All Important UPSC CSAT Formulas for Prelims 2026 – Quick Revision for Prelims

Many UPSC aspirants clear GS Paper-I but struggle with UPSC CSAT due to avoidable mistakes in math equations and overlooking simple CSAT formulas. Remember, CSAT is only a qualifying criterion, but your CSAT score can determine whether you even make it to the UPSC Mains list. That’s why we’ve put together this one-stop guide of all important UPSC CSAT formulas—short, clear, and easy to revise. 

With these formulas at your fingertips, recalling concepts in the exam becomes effortless, helping you manage time better and stay calm in UPSC Prelims 2026.

The smartest way to secure your CSAT score is to keep all important UPSC CSAT formulas at your fingertips. Below is a topic-wise collection of formulas as per the UPSC Prelims CSAT syllabus. 

Here are the most important UPSC CSAT Paper II divisibility rules: 

Mentor Tip: In CSAT, divisibility helps you eliminate options quickly without full calculation, especially in number system and data sufficiency questions.

Must see: Coding Decoding Questions and Answers: A Guide for UPSC CSAT

• Speed = Distance ÷ Time
• Distance = Speed × Time
• Time = Distance ÷ Speed

1. Relative Speed

• When moving towards each other → Speeds add
• When moving in the same direction → Faster – Slower

Useful in train problems, boat-stream questions, and meeting-time puzzles.

2. Average Speed

• If a person covers equal distances at two different speeds: x+y2xy (Harmonic Mean of the two speeds)
• If distances are unequal, use: Average Speed = Total Time/Total Distance​

3. Unit Conversion (must-know for CSAT)

• 1 km/h = 5/18 m/s
• 1 m/s = 18/5 km/h

Always convert before calculating, especially if the distance is in meters and the speed is in km/h.

4. Train Problems

• Time taken by a train to cross a pole/person = (Length of Train) ÷ (Speed)
• Time taken to cross a platform = (Length of Train + Length of Platform) ÷ (Speed)
• Two trains crossing each other (opposite direction) = (Sum of lengths) ÷ (Relative Speed)
• Two trains crossing each other (same direction) = (Difference of lengths) ÷ (Relative Speed)

5. Boat & Stream Problems

• Downstream Speed = (Boat Speed + Stream Speed)
• Upstream Speed = (Boat Speed – Stream Speed)
• Speed in Still Water = (Downstream + Upstream) ÷ 2
• Stream Speed = (Downstream – Upstream) ÷ 2

6. Circular Track / Meeting Problems

• Time for two persons running in opposite directions around a circular track to meet: Time = Sum of Speeds/Circumference of Track​

1. Simple Interest (SI): 100P×R×T​

Where:

• P = Principal (original amount)
• R = Rate of interest per annum (%)
• T = Time (in years)

Total Amount (A) = P + SI

Mentor Tip: If time is in months, use  T=12/months​

2. Compound Interest (CI)

• Formula for Amount (A): A = P (1 + R/100)^n
• Formula for Compound Interest (CI): CI = A - P

Where:

• P = Principal
• R = Rate of Interest (%)
• n = Time (years)

3. Compounded Half-Yearly: A = P (1 + R/200)^(2n)

4. Compounded Quarterly: A = P (1 + R/400)^(4n)

5. Difference Between CI and SI (for 2 years): CI - SI = (P × R²) / 100²

6. Population Growth / Depreciation (CI Application)

• Population after n years: P (1 + R/100)^n
• Population before n years: P / (1 + R/100)^n
• Depreciation (value decreases): P (1 - R/100)^n

Quick Tricks for SI & CI CSAT

• If SI for 2 years and 3 years is given, → Difference = SI of 1 year.
• If CI and SI for 2 years are close, → difference = extra interest on SI of 1 year.
• Always check if compounding is annual, half-yearly, or quarterly before solving.

• Profit = Selling Price − Cost Price
• Loss = Cost Price − Selling Price 
• Profit% % = (Profit / Cost Price) × 100
• Loss % = Loss % = (Loss / Cost Price) × 100
• Discount % = Discount % = (Discount / Marked Price) × 100
• Overall Discount % = x + y − (x × y) / 100

• Simple Average = (Sum of observations) / (Number of observations)
• Weighted Average = Weighted Average = (w1x1 + w2x2 + ... + wnxn) / (w1 + w2 + ... + wn) 
• If all values increase (or decrease) by the same amount, the average increases (or decreases) by the same amount.

• Relation between LCM and HCF (for two numbers): LCM × HCF = Product of the two numbers.
• For more than two numbers: Find using prime factorisation OR apply LCM/HCF step by step on pairs of numbers.

1. Properties of LCM & HCF

• The HCF of two or more numbers is the largest number that divides each of them exactly.
• The LCM of two or more numbers is the smallest number that is divisible by each of them. For any two numbers: HCF ≤ each number ≤ LCM.
• If two numbers are co-prime, then: LCM = Product of the numbers, HCF = 1

2. Application Tips for LCM & HCF CSAT

• Use the HCF (Highest Common Factor) in problems involving sharing, dividing, or grouping items equally.
• Use LCM in problems of repetition, synchronisation, or events happening together. (e.g., bells ringing together, traffic lights, work-cycle problems).

1. Probability Basics

• Probability of an event A: P(A) = (Number of favourable outcomes) / (Total outcomes)
• Probability of A = P(Not A) = 1 − P(A)
• P(Not A) = Odds in favour = Favourable / Unfavourable
• Odds in favour = Odds in favour = Favourable / Unfavourable
• Odds against = Unfavourable / Favourable

2. Venn Diagram Rules (Inclusion–Exclusion Principle)

• For Two Sets (A, B): |A ∪ B| = |A| + |B| − |A ∩ B|
• For Three Sets (A, B, C): |A ∪ B ∪ C| = |A| + |B| + |C| − |A ∩ B| − |B ∩ C| − |C ∩ A| + |A ∩ B ∩ C|

3. Quadratic Equation & Ratios, Proportion

• Quadratic Equation: ax² + bx + c = 0
• Roots of the equation: x = (−b ± √(b² − 4ac)) / (2a)
• Discriminant (D): D = b² − 4ac

4. Nature of roots:

• If D > 0 → Two real & distinct roots
• If D = 0 → Two real & equal roots
• If D < 0 → No real roots (imaginary)

• Ordinary Year: 365 days = 52 weeks + 1 day → 1 odd day
• Leap Year: 366 days = 52 weeks + 2 days → 2 odd days

A year is a leap year if:

• Divisible by 4
• Not divisible by 100, unless divisible by 400

1. Century Rules

• 100 years = 76 ordinary + 24 leap = 36524 days → 5 odd days
• 200 years = 3 odd days
• 300 years = 1 odd day
• 400 years = 0 odd days (calendar repeats every 400 years

2. Day of the Week Rules

• Count total odd days from year 0 to the given date, divide by 7, remainder gives the day of the week.

Quick Reference – Odd Days in First N Years

• 1 year → 1 odd day
• 2 years → 2 odd days
• 3 years → 3 odd days
• 4 years → 0 odd days (since 4 years = 1461 days = 208 weeks + 5 days = complete weeks)

• Main directions: North, South, East, West
• Intermediate directions: NE, NW, SE, SW

1. Key Rules:

• Turning Right = 90° clockwise
• Turning Left = 90° anticlockwise
• Facing opposite = 180° turn

2. Shortcut for CSAT:

Use coordinate system: Assume starting point as (0,0).

• Moving North → +y
• Moving South → −y
• Moving East → +x
• Moving West → −x

Final position = compare (x,y) to origin to find direction & distance.

Keep revising these UPSC CSAT formulas regularly, and you’ll see your confidence grow—what once felt like tough math will soon feel effortless. 

Also see: UPSC CSAT Maths Syllabus 2025, Topic Wise Download PDF

Remembering formulas is not about mugging them up. The real trick is to revise them smartly and practice using them in exam-like questions. Here are some easy tips:

1. Daily Quick Revision: Spend 10–15 minutes each day scanning through your formula list. Repetition locks them into long-term memory.
2. Use Flashcards or Sticky Notes: Keep small flashcards or sticky notes with key formulas on your study desk, laptop, or even a mirror for constant recall.
3. Create a Formula Wall/Chart: A big sheet on your wall with all important formulas makes for instant visual revision.
4. Practice Right After Revision: Apply the formulas in practice questions immediately. This builds both memory and speed.
5. Mix Them in Mocks: Don’t just revise in isolation. Use mocks and previous year CSAT papers to recall formulas under real test conditions.

Pro Tip: Revise the toughest formulas before sleeping. The brain consolidates memory better overnight.

Must see: Top CSAT Books for UPSC Prelims Exam

Imagine your personal mentor sitting beside you during the exam—this is what you need to do:

• Guard Your Time: The CSAT is a test of speed as much as accuracy. If a question feels like quicksand, skip it and return later.
• Pick Your Battles: Begin with the questions you’re most confident about. Early wins boost morale and save you from panic.
• Use Formula Questions as Warm-ups: They’re straightforward and scoring. Cracking these first will set a positive rhythm for the paper.
• Keep Perspective: You don’t need to ace every question. Your goal is to comfortably cross the cutoff. Stay calm, stay sharp.

Follow this roadmap, and you’ll see the CSAT turn from a stress point into a scoring edge.

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Start studying now and sharpen your CSAT score:

Consistency beats cramming. Revise your UPSC CSAT formulas regularly, practice them with mock questions, and watch even the toughest math problems start feeling simple and manageable. 

Stay focused, stay confident, and let your preparation shine in the exam.

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