top CAT scorers prepare their formula sheets for the CAT 2026 exam.

1. Copy the formulas by hand into your own notebook. The physical act of writing reinforces memory. Do not print this page and assume you will remember it.
2. Solve 5 problems per formula using the CAT practice question bank. A formula you have never applied in a problem is a formula you do not actually know.
3. Revise the full list every Sunday during your CAT preparation. Write each formula from memory, then check against this master list. Mark the ones you forgot. Those marked formulas get extra revision the following week.
4. Create a "last mile" sheet of the 20 formulas you forget most often. Review this sheet in the 48 hours before CAT. Your CAT 2026 preparation plan should include these revision slots explicitly.

This CAT 2026 formula sheet approach turns passive reading into active recall, which is the only form of memory that works under exam pressure. If you are preparing with Optima Learn's personalised study plan, the topic sequencing already accounts for formula revision cadence alongside problem solving. Use your CAT score prediction to track how your Quant accuracy improves as you internalise more formulas.

Common Doubts Answered

How many formulas should I memorise for CAT Quant?

You need roughly 50-60 core formulas across all topics. This master list covers the essential ones. Focus on understanding derivations rather than rote memorisation. If you understand why a formula works, you can reconstruct it under exam pressure even if memory fails.

Are CAT quant formulas enough to score well?

Formulas alone are not enough. CAT Quant tests application, not recall. You need formulas as tools but the real skill is recognising which formula to apply in a given problem. Practise 200+ problems across all topics to build this pattern recognition. Explore CAT preparation resources for structured practice sets.

Which CAT quant topics have the most formulas?

Geometry has the highest formula density (triangles, circles, quadrilaterals, coordinate geometry). Number systems and algebra are next. Arithmetic topics like time-speed-distance and profit-loss have fewer formulas but more word-problem variations. Allocate revision time proportionally.

Should I make my own formula sheet for CAT?

Yes. The act of writing formulas by hand improves retention. Use this master list as a starting point, then add formulas you discover while solving problems. A personalised formula sheet with your own shorthand and annotations will serve you better during revision than any printed reference.