CAT Important Formula (PDF): Find Topic Wise CAT Quant Formula

Important formulas for CAT exam (Quantitative Aptitude) are listed here. Make sure you are thorough with these CAT formulas in order to solve the Quantitative Aptitude accurately and score above 99 percentile.

CAT Quant Formula

To crack CAT Quantitative Aptitude, candidates need to be thorough with important Algebra and Geometry formulas. The section has a potential of getting you 100 percent marks but for that you will need to have complete clarity of the theory part of Quants topics.

CAT Quantitative Aptitude syllabus includes Number Systems, Profit, Loss and Discount, LCM and HCF, Time and Work, Averages, Logarithm, Surds and Indices, Probability, Set Theory & Function, Trigonometry, Permutation & Combination, Co-ordinate Geometry, Mensuration, etc. All these CAT quant topics have certain formulae on the basis of which the questions can be solved correctly. Check below CAT important formulas for Quants.

CAT Quantitative Aptitude Formulas

All the CAT exam topics included in Quant can be cracked with practice. But for that, you need to understand and memorise important Quant formulas. The CAT Quantitative Aptitude questions cannot be solved without applying formulas correctly. As part of your revision process for CAT 2026 exam, you will need a CAT formulas cheat sheet. So you must prepare a CAT formula sheet. You can also purchase a CAT formula book. However, to make it easier for you, we have listed below the most important formula (s) for CAT exam. Also find a CAT formula sheet PDF for download (free), for CAT 2026 preparation.

CAT Important Formulas: Mensuration

There are a number of questions in CAT which belong to Mensuration. Thus, you need to know and memorise the following important CAT formulas for Mensuration:

Triangle

Area = (1/2) × b × h
or
√[s(s – a)(s – b)(s – c)], where s = (a + b + c)/2

Square

Area = a × a
Perimeter = 4a

Rectangle

Area = l × b
Perimeter = 2(l + b)

Cube

Volume: V = a³
Lateral surface area = 4a²
Total surface area: S = 6a²
Diagonal (d) = √3 a

Cuboid

Volume: V = l × b × h
Total surface area = 2(lb + bh + hl)
Length of diagonal = √(l² + b² + h²)

Circle

Area = πr² or πd²/4
Circumference = 2πr or πd
Area of sector = (θ/360) × πr²

Also Read:

• Square Root and Cube Root
• Permutation and Combination
• Mean, Mode, Median
• Binomial Theorem

CAT Important Formulas: Coordinate Geometry

Given below are the important CAT formulas for Coordinate Geometry. You need to be thorough with these formulas to be able to solve the problems accurately.

The Distance Between two Points A(x₁, y₁) and B(x₂, y₂):

AB² = (x₂ – x₁)² + (y₂ – y₁)²

The Midpoint of a Line Joining Two Points:

The midpoint of the line joining the points (x₁, y₁) and (x₂, y₂) is:

[(x₁ + x₂)/2, (y₁ + y₂)/2]

The Equation of a Line Using One Point and the Gradient:

The equation of a line which has gradient m and passes through the point (x₁, y₁) is:

y – y₁ = m(x – x₁)

CAT Important Formulas: Number Systems

Check below important CAT formulas for Number Systems. The questions on Number Systems asked in the Quantitative Aptitude section of CAT are based on these formulas.

• 1 + 2 + 3 + 4 + ... + n = n(n + 1)/2
• 1² + 2² + 3² + ... + n² = [n(n + 1)(2n + 1)] / 6
• 1³ + 2³ + 3³ + ... + n³ = [n(n + 1)/2]²
• Sum of first n odd numbers = n²
• Sum of first n even numbers = n(n + 1)

Algebraic Expansions:

• (a – b)² = a² + b² – 2ab
• (a + b)² = a² + b² + 2ab
• (a + b)(a – b) = a² – b²
• (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
• (a³ – b³) = (a – b)(a² + ab + b²)
• (a³ + b³) = (a + b)(a² – ab + b²)
• (a³ + b³ + c³ – 3abc) = (a + b + c)(a² + b² + c² – ab – bc – ca)
• When a + b + c = 0, then a³ + b³ + c³ = 3abc
• (a + b)ⁿ = aⁿ + (ⁿC₁)a^n-1b + (ⁿC₂)a^n-2b² + ... + bⁿ

Important CAT Formulas for Profit, Loss and Discount (Arithmetic)

Check below important CAT formulas for Profit, Loss and Discount. Memorising these formulas will be helpful to you for solving CAT questions based on the topic.

• Profit (or Gain) = SP – CP
• Profit % = (Profit / CP) × 100
• SP = [(100 + Gain %) / 100] × CP
• CP = [100 / (100 + Gain %)] × SP
• Loss = CP – SP
• Loss % = (Loss / CP) × 100
• SP = [(100 – Loss %) / 100] × CP
• CP = [100 / (100 – Loss %)] × SP

CAT Important Formulas: LCM and HCF

Given below are the important CAT formulas you need to know to solve LCM and HCF questions of Quantitative Aptitude section of the exam.

LCM × HCF = Product of the two numbers
LCM of co-prime numbers = Product of the numbers

Speed, Time and Distance Formulas for CAT QA

Given below are the important CAT formulas that you should memorise to solve Speed, Time and Distance questions of the Quantitative Aptitude section.

Distance = Speed × Time
Time = Distance / Speed
Speed = Distance / Time

CAT Important Formulas: Percentages

To solve Percentages questions of CAT exam, you need to know the following formulas:

To find what percentage of x is y: (y / x) × 100
Increase N by S% = N × (1 + S/100)
Decrease N by S% = N × (1 – S/100)

CAT Important Formulas: Time and Work

To solve Time and Work questions of CAT exam, understand and memorise the following formula:

If X can do a piece of work in n days, then X’s 1 day’s work = 1/n
If X’s 1 day’s work = 1/n, then X can finish the complete work in n days.

CAT Important Formulas: Averages

Given below is the formula for Averages. To solve CAT questions based on Averages, you must know these formulas.

Average = (Sum of observations / Number of observations)

Simple and Compound Interest Formulas for CAT Exam

Simple and Compound Interest questions are regularly asked in CAT. To solve the Simple and Compound Interest questions accurately, you should memorise these formulas.

Interest Compounded Annually:

Amount = P × (1 + R/100)ⁿ

Interest Compounded Half-Yearly:

Amount = P × (1 + R/200)²ⁿ

Interest Compounded Quarterly:

Amount = P × (1 + R/400)⁴ⁿ

When Interest is Compounded Annually with Fractional Time (e.g., 3 a/b years):

Amount = P × (1 + R/100)³ × [1 + (R × a/b)/100]

When Interest Rates Vary by Year (R₁%, R₂%, R₃% for 1st, 2nd, 3rd year):

Amount = P × (1 + R₁/100) × (1 + R₂/100) × (1 + R₃/100)

Present Worth of Rs. x due n years hence:

Present Worth = x / (1 + R/100)ⁿ

CAT Important Formulas: Probability

Given below is the formula that you must memorise for solving CAT questions on Probability.

Sample Space: When an experiment is performed, the set S of all possible outcomes is the sample space.
Event: Any subset of a sample space is called an event.
Probability of Occurrence of an Event: P(E) = n(E) / n(S)

CAT Quantitative Aptitude formulas: Logarithm

To crack the questions based on Logarithm, here are the important CAT formulas you need to know:

• log_a(xy) = log_a x + log_a y
• log_a(x/y) = log_a x – log_a y
• log_x x = 1
• log_a 1 = 0
• log_a(xⁿ) = n × log_a x
• log_a x = 1 / (log_x a)
• log_a x = (log_b x) / (log_b a) = log x / log a

CAT Algebra & Modern Math Formulas: Set Theory and Functions

Given below are the important CAT formulas for Set Theory and Function:

De Morgan’s Laws:
(A ∩ B)’ = A’ ∪ B’
(A ∪ B)’ = A’ ∩ B’

Equivalence Relations on Set A (R ⊂ A × A):

• Reflexive: If aRa for all a ∈ A.
• Symmetric: If aRb, then bRa for all a, b ∈ A.
• Transitive: If aRb and bRc, then aRc for all a, b, c ∈ A.

A relation R that is reflexive, symmetric, and transitive is known as an equivalence relation.

Permutations: Ordered arrangements of r items chosen from n items without replacement: ⁿP_r = n! / (n – r)!

Combinations: Selections of r items chosen from n items where order does not matter: ⁿC_r = n! / [r! × (n – r)!]

CAT Quantitative Aptitude formulas: Trigonometry

Here are important formulas for CAT Trigonometry section. Understand and memorise these formulas for solving Trigonometry questions of CAT Quantitative Aptitude.

Trigonometric Ratios:

• Sine = Opposite / Hypotenuse
• Cosine = Adjacent / Hypotenuse
• Tangent = Opposite / Adjacent
• Cosecant = Hypotenuse / Opposite
• Secant = Hypotenuse / Adjacent
• Cotangent = Adjacent / Opposite

Reciprocal Identities:

• cosec θ = 1 / sin θ
• sec θ = 1 / cos θ
• cot θ = 1 / tan θ
• sin θ = 1 / cosec θ
• cos θ = 1 / sec θ
• tan θ = 1 / cot θ

Also Read: CAT Quant Topic-wise Weightage

CAT Important Formulas: Mixtures and Alligations

To solve questions on Mixtures and Alligations, apply the fundamental Rule of Alligation:

(Quantity of Cheaper / Quantity of Dearer) = (CP of Dearer – Mean Price) / (Mean Price – CP of Cheaper)

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