Percentage Calculator

When people search for a percentage increase calculator — or type percent increase calculator instead — this is the job they mean: one number grew into another, and they want the growth expressed as a percent of the original. The Increase / decrease and % change tabs above both run it. I use % change when I have the start and end values, and Increase / decrease when I know the starting value and the percent.

Worked example. I use this as a price increase calculator most weeks: a jacket was $80 last season and is $100 now. To calculate percent increase by hand, I subtract first, then divide by the starting price: (100 − 80) ÷ 80 × 100 = 25%. To calculate percentage increase the fast way, I just enter 80 and 100 in the % change tab and read the +25% off the screen.

The asymmetry nobody warns you about. A 25% rise is not undone by a 25% fall. If that $100 jacket drops 25%, it lands on $75, not $80 — because the fall is calculated on the bigger base. To get back to $80 it only needs a 20% fall ((100 − 80) ÷ 100 × 100). I check this every time a headline quotes a rise and a fall as if they cancel out: they never do, and the bigger the percentages, the wider the gap.

The same math runs the other direction for decreases — a negative answer from the % change tab is a percent decrease, measured against the same original base. However you phrase it — increase calculator, growth check or markup check — the rule never changes: always divide by the number you started from.

A percentage change calculator is what I open when the question is really “how much did this move?” Percent change is the general form of increase and decrease: it keeps the sign, so growth comes out positive and shrinkage negative, and it always divides by the old value — the base is wherever you started, not where you ended.

Worked example — two years of raises. Say my salary is $52,000 and I get a 5% raise two years running. Year one takes me to $52,000 × 1.05 = $54,600; year two to $54,600 × 1.05 = $57,330. The total change across both years is (57,330 − 52,000) ÷ 52,000 × 100 = +10.25% — not 10%. The second raise applied to a bigger salary, so the changes compound instead of adding. Run over several periods like this, the tool doubles as a percentage growth calculator: I paste in the start and end values and it hands me the whole period’s growth in one number.

One trap I always check when the two values are themselves percentages — an interest rate moving from 4% to 5%, say. That is 1 percentage point, but a 25% relative change. Percent change answers the relative question; if someone means the plain gap, they should be talking in points. There is a full explainer on that trap in the guide below.

Half the comparison questions I get are not really change questions at all. Two prices, two measurements, two quotes — there is no before and after, so picking either one as the base would rig the answer. That is exactly what the percent difference calculator mode above is for: it treats both values symmetrically, so the answer is the same whichever order I enter them.

Here is how to calculate percent difference, step by step, on the pair I use to test it: 80 vs 100. The gap is 20. The average of 80 and 100 is 90. So the percentage difference between two numbers — 80 and 100 here — is 20 ÷ 90 × 100 = 22.22%. Run the same pair through percent change instead and I would get +25% (80 as the base) or −20% (100 as the base) — three different answers, which is why choosing the right mode matters more than the arithmetic.

I use percent difference for lab-style comparisons, two suppliers’ quotes, and checking whether two measurements of the same thing actually agree. In laboratory quality control the same formula has its own name — RPD, relative percent difference — and my supporting guide on percent difference vs percent change digs into that lab use with a worked QC example.

🧮The six percentage problems — and their formulas

Everyday percentage questions fall into six shapes. Each has one percentage calculation formula — pick the matching tab above:

Notice the symmetry: “20% of 150” and “30 is 20% of what” are the same relationship solved for different unknowns. If you can do one, you can do them all.

⚖️Percentage points vs percent — the classic trap

Going from 20% to 25% is a 5 percentage point increase — but a 25% relative increase (5 ÷ 20 × 100). Mixing these up is one of the most common mistakes in news, finance and marketing claims.

Why it matters: a “5% pay rise” on a 20% tax rate is 5 points off your income but a 25% relative jump in what you keep after that tax — wildly different stories. Always check which base a percentage refers to before reacting to it.

💵Increase & decrease: discounts, tips, markups

The increase/decrease tab answers “what’s the final number?” directly — and shows the delta too. 500 + 10% → delta 50, result 550. 500 − 10% → delta 50, result 450.

The reverse problem is just as common: a jacket costs $80 after 20% off — what was the original price? That’s the “whole” tab: 80 is 80% of the original, so 80 ÷ 0.8 = $100. (Enter X=80, Y=80 above and see.)

Stacked discounts don’t add: 50% off, then 20% off the sale price is 60% off the original — not 70%. Each discount applies to a smaller base: 0.5 × 0.8 = 0.4 of the price remains.

📊Percentage change vs percentage difference

Percentage change picks a base: (new − old) ÷ old × 100. From 150 to 180 it’s +20%; from 180 back to 150 it’s −16.67% — asymmetric, because the base moved. A negative result means a decrease; that’s normal, not an error.

Percentage difference treats neither value as the base: |a−b| ÷ average × 100. For 10 vs 6: 4 ÷ 8 × 100 = 50% — the same whichever order you enter. Use it when comparing two measurements, prices, or scores neutrally.

⚠️Common percentage mistakes

1. Forgetting the base: “20% off” means nothing without the starting price.
2. Adding percentages with different bases: 50% off then 20% off is 60% off total, not 70%.
3. “200% increase” triples a value — it doesn’t double it. (100% increase doubles; 200% adds twice more.)
4. Rounding money too early: carry full precision through the calculation and round only the final cents.
5. Dividing by zero: “X is what % of 0” is undefined — the calculator blocks it with a clear message.

🎯What percentage of X is Y?

This is the question I hear most often in everyday clothes: what percentage of my budget went on rent? What percentage of the test did I get right? It is the second tab above — “X is what percent of Y” — and the method never changes: divide the part by the whole, then multiply by 100.

Worked example. I answered 45 questions correctly out of 60: 45 ÷ 60 × 100 = 75%. Test scores are the classic case — 25 out of 30 is 83.33% — and if I want the letter grade that goes with a score, I take that percentage to the Grade Calculator, which is built for exactly that. On this page I stick to the percentage itself.

The mistake I see constantly is swapping the two numbers: 60 ÷ 45 gives 133.33%, which should set off alarm bells whenever the part is smaller than the whole — the answer has to come out under 100%. If “X is what percent of Y” is the question, X (the part) is always the number being divided.

🔍How to find percentage of a number

If you have ever wondered how to calculate percentages without reaching for a phone, this is the block I would bookmark. There are three methods I actually use, and they all land on the same answer.

Method 1 — the decimal shortcut. This is how to find a percentage of a number in one step: turn the percent into a decimal (move the point two places left) and multiply. For 35% of 240: 0.35 × 240 = 84.

Method 2 — the 10% building block. Here is how to find the percent of a number in your head: 10% of 240 is 24 (just shift the decimal point). Then 30% is 3 × 24 = 72, 5% is half of 10% = 12, and 35% = 72 + 12 = 84 again. Slow the first time, fast forever after.

Method 3 — the proportion. Set the problem up as part ÷ whole = percent ÷ 100 — the classic percent equation. For “84 is what percent of 240?” I write 84 ÷ 240 = p ÷ 100, so p = 84 ÷ 240 × 100 = 35%. Whenever I am unsure which number divides by which, the proportion keeps me honest.

How to add percentages. Carefully — because you usually can’t, not directly. If $100 grows by 10% it becomes $110; grow it another 10% and it becomes $121. That is a 21% total rise, not 20%, because the second 10% was charged on $110, not on $100. It is the single most useful thing I know about how to do percentages in real life: percentages only add when they share the same base, and the moment one applies, the base moves. If you are still asking how to figure out percentage problems quickly, my honest answer is: name the base first, then pick the method — the arithmetic after that is the easy part.

↩Working backwards: reverse percentages

The reverse question — “X is 20% more than what number?” — is one I get constantly, and it deserves its own method. I never subtract the percentage back off; that is the trap. The percentage was taken from the original, so I divide by the multiplier instead: after an increase, original = final ÷ (1 + p ÷ 100); after a decrease, original = final ÷ (1 − p ÷ 100).

Worked example. My salary is $55,000 after a 10% raise. Before the raise it was 55,000 ÷ 1.10 = $50,000. (Subtracting 10% of $55,000 would give $49,500 — wrong, because the raise was 10% of the old salary, not of the new one.) The sale-price version of the same trick lives in the Increase & decrease block above: $80 after 20% off means ÷ 0.8, back to $100.

🌐Percentages in real life

• Tips & tax: 20% on a $85 bill = $17. Stack tax (8%) and tip on the pre-tax subtotal, not on each other.
• Interest: 5% APY on $10,000 = $500/year — before compounding.
• Investing: I use this page as a quick percent gain calculator — buy at $250, sell at $315, and the gain is (315 − 250) ÷ 250 × 100 = 26%.
• Statistics: a poll moving from 40% to 44% is +4 points but +10% relative — headlines usually quote the bigger-sounding one.
• Health: “30% less sugar” is relative to the original recipe — check the grams, not just the claim.