Percentage calculator

Nearly every percentage question you'll run into is one of these three, worked here with the values above.

These three are interchangeable, but each one is more convenient in a different context, and switching between them is usually the fastest way to sanity-check a calculation by hand.

Percentages read well in conversation because they're standardised on a base of 100 — “18% GST” means the same thing regardless of the price it's applied to. Decimals are what a spreadsheet or a calculator actually multiplies by, which is why entering 15% into a formula usually means typing 0.15 instead. Fractions matter most when a rounded decimal would lose real precision — a recipe or a measurement, for instance, where 1/3 is exact and 0.33 quietly isn't.

Applying different rates to the same base of 250 shows how fast small percentage differences pull apart:

Read the two tables side by side and the asymmetry is already visible: a 15% increase and the matching 15% decrease don't land the same distance from 250 in either direction, because each one is a percentage of the same starting number, not of each other's result.

If an interest rate moves from 5% to 8%, that's a rise of 3 percentage points, but a 60% relative increase (3 ÷ 5). Both are correct descriptions of the same move — they just answer different questions, and headlines swap between them freely, which is exactly why the same change can be made to sound big or small depending on which framing gets used. A rate rising from 5% to 8% and a rate rising from 40% to 43% are both “3 points,” but the second is a much smaller relative jump — 7.5% versus 60% — which is the kind of detail that gets lost the moment a headline picks one framing and drops the other.

The same base problem shows up when percentages are applied one after another instead of just once. Increase 100 by 10% and you get 110. Decrease that 110 by 10% and you land on 99 — not back at 100 — because the second percentage is calculated on the new, already-changed number, not the original one. Stacked retail discounts work exactly the same way. Take an item priced at ₹250 with 15% off, then an extra 10% off the already-discounted price (a common “extra 10% off sale items” promotion):

1. Original price: ₹250.
2. After 15% off: 250 × (1 − 15/100) = ₹212.50.
3. After an additional 10% off that reduced price: 212.50 × 0.90 = ₹191.25.
4. The combined discount is 23.5%, not 25% — the second discount was never applied to the original ₹250.

The same asymmetry means recovering from a loss always needs a bigger percentage gain than the loss itself: a 10% loss needs an 11.1% gain to break even, a 25% loss needs 33.3%, and a 50% loss needs a full 100%, because the recovery is calculated on the smaller, already-reduced amount. It's worth remembering the next time a “down 20%, then up 20%” chart looks like it should be back to flat.

GST rates (5%, 12%, 18%, 28% are the common slabs) get quoted both ways in practice: tax already folded into the sticker price, or added on top at checkout. Tax-inclusive pricing pulls the GST component out using price × rate ÷ (100 + rate); tax-exclusive pricing just adds price × rate ÷ 100 on top of the base price. The two produce different final rupee figures even when the headline rate looks identical, so it's worth checking which one a quote actually means before comparing two prices side by side. The GST calculator handles this conversion directly if you need the exact figure rather than the shape of it.

Retail pricing runs into a related mix-up between markup and margin. An item that costs ₹100 to make and sells for ₹150 has ₹50 of profit — a 50% markup (profit ÷ cost) but only about 33.3% margin (profit ÷ selling price). It's the same ₹50, reported two different ways depending on which number sits on the bottom of the fraction, and it's a common source of disagreement when a shop owner and a supplier are quoting percentages to each other without saying which base they mean.

Bank and NBFC quotes add a third layer: a fixed deposit or savings account rate is always an annual percentage, but whether it compounds annually, quarterly, or monthly changes the real return even when the quoted rate is identical. Two FDs advertised at the same headline percentage can pay out different amounts over the same term for exactly this reason — the section below shows why.

A single percentage change is easy to picture. Applied repeatedly — compound interest, a recurring price hike, population growth — it behaves differently, because each round is calculated on the previous round's already-grown number, not the original one. That's the same multiplicative logic as the stacked discount above, just running upward instead of down, and over longer stretches of time.

Watch the gap between years widen rather than stay constant — that's compounding, not a rounding error, and it's the reason two loans or two deposits at the same headline rate can pay out noticeably different amounts once the compounding frequency differs. If 15% is meant to represent an ongoing annual rate rather than a one-off change, the compound interest calculator carries this further and accounts for the compounding frequency directly.

Two questions matter more than the number itself. First: is it a percentage change or a percentage-point change? “Rates rose 3%” means something very different depending on which one the writer meant, and the two get swapped constantly in casual reporting. Second: what's the base? 60% of a sample of 20 people is a far shakier claim than 60% of 20,000, even though the percentage figure printed on the page is identical either way — and the digit alone never tells you which situation you're looking at. The same instinct is worth carrying into a “flat 50% off” sale sign: 50% off what price, and is that the price before or after the last markdown? A tag reading “MRP ₹250, now 213” is answering that question directly; a tag that just says “15% off” with no starting price isn't, and it's worth a second look before assuming the deal is as good as the number alone suggests.

• Adding instead of multiplying. A 20% discount plus a 20% discount is not a 40% discount — it's roughly 36%, because the second one applies to an already-reduced price. Apply successive percentages one after another, never by summing them first.
• Using the wrong base. A percentage-change calculation always divides by the old, starting value — not the new one — even when the new value happens to be the one you know first.
• Mixing up points and change. A percentage-point difference and a percentage change describe the same move in two different, non-interchangeable ways, and only one of them tells you the relative size of the shift.
• Assuming symmetry. A loss and an equal-sized percentage gain don't cancel out — recovering from a loss always takes the larger of the two percentages, and the gap widens as the loss grows.
• Reversing the operation. Finding the whole from a part uses division, not multiplication — the formula genuinely runs backward, and multiplying by mistake gives an answer that's too small, not just slightly off.
• Leaving out the base. A percentage quoted without saying what it's a percentage of can't actually be judged for size — “up 30%” means very different things depending on whether the starting number was 10 or 10,000.

• 10% of any number: move the decimal point one place left — 10% of 250 is 25.0.
• 5% is half of 10%, and 15% is 10% plus 5% — handy for tips and quick discounts.
• 1%: move the decimal two places left, then scale up or down from there.
• Converting to a decimal is one division (15% = 0.15); as a fraction it's 15/100, worth simplifying when it lines up neatly (50% = 1/2, 25% = 1/4).
• Round the numbers first when estimating in your head, then correct the estimate afterward.

Nearly everything above comes down to the same three moves — find a piece of a number, compare two numbers, or work backward to the whole — plus one habit that prevents most of the actual mistakes: check which number is the base before you divide by it. Get that right and discounts, GST, exam marks, and interest rates all fall out of the same small toolkit. Get it wrong, and even a correctly-performed calculation ends up answering a question nobody actually asked.

Figures above are computed live from the numbers you entered, or the illustrative defaults shown, using standard percentage arithmetic with full precision carried through each step; rounding is applied only at the final display stage of each result, not partway through a multi-step calculation. This is educational content, not financial, tax, or business advice for a specific decision.