Percentage Calculator

1) X% of Y        = Y × X ÷ 100
2) X as % of Y    = X ÷ Y × 100
3) % change       = (New − Old) ÷ Old × 100

Every everyday percentage task reduces to one of these. The discipline is identifying which question you're answering — and, for #2 and #3, which number is the base (the denominator). The base is always the 'of' value or the original value.

Worked examples of each type

1. Type 1 — discount: What is 24% of ₹3,499? → 3,499 × 24 ÷ 100 = ₹839.76 off, so you pay ₹2,659.24.
2. Type 2 — score: 43 marks out of 60 is what percent? → 43 ÷ 60 × 100 = 71.67%.
3. Type 3 — growth: Rent rose from ₹18,000 to ₹19,800. → (19,800 − 18,000) ÷ 18,000 × 100 = +10%.
4. Reverse type 1 — unknown whole: 15% of a bill is ₹270; what's the bill? → 270 ÷ 15 × 100 = ₹1,800.
5. Reverse type 3 — original price: After a 20% discount you paid ₹960. Original = 960 ÷ (1 − 0.20) = ₹1,200 — not 960 × 1.20 = ₹1,152, the single most common percentage mistake.

Mental math shortcuts

• 10% = shift the decimal: 10% of 640 = 64. Build others from it: 5% is half of that (32); 20% is double (128); 1% is 6.4.
• X% of Y = Y% of X: 8% of 50 feels hard; 50% of 8 = 4 is instant.
• 15% tip = 10% + half of 10%. 18% = 20% − 10% of the 20%.
• A ↑ then ↓ by the same percent never returns to start: +10% then −10% = −1% (×1.1×0.9 = 0.99).

Percentage points vs percent

If interest rises from 4% to 6%, it rose 2 percentage points but 50 percent (2 ÷ 4 × 100). News reports mix these constantly. Points measure absolute gaps between percentages; percent measures relative change. A '100% increase in risk' from 0.01% to 0.02% is two very different-sounding truths.

The base matters — and reverses don't cancel

Because the base shrinks after a fall, the percentage climb back is always larger. This is why portfolio drawdowns hurt more than the symmetric-sounding number suggests, and why 'stock fell 50%, then rose 50%' leaves you down 25%.

Chained percentages multiply, never add

A 30% discount plus an extra 20% off is not 50% off: ×0.70 ×0.80 = ×0.56, i.e. 44% off. GST of 18% on top of a 12% markup is ×1.12 ×1.18 = ×1.3216, a 32.16% total increase. Convert to multipliers, multiply, convert back.

1. Identify your question type: finding a part (X% of Y), finding a rate (X as % of Y), or measuring change.
2. Enter the percent and the base value — the base is the 'of' number or the original value.
3. Read the result; for discounts and taxes, apply it to the price mentally with the multiplier check (×0.76 for 24% off).
4. For percentage change, keep the sign: negative means decrease.

Everyday applications

• Shopping: stack discounts correctly and spot fake 'was' prices by reversing the math.
• Exams and grading: convert marks across different maximums to comparable percentages.
• Salary: a hike from ₹6.0 LPA to ₹7.2 LPA is +20%; the same ₹1.2 lakh on ₹12 LPA is +10% — always quote both figures in negotiations.
• Finance: interest, inflation, returns and tax are all percentage machinery; the multiplier method chains them safely.
• Data literacy: check whether a headline means points or percent, and what base a '40% jump' is measured from.