How to Calculate Percentage — Formula, Examples & Common Mistakes
What is a percentage?
A percentage is simply a fraction expressed out of 100. The word comes from the Latin per centum — "out of a hundred". So 25% means 25 out of every 100, which is the same as the fraction 25/100 or the decimal 0.25.
The one formula behind every percentage problem
Every percentage calculation uses the same relationship:
Rearrange it and you can solve any percentage problem:
- Find the percentage: Part ÷ Whole × 100
- Find the part: Whole × (Percentage ÷ 100)
- Find the whole: Part ÷ (Percentage ÷ 100)
Worked examples
Example 1 — What percentage is 25 of 200?
Percentage = (25 ÷ 200) × 100 = 0.125 × 100 = 12.5%
Example 2 — What is 18% of 450?
Part = 450 × (18 ÷ 100) = 450 × 0.18 = 81
Example 3 — Percentage increase (price rise)
A price rises from $80 to $100. Increase = ((100 − 80) ÷ 80) × 100 = (20 ÷ 80) × 100 = 25%.
Note the increase is relative to the old value ($80), not the new one.
Example 4 — Reverse percentage (find the whole)
30 is 15% of what number? Whole = 30 ÷ 0.15 = 200.
Common mistakes to avoid
- Adding percentages of different wholes: a 50% increase followed by a 50% decrease does not return to the original. $100 → $150 → $75. The second 50% applies to $150, not $100.
- Using the wrong base for increases: a price rise from $80 to $100 is a 25% increase of the old price, not 20%.
- Confusing percentage points with percent: an interest rate moving from 5% to 6% rose by 1 percentage point, but by 20% relative.
Reverse percentages: working backwards from the result
The hardest percentage questions in exams and in shops are the ones where the percentage is applied to a number you don't know yet. Two patterns cover almost all of them:
- Find the whole: "30 is 15% of what?" → whole = 30 ÷ 0.15 = 200. Divide by the decimal form of the percentage.
- Undo a change: a shirt costs $45 after a 25% discount. The $45 is 75% of the original, so original = 45 ÷ 0.75 = $60 — not 45 ÷ 0.25. A frequent exam trap is dividing by the percentage instead of by what's left.
- Selling price → profit margin: an item bought at $40 sold at $50 has markup of $10 (25% of cost) but margin of $10 ÷ $50 = 20% (fraction of the selling price). Same $10, two different bases — see the margin vs markup calculator.
- GST/VAT back-calculation: an invoice total of $115 at 15% GST means $100 + $15 tax, because the total is 115% of the base. Base = 115 ÷ 1.15 = $100. Our sales tax calculator does the forward and reverse computation.
Where percentages appear in real decisions
The same one formula powers a surprising range of everyday calculations — each link goes to a guide or calculator that shows the working:
- Stacked discounts — why 30% + 20% off is 44%, not 50% (the multiplication rule).
- Grades — marks obtained ÷ total marks × 100, then mapped to a grade boundary.
- Discounts — final price = price × (1 − discount%).
- Tipping — bill × 15% (or 18/20%), split per person.
- Salary changes — a hike is computed on the old salary; a discount on the marked price.
Percentage points vs percent: the distinction that changes headlines
A rate moving from 5% to 6% rose by 1 percentage point but by 20 percent (1 ÷ 5). Both statements are true; they answer different questions, and news headlines exploit the ambiguity in both directions. Bank keeps "just a 0.5-point hike" sounds small; "rates up 10%!" sounds alarming — they're describing the same move.
Three places the distinction costs real money:
- Loan rates: refinancing from 12% to 11% saves far more than "1%" suggests on a large balance — on a $100,000 / 5-year loan, dropping the rate one point cuts total payments from $133,467 to $130,455 — a $3,012 saving, about 3% of the borrowed amount, not 1% of anything.
- Surveys and margins: support moving from 40% to 44% is a 4-point gain and a 10% gain. Political coverage almost always says the bigger-sounding one.
- Compound context: a fund returning 8% after two years of 4% is not averaging 6% — 1.04 × 1.04 = 1.0816, so 4.08% per year. Percentage-point reasoning fails whenever the base compounds; the compound interest guide shows why.
Quick test before quoting any change: is the base itself a percentage? If yes, say "points" for the difference and "percent" for the ratio — and check which one the claimant is using.
Try it instantly
Check your working with the Percentage Calculator — it shows the step-by-step solution, not just the answer. Related tools:
Worked example: Profit Margin Calculator at its default inputs
A worked example is only useful if you can reproduce it. The defaults on Profit Margin Calculator give exactly the figures in this section, with no rounding done by us.
| Input | Default |
|---|---|
| Revenue | 50000 |
| Cost | 35000 |
Result: Margin: 30.00%
The steps behind that answer
- Formula: Margin = (Revenue - Cost) / Revenue × 100
- Step 1: Profit = $50000 - $35000 = $15000.00
- Step 2: Margin = $15000.00 / $50000 × 100 = 30.00%
Revenue — three values, three answers
Revenue is the first input worth testing, so here it is at three sizes.
| Revenue | Result |
|---|---|
| 25,000 | Margin: -40.00% |
| 50,000 | Margin: 30.00% |
| 75,000 | Margin: 53.33% |
If the rows barely differ, revenue is not your lever — change a different input. If they swing widely, get that number right before trusting the total.
Related guides
Percent changes multiply, they do not add
A 10% rise followed by a 10% fall leaves you 1% below where you started, because the second change applies to the larger base. That single fact explains most of the disagreements people have about "getting back to even" after a loss.
To recover a 20% loss you need a 25% gain, not 20%: the required gain is loss ÷ (1 − loss). The deeper the drawdown, the more asymmetric the recovery becomes.
Percentage points are not percent
A rate moving from 5% to 7% has risen 2 percentage points, which is a 40% increase in the rate itself. Both statements are true and they answer different questions — which is why headlines about "a 40% rise in rates" and "a 2-point rise" describe the same event.
Use points when the quantity is itself a percentage (interest rates, tax rates, unemployment). Use percent when the quantity is a count, a price or a size.
Stacked discounts apply in sequence
Twenty percent off and then a further ten percent off is 28% off, not 30%: the second discount applies to the already-reduced price. The formula is 1 − (1 − a)(1 − b).
The same logic works in reverse for tax. To strip a tax out of a gross figure, divide by 1 + the rate instead of subtracting the rate from the total — 120 gross at 20% is 100 net, not 96.
Frequently asked questions
What is the formula for percentage?
Percentage = (Part ÷ Whole) × 100. For example, 25 out of 200 is (25 ÷ 200) × 100 = 12.5%.
How do I calculate percentage increase?
Percentage increase = ((New value − Old value) ÷ Old value) × 100. If a price rises from $80 to $100, the increase is ((100 − 80) ÷ 80) × 100 = 25%.
How do I find a number when I know the percentage?
Divide the part by the percentage as a decimal. If 30 is 15% of a number, the number is 30 ÷ 0.15 = 200.
What is the most common percentage mistake?
Adding percentages of different wholes. A 50% increase followed by a 50% decrease lands at 75% of the original, because the second percentage applies to the already-changed amount.
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