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What is a Percentage and How It Works
A percentage is a way of expressing a number as a fraction of 100. When we say 25%, we mean 25 out of every 100, or the fraction 25/100 = 0.25. Percentages are ubiquitous in everyday life in India — from GST on purchases and discount offers to exam marks, salary increments, and interest rates.
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Shopping & Discounts
Calculate how much you save on a 30% off sale, or find the final price after stacking multiple discounts.
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GST & Taxes
Calculate GST inclusive/exclusive prices, split into CGST and SGST, for Indian B2C invoices.
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Exam Marks
Convert raw marks to percentage, find aggregate across subjects, and determine grade and division.
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Finance
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?
Formula
Result = (X ÷ 100) × Y
Example: 18% of ₹2,500 = (18 ÷ 100) × 2,500 = ₹450
Example: 18% of ₹2,500 = (18 ÷ 100) × 2,500 = ₹450
Formula 2: What percentage is X of Y?
Formula
Percentage = (X ÷ Y) × 100
Example: 450 of 600 = (450 ÷ 600) × 100 = 75%
Example: 450 of 600 = (450 ÷ 600) × 100 = 75%
Formula 3: Percentage Change
Formula
% Change = ((New − Old) ÷ Old) × 100
Example: ₹40,000 → ₹46,000 = ((46,000−40,000)÷40,000)×100 = +15%
Example: ₹40,000 → ₹46,000 = ((46,000−40,000)÷40,000)×100 = +15%
Formula 4: Reverse Percentage
Formula
If % was added: Original = Final ÷ (1 + rate/100)
If % was removed: Original = Final ÷ (1 − rate/100)
Example: ₹1,180 incl. 18% GST → ₹1,180 ÷ 1.18 = ₹1,000
If % was removed: Original = Final ÷ (1 − rate/100)
Example: ₹1,180 incl. 18% GST → ₹1,180 ÷ 1.18 = ₹1,000
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.
| GST Slab | CGST | SGST | On ₹1,000 | Total |
|---|---|---|---|---|
| 5% | 2.5% | 2.5% | ₹25 + ₹25 | ₹1,050 |
| 12% | 6% | 6% | ₹60 + ₹60 | ₹1,120 |
| 18% | 9% | 9% | ₹90 + ₹90 | ₹1,180 |
| 28% | 14% | 14% | ₹140 + ₹140 | ₹1,280 |
CGST vs IGST: For intra-state (within the same state) supplies, GST splits equally between CGST and SGST. For inter-state supplies, only IGST (the full rate) is charged — no split. The GST mode above shows the CGST/SGST split for intra-state.
Percentage Marks and Exam Grading in India
Calculating exam percentage is one of the most common uses of percentage in India. The formula is always the same — but the grading scale varies significantly by board and institution.
| Board / System | Pass % | Distinction | Notes |
|---|---|---|---|
| CBSE Class 10 / 12 | 33% | 90%+ | CGPA × 9.5 = approx. percentage |
| Most State Boards | 35% | 75%+ | Varies by state — verify with board |
| University (UGC CBCS) | CGPA 4.5+ | CGPA 7.5+ | O, A+, A, B+, B, C, P, F grades |
CBSE CGPA tip: Your CGPA × 9.5 = approximate percentage. CGPA 9.0 ≈ 85.5%, CGPA 8.0 ≈ 76%. Use the Marks % mode above with 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 20% off = 50% off total"
✓ Right: 30% off then 20% off = only 44% off total (successive discounts don't add)
A 30% discount on ₹1,000 gives ₹700. Then 20% off ₹700 = ₹560. Total effective discount is ₹440 out of ₹1,000 = 44%, not 50%.
Mistake 2 — Confusing percentage points 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
An interest rate moving from 8% to 10% is +2 percentage points, but the rate itself increased by 25% ((10-8)/8 × 100).
Mistake 3 — Adding GST on top of a GST-inclusive price
✗ Wrong: Charging 18% GST on ₹1,180 (which already includes GST)
✓ Right: ₹1,180 already includes GST. Original = ₹1,180 ÷ 1.18 = ₹1,000. GST = ₹180
GST is always calculated on the base (exclusive) price. Use the Reverse mode to extract the original from a GST-inclusive price.
Mistake 4 — Using wrong base for percentage change
✗ Wrong: Price fell from ₹100 to ₹80 → "25% cheaper because 20/80 = 25%"
✓ Right: % decrease = ((100-80)/100) × 100 = 20% decrease (base is the original price)
Percentage change is always relative to the starting value, not the ending value.
Mistake 5 — Averaging individual subject percentages instead of totalling marks
✗ Wrong: Adding individual subject % 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 individual percentages gives a wrong result. Always total marks obtained ÷ total maximum marks × 100.
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%.
Subtract the original value from the new value, divide by the original, multiply by 100. Formula: ((New − Old) ÷ Old) × 100. Example: salary from ₹40,000 to ₹46,000: ((46,000 − 40,000) ÷ 40,000) × 100 = 15%.
To add GST: GST = Base price × rate/100. Final = Base + GST. To remove GST: Base = Inclusive price ÷ (1 + rate/100). Use the GST mode in this calculator — it also splits into CGST and SGST for intra-state supplies.
Divide total marks obtained by total maximum marks and multiply by 100. For multiple subjects with different maximum marks, always add all obtained marks and all maximum marks — do not average individual percentages.
10% of 1000 is 100. Formula: (10 ÷ 100) × 1000 = 100. Quick trick: to find 10% of any number, move the decimal point one place to the left.
Divide the final price by (1 - discount%/100). Example: ₹800 after 20% off. Original = ₹800 ÷ (1 - 0.20) = ₹800 ÷ 0.80 = ₹1,000. Use the Reverse mode in this calculator.
For CBSE Class 10, multiply your CGPA by 9.5. CGPA 9.0 ≈ 85.5%, CGPA 8.0 ≈ 76%. This is CBSE's own official formula.
Percentage decrease = ((Old − New) ÷ Old) × 100. Example: ₹1,000 to ₹750: ((1000 − 750) ÷ 1000) × 100 = 25% decrease. The base is always the original value.
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