The Three Percentage Questions
- •What is X% of Y? → (X ÷ 100) × Y. Used for discounts, tips, and commissions.
- •X is what percent of Y? → (X ÷ Y) × 100. Used for scores, shares, and proportions.
- •Percentage change from X to Y? → ((Y − X) ÷ X) × 100. Used for price rises, salary hikes, and growth.
- •Percentage change and percentage of are different calculations — mixing them up is the most common error.
The Real Problem This Solves
Percentage questions look simple until you have to decide which of the three formulas applies. "My rent went from ₹25,000 to ₹30,000" is a percentage change. "I scored 45 out of 180" is a what-percent question. "20% off ₹500" is a percent-of question. Each uses a different formula, and using the wrong one gives a confidently wrong answer.
This calculator keeps all three separate, so you pick the question first and the right formula follows.
How Each Mode Works
Percent of: 20% of 500 = (20 ÷ 100) × 500 = 100.
What percent: 45 out of 180 = (45 ÷ 180) × 100 = 25%.
Percentage change: 250 rising to 300 = ((300 − 250) ÷ 250) × 100 = +20%. Going the other way, 1,200 falling to 900 = ((900 − 1,200) ÷ 1,200) × 100 = −25%.
Note that a 20% increase followed by a 20% decrease does not return you to the starting number — the second percentage applies to the new, larger base.
| Question | Formula | Example | Answer |
|---|---|---|---|
| What is 20% of 500? | (20 ÷ 100) × 500 | 20% of 500 | 100 |
| 45 is what % of 180? | (45 ÷ 180) × 100 | 45 out of 180 | 25% |
| Change from 250 to 300? | ((300 − 250) ÷ 250) × 100 | 250 → 300 | +20% |
| Change from 1,200 to 900? | ((900 − 1,200) ÷ 1,200) × 100 | 1,200 → 900 | −25% |
Frequently Asked Questions
What is the difference between percentage change and percentage points?
Percentage change is relative to the starting value — going from 5% to 10% is a 100% increase. Percentage points are the plain arithmetic difference — that same move is a rise of 5 percentage points. News reports about interest rates and inflation usually mean percentage points, so read carefully.
Why does a 20% increase followed by a 20% decrease not bring me back to the original number?
Because the second percentage is applied to a larger base. ₹100 increased by 20% is ₹120; decreasing ₹120 by 20% removes ₹24, leaving ₹96, not ₹100. To reverse a 20% increase exactly, you need a decrease of about 16.67%.
How do I calculate a discount with this?
Use the "X% of Y" mode to find the discount amount — 25% of ₹2,000 is ₹500 — then subtract it from the original price to get ₹1,500. The same mode works for tips, commissions, and GST amounts.