CAT 2026 Formula Sheet PDF: Complete Quant Formulas, Shortcuts & Last-Minute Revision Guide

CAT 2026 Quantitative Aptitude Formula Sheet PDF Download

Download the CAT 2026 formula PDF designed for fast revision and last-minute preparation. This free formula sheet covers all the important formulae that will be helpful to solve questions quickly in the CAT exam.

Download Now: CAT 2026 Important Formulas

CAT 2026 Formula Sheet: Why You Need It?

A CAT 2026 Formula Sheet acts as a quick revision companion that brings all important Quant formulas together in one place. It helps candidates revise faster, improve formula recall, and solve questions more accurately during CAT preparation.

CAT 2026 Quantitative Aptitude Syllabus Overview

The CAT Quantitative Aptitude section primarily covers five major areas: Arithmetic, Algebra, Geometry & Mensuration, Number System, and Modern Mathematics. Understanding these topics can help candidates organize their preparation and revise formulas more effectively.

Arithmetic Topics

Algebra Topics

Geometry and Mensuration Topics

Number System Topics

Modern Mathematics Topics

These topics form the core of the CAT Quant syllabus and are the source of most formula-based questions asked in the exam.

CAT 2026 Important Formulas of Geometry

Mastering important geometry formulas is crucial for cracking the CAT exam, as geometry is a key topic in the Quantitative Aptitude section. The following section covers all essential CAT geometry formulas, including areas, polygons, angles, and properties of triangles and circles to help you solve problems quickly and accurately.

CAT 2026 Important Formulas of Trigonometry

Trigonometry plays a vital role in the CAT Quantitative Aptitude section, making it essential to learn and memorise key formulas. This comprehensive list of important CAT trigonometry formulas helps aspirants solve complex problems with speed, accuracy, and confidence during the exam.

1. Basic Trigonometric Ratios

These are defined in relation to a right-angled triangle:

$\sin\theta=\frac{\text{Opposite Side}}{\text{Hypotenuse}}$

$\cos\theta=\frac{\text{Adjacent Side}}{\text{Hypotenuse}}$

$\tan\theta=\frac{\text{Opposite Side}}{\text{Adjacent Side}}$

$\csc\theta=\frac{\text{Hypotenuse}}{\text{Opposite Side}}$

$\sec\theta=\frac{\text{Hypotenuse}}{\text{Adjacent Side}}$

$\cot\theta=\frac{\text{Adjacent Side}}{\text{Opposite Side}}$

2. Pythagorean Identities

$\sin^2\theta+\cos^2\theta=1$

$1+\tan^2\theta=\sec^2\theta$

$1+\cot^2\theta=\csc^2\theta$

3. Trigonometric Functions of Negative Angles

$\sin(-\theta)=-\sin\theta$

$\cos(-\theta)=\cos\theta$

$\tan(-\theta)=-\tan\theta$

$\csc(-\theta)=-\csc\theta$

$\sec(-\theta)=\sec\theta$

$\cot(-\theta)=-\cot\theta$

4. Angle Sum and Difference Formulas

$\sin(A+B)=\sin A\cos B+\cos A\sin B$

$\sin(A-B)=\sin A\cos B-\cos A\sin B$

$\cos(A+B)=\cos A\cos B-\sin A\sin B$

$\cos(A-B)=\cos A\cos B+\sin A\sin B$

$\tan(A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}$

$\tan(A-B)=\frac{\tan A-\tan B}{1+\tan A\tan B}$

Quantitative Aptitude Formulae for CAT 2026

Quantitative Aptitude formulas form the foundation of the Quantitative Aptitude section in the CAT 2026 exam. Here are some important CAT 2026 quant section-wise formulae for CAT 2026 preparation:

Arithmetic

The Arithmetic section is the most important section in the Quantitative Aptitude Section, which is also useful for solving the Data Interpretation problems. Following are some 50+ Important Formulas for CAT Preparation of this section, which are given in this CAT Formula Sheet:

Percentage

Following are some Important CAT Formulas of percentage:

$X$ is what percentage of $Y$:

$\frac{X}{Y}\times100%$

$X$ is what percentage more/less than $Y$:

$\frac{|X-Y|}{Y}\times100%$

Shortcut Formulas

Following are some formulas which can be used as CAT Quant Formulae:

Profit & Loss

Following are some Important CAT Formulas of this topic:

Simple Interest (S.I.) & Compound Interest (C.I.)

The following are some basic and Important Formulas for CAT 2026 related to Simple Interest and Compound Interest:

where $P=$ Principal, $R=$ Rate of Interest, and $T=$ Time.

Shortcut Formulas

Following are some formulas which can be used as CAT Quant Formula Cheat Sheet for the preparation and exam point of view:

where $R=$ annual interest rate.

Time, Speed & Distance

The following are some basic and Important Formulas for CAT 2026 related to Time, Speed, and Distance:

Trains

Where:

$l=$ Length of the train
$d=$ Length of platform/tunnel
$s=$ Speed of the train
$l_1,l_2=$ Lengths of Train 1 and Train 2
$s_1,s_2=$ Speeds of Train 1 and Train 2

Boat & Streams

Clocks

Shortcut Formulas

We have provided below the shortcut formulae related to average speeds, boat stream, circular tracks, meeting point, to make your calculations faster in the CAT 2026 exam.

1. Average Speed Formulas

Case 1: Equal distances, different speeds

If the distance covered in each stage of a journey is the same, but speeds are different, the average speed is the harmonic mean:

$\text{Average Speed}=\frac{2s_1s_2}{s_1+s_2}$

Example:

Distance from $A$ to $B$ and $B$ to $C$ is the same. Speeds: $s_1$ and $s_2$. Then:

$\text{Average Speed}=\frac{2s_1s_2}{s_1+s_2}$

Case 2: Equal time, different speeds

If the time taken in each stage is the same but speeds differ, the average speed is the arithmetic mean:

$\text{Average Speed}=\frac{s_1+s_2}{2}$

2. Circular Track – Same Direction

If two people start from the same point on a circular track of length $D$ km with speeds $a$ and $b$ kmph in the same direction:

Time for first meeting:

$t_{\text{first}}=\frac{D}{|a-b|}$

Time to meet again at the starting point:

$t_{\text{start}}=\operatorname{LCM}\left(\frac{D}{a},\frac{D}{b}\right)$

Number of distinct meeting points:

$\text{Meeting Points}=|x-y|$

where $x:y$ is the simplified ratio of speeds.

Example: If $a=12$ kmph, $b=9$ kmph:

$x:y=12:9=4:3$

Therefore, $x=4$ and $y=3$.

3. Circular Track – Opposite Direction

If two people start from the same point in opposite directions:

Time for first meeting:

$t_{\text{first}}=\frac{D}{a+b}$

Time to meet again at the starting point:

$t_{\text{start}}=\operatorname{LCM}\left(\frac{D}{a},\frac{D}{b}\right)$

Number of distinct meeting points:

$\text{Meeting Points}=x+y$

where $x:y$ is the simplified ratio of speeds.

4. Meeting Point Between Two Opposite Travellers

If a person $P$ starts from $A$ towards $B$, and $Q$ starts from $B$ towards $A$, and they meet after time $t$:

$t=\sqrt{xy}$

where:

$x=$ time taken by $P$ to reach $B$ after meeting

$y=$ time taken by $Q$ to reach $A$ after meeting

5. Boats and Streams

If the speed of the boat downstream is $u$ kmph and upstream is $v$ kmph:

Speed of boat in still water:

$\text{Boat Speed}=\frac{u+v}{2}\text{ kmph}$

Rate of stream:

$\text{Stream Speed}=\frac{u-v}{2}\text{ kmph}$

While preparing for the arithmetic section, also check out this PDF, to practice topic-wise questions:

The CAT Arithmetic Hackbook PDF: Zero Math Background

Geometry

The Geometry section is the lengthiest section in the Quantitative Aptitude Section which has lots of properties and formulas.

1. Triangles

Properties of Triangles

The sum of all interior angles in a triangle is $180^\circ$ and the sum of all exterior angles is $360^\circ$.

The sum of any two sides is always greater than the third one and the difference of any two sides is less than the third one.

Let $a,b,c$ be the sides of a triangle, then

$|b-c|<a<b+c$

In a scalene triangle the greatest side is always greater than one-third of the perimeter and less than half of the perimeter.

Let $a,b,c$ be the sides of the triangle and $a$ be the greatest side. Let the perimeter be $P$. Then

$\frac{P}{3}<a<\frac{P}{2}$

Example: In a scalene triangle $ABC$, the perimeter is $24$ cm and all sides are integers.

Let $a,b,c$ be sides of the triangle with $a$ the greatest side. Then

$\frac{24}{3}<a<\frac{24}{2}$

$8<a<12$

So possible values are $9,10,11$ cm.

For $a,b,c$ sides of a triangle and $a$ the greatest side:

If $a^2<b^2+c^2$, then the triangle is acute angled.

If $a^2=b^2+c^2$, then the triangle is right angled (Pythagoras theorem).

If $a^2>b^2+c^2$, then the triangle is obtuse angled.

Here $D$ is the midpoint of side $AC$, so $AD=DC$.

Midpoint of a Triangle

Length of the Median:

$BD=\frac{1}{2}\sqrt{2(AB^2+BC^2)-AC^2}$

$3\times(\text{Sum of squares of sides})=4\times(\text{Sum of squares of medians})$

That is,

$3(a^2+b^2+c^2)=4(M_a^2+M_b^2+M_c^2)$

where $a,b,c$ are the sides of the triangle and $M_a,M_b,M_c$ are the medians.

In a right-angled triangle,

$\text{Median of Hypotenuse}=\frac{1}{2}\times\text{Hypotenuse}$

That is,

$CD=\frac{AB}{2}$

If all the medians are drawn in the triangle, then the 6 small triangles are generated in the triangle, which are equal in the Area.

Area of Triangle

Heron’s Formula

If all sides of a triangle are given. Let $a,b,c$ be the sides of the triangle:

$\text{Area}=\sqrt{s(s-a)(s-b)(s-c)}$

where

$s=\frac{a+b+c}{2}$

is the semiperimeter.

If two sides and the included angle are given:

$\text{Area}=\frac{1}{2}\times(\text{Product of given sides})\times\sin(\text{included angle})$

$\text{Area}=\frac{1}{2}ab\sin C$

(Example: sides $a,b$ and included angle $C$ are given.)

If a side and its respective altitude (perpendicular drawn from the opposite vertex) is given, then:

$\text{Area of the triangle}=\frac{1}{2}\times\text{Base}\times\text{Height (Altitude)}$

Shortcut Formulas

Area of an equilateral triangle:

$\text{Area}=\frac{\sqrt{3}}{4}a^2$

Height (Altitude) of an equilateral triangle:

$h=\frac{\sqrt{3}}{2}a$

Area of a triangle:

$\text{Area}=r\times s$

where $r$ is the inradius and $s$ is the semiperimeter.

Area of a triangle:

$\text{Area}=\frac{abc}{4R}$

where $a,b,c$ are sides and $R$ is the circumradius.

Quadrilaterals:

3. Circle:

Let $r$ be the radius of the circle.

Semi-Circle

Let $r$ be the radius of the semi-circle.

Sector and Segment of a Circle

$OAXC$ is called the sector of the circle, and $AXC$ is called the segment.

Where:

• $\theta$ = angle subtended at the center (in degrees)
• $r$ = radius of the circle

Direct Common Tangent

$PQ$ and $RS$ are the direct common tangents of the two circles and are equal in length.

The length of the direct common tangent is:

$$L^2=d^2-(r_1-r_2)^2$$ or $$L=\sqrt{d^2-(r_1-r_2)^2}$$

Where:

• $L$ = length of the direct common tangent
• $d$ = distance between the centers of the two circles
• $r_1,r_2$ = radii of the two circles

Transverse Common Tangents of Two Circles

$PQ$ and $RS$ are the transverse common tangents of the two circles and are equal in length.

The length of the transverse common tangent is:

$$L^2=d^2-(r_1+r_2)^2$$ or $$L=\sqrt{d^2-(r_1+r_2)^2}$$

Where:

• $L$ = length of the transverse common tangent
• $d$ = distance between the centers of the two circles
• $r_1, r_2$ = radii of the two circles

CAT 2026 Mensuration Formula Sheet

Mensuration questions in CAT 2026 require a clear understanding of surface area and volume formulas for common 3D figures. The key formulas for cubes, cuboids, cylinders, cones, spheres, and hemispheres are given below for quick revision.

Cube

Let $a$ be the side of the cube.

Cuboid

Let $l=$ length, $b=$ breadth, and $h=$ height.

Cylinder

Let $r=$ radius of the circular base and $h=$ height.

Cone

Let $r=$ radius of the circular base, $h=$ height, and $l=$ slant height.

Sphere

Let $r$ be the radius of the sphere.

Hemisphere

Let $r$ be the radius of the hemisphere.

CAT 2026 Algebra Formula Sheet

Algebra is an important part of CAT 2026 Quantitative Aptitude, covering topics such as quadratic equations, progressions, indices, surds, and logarithms. The key Algebra formulas are listed below for quick revision.

Quadratic Equations

Root Nature Based on Discriminant

Arithmetic Progression (AP)

Geometric Progression (GP)

Harmonic Progression (HP)

Important Series Formulae

Indices and Surds

Logarithms

While preparing for algebra, you can check out this PDF and strengthen your concepts and practice questions:

CAT Algebra PDF Handbook 2026: Everything You Need

Quick Revision Tips for CAT 2026 Algebra

• Memorise the roots, sum of roots, and discriminant formulas for Quadratic Equations.

• Revise AP, GP, and Series formulas regularly as they are frequently tested.

• Practice Logarithm properties and index rules together since questions often combine both concepts.

• Maintain a separate Algebra formula sheet for last-minute CAT 2026 revision.

• Focus on formula application through CAT previous year questions and mock tests rather than rote memorisation.

CAT 2026 Quantitative Aptitude Cheat Sheet PDF

The CAT 2026 Quantitative Aptitude Cheat Sheet PDF is a compact, high-utility resource covering all essential formulas, theorems, and shortcuts from Arithmetic, Algebra, Geometry, Modern Math, and Number Systems.

Download Now: CAT 2026 Quantitative Aptitude Cheat Sheet PDF

Approximation and Mental Calculation Tricks

Approximation and mental calculation can help CAT 2026 aspirants reduce calculation time, particularly when the answer choices are sufficiently far apart. However, approximation should be used selectively; if two choices are very close, accurate calculation is safer.

Some useful CAT Quant calculation tricks include:

Aspirants should also memorise common fraction-percentage equivalents such as $1/2=50%$, $1/3\approx33.33%$, $1/4=25%$, $1/5=20%$, and $1/8=12.5%$. These conversions are especially useful in Arithmetic and DI calculations.

How to Memorise CAT Quant Formulas Without Forgetting Them

Memorising every CAT Quant formula at once is usually ineffective. Formulas are easier to retain when they are repeatedly applied to questions rather than simply reread.

Use these techniques to improve formula retention:

1. Create topic-wise formula groups: Keep Arithmetic, Algebra, Geometry, Number System, and Modern Maths formulas separate.

2. Understand before memorising: Know what each variable represents and when the formula applies.

3. Use active recall: Cover the formula and try writing it from memory.

4. Solve 3–5 questions: Apply each newly revised formula to CAT-level problems.

5. Mark frequently forgotten formulas: Maintain a separate list of formulas you repeatedly miss.

6. Follow spaced revision: Revisit important formulas after 1 day, 3 days, and 7 days.

7. Maintain a one-page final sheet: Keep only the formulas, identities, and conversions you genuinely need.

The aim is not memorisation alone but quick formula recognition and correct application under time pressure.

How to Use the CAT Formula Sheet During Last-Minute Revision

During the final weeks before CAT 2026, use the formula sheet for rapid recall rather than learning new concepts. Divide formulas into Strong, Needs Revision, and Frequently Forgotten categories and focus mainly on the latter two.

A practical revision cycle is:

Formula → Recall → 2–3 Questions → Check Mistakes → Revise Again

For example, after revising Time, Speed and Distance formulas, solve a few mixed questions without referring to the sheet. Mark any formula you cannot recall or apply correctly for another revision.

In the final few days, prioritise frequently used formulas, standard values, fraction-percentage conversions, geometry results, algebraic identities, and calculation shortcuts.

CAT 2026 Quant Formula Revision Checklist

Use this checklist to track the major Quant formula areas you need to revise before CAT 2026.

Use these topic links to quickly revisit the relevant CAT Quant concepts and formulas:

After completing the checklist, test yourself without looking at the sheet to ensure you can both recall formulas and identify where to apply them.

Last-Minute CAT Quant Revision Strategy Using Formula Sheets

As CAT 2026 approaches, focus on revising and applying known formulas rather than trying to learn large amounts of new material.

30-Day Revision Plan

Use the first phase to complete one full revision cycle across all major Quant topics.

Focus Areas:

• Complete formula revision of all topics

• Solve sectional tests regularly

• Maintain a formula error notebook

• Revise high-frequency CAT formulas

15-Day Revision Plan

With 15 days left, shift the focus towards applying formulas through mocks and previous-year questions.

Focus Areas:

• Revise formula sheets every day

• Analyse mock-test mistakes

• Practise formula-based questions

• Strengthen weak topics

7-Day Revision Plan

Use the final week for quick revision, error correction, and confidence building rather than learning unfamiliar concepts.

Focus Areas:

• Quickly revise all formula sheets

• Memorise important shortcuts

• Revise error logs and notes

• Take limited mocks and focus on analysis

Formula Revision Before Mock Tests

Before each CAT mock, spend 15–20 minutes revising key formulas from Arithmetic, Algebra, Geometry, Number System, and Modern Maths. This improves recall, speed, and accuracy.

Use this quick checklist to cover the most important formulas before starting a mock:

A quick review of these areas can help reduce formula-based errors and improve calculation speed during the mock.

How to Create Your CAT 2026 Formula Sheet?

A personalised formula sheet can make revision more effective by focusing on frequently tested concepts, shortcuts, and areas where you make mistakes.

Follow these steps to build a concise and useful CAT 2026 formula sheet:

Keep the sheet concise, highlight frequently used formulas, and update it regularly based on your mock-test performance.

Quick Tips

• Keep it concise and easy to scan.

• Limit each topic to one or two pages.

• Highlight frequently used formulas.

• Update it after every mock.

• Revise it regularly, especially in the final months.

Best Books for CAT 2026 Quantitative Aptitude Preparation

The right study material can strengthen both concepts and problem-solving skills, from Quant fundamentals to CAT-level practice and revision.

Recommended Book Sequence for CAT 2026

Preparation Tip: If you are starting from scratch, begin with NCERT and Arun Sharma. Candidates targeting a 99+ percentile in CAT 2026 Quant should additionally practice from Nishit K. Sinha, Quantum CAT, previous year papers, and high-quality mock tests.

CAT 2026 Recommended eBooks and Study Materials for QA

Explore the best CAT 2026 eBooks and study materials recommended by experts for complete preparation of Quantitative Aptitude. These resources will help aspirants revise efficiently and boost exam preparation.