📋 In This Page
What is a Percentage and How It Works
A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin "per centum" — literally "per hundred." When we say 25%, we mean 25 out of every 100, or equivalently the fraction 25/100 = 0.25.
Percentages are ubiquitous in everyday life in India — from GST on purchases and discount offers in shopping to exam marks, salary increments, interest rates, and election results. Understanding how to calculate percentages quickly and accurately saves time, prevents errors on invoices and returns, and helps you make better financial decisions.
🛒
Shopping & Discounts
Calculate how much you save on a 30% off sale, or what the final price is after stacking multiple discounts.
🧾
GST & Taxes
Calculate GST inclusive/exclusive prices, split into CGST and SGST, for invoicing and tax compliance in India.
📝
Exam Marks
Convert raw marks to percentage, find aggregate across subjects, and determine grade and division.
📈
Finance & Investment
Calculate returns, interest rates, portfolio gains/losses, and year-on-year growth in income or savings.
All Percentage Formulas — Explained with Examples
Formula 1: What is X% of Y?
X% of Y
Result = (X ÷ 100) × Y
Use for: discounts, GST amounts, tips, commissions, interest calculations
Example: What is 18% of ₹2,500? (GST calculation)
GST = (18 ÷ 100) × 2,500
= 0.18 × 2,500 = ₹450
18% GST on ₹2,500 = ₹450 | Total price = ₹2,950
Formula 2: What percentage is X of Y?
What % is X of Y
Percentage = (X ÷ Y) × 100
Use for: exam marks, attendance, market share, batting averages, profit margins
Example: What percentage is 450 of 600? (Exam marks)
Percentage = (450 ÷ 600) × 100
= 0.75 × 100 = 75%
450 marks out of 600 = 75% — Grade: A (Very Good)
Formula 3: Percentage Change (Increase or Decrease)
Percentage Change
% Change = ((New − Old) ÷ Old) × 100
Positive result = increase | Negative result = decrease
Use for: price changes, salary hikes, population growth, inflation
Use for: price changes, salary hikes, population growth, inflation
Example: Salary increased from ₹40,000 to ₹46,000
% Change = ((46,000 − 40,000) ÷ 40,000) × 100
= (6,000 ÷ 40,000) × 100 = +15% salary increment
₹40,000 → ₹46,000 = +15% increase
Formula 4: Reverse Percentage (Find original before % was applied)
Reverse Percentage
Original = Final ÷ (1 + rate/100) [if % was added]
Original = Final ÷ (1 − rate/100) [if % was removed]
Original = Final ÷ (1 − rate/100) [if % was removed]
Use for: finding pre-GST price, pre-discount price, base salary before deduction
Example: Item costs ₹1,180 inclusive of 18% GST — what was the original price?
Original = ₹1,180 ÷ (1 + 18/100) = ₹1,180 ÷ 1.18
Original price = ₹1,000 | GST = ₹180
GST Percentage Calculations in India
India's Goods and Services Tax (GST) system has 5 rate slabs — 0%, 5%, 12%, 18%, and 28%. For most everyday transactions, the most important calculations are: adding GST to get the final price, removing GST to find the base price, and splitting GST into CGST and SGST for invoicing.
How intra-state GST is split (CGST + SGST)
| GST Slab | CGST | SGST | Total GST | Example: on ₹1,000 |
|---|---|---|---|---|
| 5% | 2.5% | 2.5% | 5% | ₹25 CGST + ₹25 SGST = ₹50 total → ₹1,050 |
| 12% | 6% | 6% | 12% | ₹60 CGST + ₹60 SGST = ₹120 total → ₹1,120 |
| 18% | 9% | 9% | 18% | ₹90 CGST + ₹90 SGST = ₹180 total → ₹1,180 |
| 28% | 14% | 14% | 28% | ₹140 CGST + ₹140 SGST = ₹280 total → ₹1,280 |
CGST vs IGST: For intra-state (within the same state) supplies, GST is split equally between CGST (central) and SGST (state). For inter-state (between different states) or import supplies, only IGST (Integrated GST, the full rate) is charged — no split. The GST mode in this calculator shows CGST/SGST split (intra-state). For inter-state, the total GST applies as IGST.
Common GST calculations in India
| Situation | GST Rate | Base Price | GST Amount | Final Price |
|---|---|---|---|---|
| Restaurant (AC, non-alcohol) | 5% | ₹1,000 | ₹50 | ₹1,050 |
| Mobile phone | 12% | ₹15,000 | ₹1,800 | ₹16,800 |
| Clothing (branded, >₹1000) | 12% | ₹2,000 | ₹240 | ₹2,240 |
| Professional services | 18% | ₹50,000 | ₹9,000 | ₹59,000 |
| Insurance premium | 18% | ₹20,000 | ₹3,600 | ₹23,600 |
| Luxury car (above ₹10L) | 28% | ₹30,00,000 | ₹8,40,000 | ₹38,40,000 |
Percentage Marks and Exam Grading in India
Calculating exam percentage is one of the most common uses of percentage in India. Whether for Class 10/12 boards, competitive exams, college exams, or university results, the formula is always the same — but the grading scale varies significantly by board and institution.
| Board / System | Grading Scale | Pass Percentage | Distinction | Notes |
|---|---|---|---|---|
| CBSE Class 10 / 12 | CGPA / Grade | 33% | 90%+ | CGPA × 9.5 = approximate percentage |
| Most State Boards | % marks | 35% | 75%+ (Distinction) | Varies by state — check board notification |
| University (UGC CBCS) | CGPA (10-point) | CGPA 4.5+ | CGPA 7.5+ | O, A+, A, B+, B, C, P, F grades |
| UPSC Civil Services | % of marks | Cutoff varies | — | Prelims cutoff changes each year |
| IIT JEE (Advanced) | Rank + Score | Category cutoff | — | Percentage is not the primary metric |
💡For CBSE, your CGPA on the marksheet is not the same as percentage. Multiply your CGPA by 9.5 to get an approximate percentage. So CGPA 8.0 ≈ 76%, CGPA 9.0 ≈ 85.5%, CGPA 10.0 ≈ 95%. Use the Marks % mode above with your total and maximum marks for an exact percentage.
5 Common Percentage Calculation Mistakes
Mistake 1 — Calculating percentage of a percentage incorrectly
✗ Wrong: "30% off then an additional 20% off = 50% off total"
✓ Right: 30% off then 20% off the discounted price = only 44% off total
Successive percentage discounts do not add up linearly. A 30% discount on ₹1,000 gives ₹700. Then 20% off ₹700 gives ₹560. The total effective discount is ₹440 out of ₹1,000 = 44%, not 50%. Retailers exploit this by advertising "additional 20% off" on already-discounted items. Always calculate on the actual final price, not by adding percentages together.
Mistake 2 — Confusing percentage point change with percentage change
✗ Wrong: "Interest rate went from 8% to 10% — that's a 2% increase"
✓ Right: It is a 2 percentage point increase, but a 25% increase in the rate itself
This distinction is critical in finance. An interest rate moving from 8% to 10% is an increase of 2 percentage points — but the interest rate itself has increased by 25% ((10-8)/8 × 100). When RBI raises rates by "25 basis points" (0.25 percentage points), that is a 3.1% increase in a 8% rate. News reports often blur this distinction — always check whether a change is in percentage points or percentage of the original rate.
Mistake 3 — Adding GST on top of a GST-inclusive price
✗ Wrong: Charging 18% GST on ₹1,180 (which already includes 18% GST) = ₹212.40 extra
✓ Right: ₹1,180 already includes GST. Original price = ₹1,180 ÷ 1.18 = ₹1,000. GST = ₹180
This is a common billing error — applying GST to a GST-inclusive price results in double taxation. If a quoted price is "inclusive of GST," use the Reverse Percentage mode to extract the original price. GST is always calculated on the base (exclusive) price, never on the final price. Use the GST mode in this calculator to handle both "add GST" and "remove GST" scenarios correctly.
Mistake 4 — Using the wrong base for percentage change
✗ Wrong: Price fell from ₹100 to ₹80 → "that's 25% cheaper because 20/80 = 25%"
✓ Right: % decrease = ((100-80)/100) × 100 = 20% decrease (the base is the original price)
Percentage change is always relative to the starting value (the original), not the ending value. If a price drops from ₹100 to ₹80, the 20-point drop is 20% of ₹100 (the original) — not 25% of ₹80 (the final price). This also applies when a price rises: from ₹80 back to ₹100 is a 25% increase (because the base is now ₹80). The same absolute change represents different percentages depending on the direction.
Mistake 5 — Confusing percentage marks with total percentage
✗ Wrong: Adding individual subject percentages and dividing by number of subjects
✓ Right: Add all marks obtained, divide by total maximum marks, multiply by 100
If subjects have different maximum marks, averaging the individual percentages gives a wrong result. For example: Maths 90/100 = 90%, Science 80/100 = 80%, English 120/150 = 80%. Averaging: (90+80+80)/3 = 83.3%. But correct calculation: (90+80+120)/(100+100+150) × 100 = 290/350 × 100 = 82.86%. The difference is small here but can be significant when subjects have very different maximum marks. Use the Marks % mode above for correct aggregate calculation.
% Calculate Any Percentage Instantly
Use the free calculator above — 6 modes covering every percentage calculation from GST to exam marks to reverse percentage. Instant results, full formula shown.
Calculate Now →Frequently Asked Questions
Divide X by Y and multiply by 100. Formula: (X ÷ Y) × 100. Example: what percent is 25 of 200? (25 ÷ 200) × 100 = 12.5%. Use the "What % is X of Y" mode in the calculator above — enter X in the first field and Y in the second for instant results.
Subtract the original value from the new value, divide by the original, multiply by 100. Formula: ((New − Old) ÷ Old) × 100. Example: salary increased from ₹40,000 to ₹46,000: ((46,000 − 40,000) ÷ 40,000) × 100 = 15% increase. For a decrease, the result is negative. Use the % Change mode in the calculator above for both increases and decreases.
To add GST: GST amount = Base price × GST rate/100. Final price = Base price + GST. For 18% GST on ₹1,000: GST = ₹180, Final = ₹1,180. To remove GST from an inclusive price: Base price = Inclusive price ÷ (1 + GST rate/100). ₹1,180 ÷ 1.18 = ₹1,000. Use the GST mode in this calculator — it also automatically splits the GST into CGST and SGST (each at half the rate) for intra-state supplies.
Divide total marks obtained by total maximum marks and multiply by 100. Formula: (Total Obtained ÷ Total Maximum) × 100. Example: 450 out of 600 = 75%. For multiple subjects with different maximum marks, always add all obtained marks and all maximum marks first — do not average the individual percentages. Use the Marks % mode above, which handles multiple subjects correctly.
10% of 1000 is 100. Formula: (10 ÷ 100) × 1000 = 100. A quick mental trick: to find 10% of any number, just divide it by 10 (move the decimal point one place left). 10% of 5,000 = 500; 10% of 1,25,000 = 12,500. For 5%, halve the 10% value. For 20%, double it.
Divide the final price by (1 - discount%/100). Example: product costs ₹800 after a 20% discount. Original price = ₹800 ÷ (1 - 20/100) = ₹800 ÷ 0.80 = ₹1,000. This is the Reverse Percentage formula — use the Reverse mode in the calculator above and select "Was Removed" to find the original price before a percentage was taken off.
For CBSE Class 10, multiply your CGPA by 9.5 to get an approximate percentage. CGPA 8.0 ≈ 76%, CGPA 9.0 ≈ 85.5%, CGPA 9.8 ≈ 93.1%. This is CBSE's own formula. For university CGPA (on a 10-point scale under UGC CBCS), there is no single universal conversion — different colleges use different formulas. Check your university's official grading guidelines.
Percentage decrease = ((Old Value − New Value) ÷ Old Value) × 100. Example: price dropped from ₹1,000 to ₹750: ((1000 − 750) ÷ 1000) × 100 = 25% decrease. The base is always the original (old) value. The % Change mode in this calculator handles both increases and decreases automatically — a negative result means a decrease.