Percentage Calculator
Calculate percentages, percentage increase and decrease, and what percent one number is of another. Four calculators in one.
15% of 200 is
30
15% × 200 = 15 ÷ 100 × 200
About Percentage Calculator
Four related calculations in one place: a percentage of a number, what percentage one number is of another, the change between two values, and the reverse — finding the original number before a percentage was applied. Each shows the formula it used so you can check the working.
How to use it
- Pick the calculation that matches your question.
- Enter your numbers.
- Read the result and the formula used.
Frequently asked questions
What is the difference between percentage change and percentage points?
Going from 10% to 15% is a 5 percentage point rise but a 50% increase. Financial and polling reports use percentage points to avoid exactly this ambiguity.
How do I reverse a percentage?
Divide, do not subtract. If a price is 120 after a 20% rise, the original was 120 ÷ 1.2 = 100, not 120 − 20% = 96.
Why is a 50% loss not undone by a 50% gain?
Percentages compound on the current value. 100 falls to 50, and 50% of 50 is only 25 — you need a 100% gain to get back to where you started.
Percentage Calculator — the complete guide
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Key takeaways
- To reverse a percentage you divide, never subtract: ₹120 after a 20% rise came from ₹120 ÷ 1.20 = ₹100.
- A percentage point is the gap between two percentages; percent is the change relative to the start. 4% to 5% is one point and a 25% rise.
- Recovering a loss needs a larger gain than the loss — down 50% requires up 100%.
- Stacked discounts multiply rather than add: 50% then 20% off is 60% off, not 70%.
- x% of y always equals y% of x, which turns awkward sums into easy ones.
The four questions people actually ask
Almost every percentage problem is one of four shapes. Knowing which one you are looking at is most of the work, because each has a different formula and mixing them up is where the wrong answers come from.
| Question | Formula |
|---|---|
| What is 15% of 200? | (15 ÷ 100) × 200 = 30 |
| 30 is what percent of 200? | (30 ÷ 200) × 100 = 15% |
| From 200 to 250 is what change? | ((250 − 200) ÷ 200) × 100 = +25% |
| 250 is after a 25% rise — from what? | 250 ÷ 1.25 = 200 |
The fourth is the one that catches people out, and it gets its own section below.
Percent versus percentage point
These are different units, and news reports blur them constantly. If an interest rate moves from 4% to 5%, that is a rise of one percentage point — but it is also a 25% increase in the rate. Both statements are true and they describe the same event with very different emotional weight.
Rule of thumb: percentage points measure the gap between two percentages. Percent measures the change relative to where you started.
This is why a bank advertising "rates up 25%" and a regulator reporting "rates up 1 point" can both be describing 4% to 5%. When a number sounds surprising, check which unit is being used.
Why you cannot subtract a percentage to reverse it
This is the single most common percentage error. If a price rose 20% to reach ₹120, the original was not ₹120 minus 20%. Subtracting gives ₹96, which is wrong. The 20% was applied to the original, not to the total.
The correct move is division: ₹120 ÷ 1.20 = ₹100. Check it forward — ₹100 plus 20% is indeed ₹120. The general rule is to divide by (1 + rate) to undo an increase, and by (1 − rate) to undo a decrease.
| Situation | Wrong (add or subtract the %) | Right (divide) |
|---|---|---|
| ₹120 after a 20% rise | ₹96 | ₹100 |
| ₹80 after a 20% fall | ₹96 | ₹100 |
| ₹1,180 after 18% GST | ₹967.60 | ₹1,000 |
Notice the middle row: both directions land on the same wrong answer of ₹96, which is a useful tell that the subtract method is not doing what you think.
Why a 50% loss needs a 100% gain
Percentages compound on whatever the current value is, not on the original. That makes losses structurally harder to recover than the symmetry of the numbers suggests.
| Loss | Gain needed to break even |
|---|---|
| −10% | +11.1% |
| −25% | +33.3% |
| −50% | +100% |
| −75% | +300% |
| −90% | +900% |
Fall 50% from 100 and you are at 50. A 50% gain on 50 is only 25, taking you to 75 — still well short. You need to double from 50 to get back to 100. The formula is gain = loss ÷ (1 − loss), which is why the required recovery accelerates so sharply at the bottom of the table.
Stacked discounts are not additive
"50% off, then an extra 20% off" is not 70% off. The second discount applies to the already-reduced price, so the two multiply rather than add.
On a ₹1,000 item: 50% off gives ₹500, then 20% off ₹500 gives ₹400. That is 60% off in total, not 70%. The arithmetic is 1,000 × 0.5 × 0.8 = 400.
To combine discounts, multiply what remains: 0.5 × 0.8 = 0.4, so you pay 40% and save 60%. The order you apply them in does not change the result.
Quick mental shortcuts
- x% of y always equals y% of x. 16% of 25 is awkward; 25% of 16 is obviously 4.
- 10% is one decimal place left. 5% is half of that, and 15% is the two added together.
- To add a percentage, multiply by 1.something — 1.18 for 18% GST — rather than calculating the tax and adding it separately.
- A 1% change is the number with two decimal places moved left, which makes it an easy unit to scale up from.
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