Percentage calculator
Most percentage questions are quick. The ones that cost you money aren't the calculation — they're the trap hiding inside it. This tool runs the five percentages people actually search for, saves the ones you want to keep, and the page underneath explains the three that catch almost everyone out.
Percentage calculator
five modes, instantPick what you're working out, type your two numbers, and the answer updates as you go.
Going from 80 to 100 is a 25% increase.
Results round to two decimal places. The "Change" mode uses the original value as the base — see the worked examples below.
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A 50% loss needs a 100% gain to get back
This is the single most expensive percentage mistake. A $100 investment that falls 50% is worth $50. To climb back to $100 it has to rise by $50 — but $50 is now 100% of the smaller balance, not 50%. The fall and the recovery look like the same percentage, yet they're measured against different starting numbers, so they never match. A 20% drop needs a 25% rise to recover; an 80% crash needs a 400% gain. It's why a portfolio that halves in a downturn has to double, not half-recover, to break even.
Two discounts don't add up
"20% off, then an extra 10% off at the till" is not 30% off. Take 20% off $100 and you're at $80; take 10% off that and you land on $72 — a real discount of 28%. Stacked percentages multiply rather than add: 0.8 × 0.9 = 0.72. The order doesn't matter (10% then 20% gives the same $72), but the headline "30%" never arrives. The same maths runs in reverse for tax and tips: adding 10% then another 5% to a bill is a 15.5% increase, not 15%.
Percentage points are not percent
When a central bank lifts an interest rate from 2% to 3%, that's a rise of one percentage point — but a 50% increase in the rate. Report it the wrong way and you've overstated the move fifty-fold. The same gap shows up in polls ("support rose from 40% to 44%" is four points, or a 10% relative lift) and in fees and tax brackets. Statistical agencies like the Australian Bureau of Statistics and the UK's Office for National Statistics write "percentage points" on purpose, precisely to stop the two being mixed up.
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The five calculations — and the formulas
Each tab in the calculator above is one of these. The formulas are worth knowing for the times you don't have the tool open:
- Percentage change: (new − original) ÷ original × 100. Positive is an increase, negative a decrease.
- Increase or decrease by %: number × (1 + percent ÷ 100) to add, or × (1 − percent ÷ 100) to take off. "Increase 200 by 15%" → 200 × 1.15 = 230; decrease → 200 × 0.85 = 170.
- Percentage of a number: (percent ÷ 100) × number. "15% of 200" → 0.15 × 200 = 30.
- X is what % of Y: (X ÷ Y) × 100. "25 out of 80" → 25 ÷ 80 × 100 = 31.25%. This is also how you turn a test mark into a grade percentage.
- Discount (% off): price × (1 − percent ÷ 100). The saving is price × percent ÷ 100.
One more worth knowing: percentage difference is a different thing again — |A − B| ÷ ((A + B) ÷ 2) × 100, measured against the average of the two numbers rather than the original. Most people who search for "percentage difference" actually want percentage change above; reach for the symmetric version only when neither number is the clear starting point.
Frequently asked
How do I calculate percentage change?
Subtract the original from the new value, divide by the original, then multiply by 100. From 80 to 100 is (100 − 80) ÷ 80 × 100 = 25%. A negative answer is a decrease.
How do I increase a number by a percentage?
Multiply the number by 1 plus the percent over 100. To increase 200 by 15%, do 200 × 1.15 = 230. To decrease, multiply by 1 minus the percent: 200 × 0.85 = 170.
How do I work out a percentage of a number?
Divide the percentage by 100 and multiply by the number. 15% of 200 is 0.15 × 200 = 30.
What's the difference between percent and percentage points?
A rate going from 2% to 3% is one percentage point higher, but 50% higher as a rate. The first compares the two rates directly; the second compares the change to the starting rate.
How do I calculate a discount?
Multiply the price by the percent off divided by 100 to get the saving, then subtract it from the price. 20% off $59.99 saves $12.00, leaving $47.99.
Why does a 50% loss need a 100% gain to recover?
Because the gain is measured against the smaller post-loss balance. $100 down 50% is $50; getting back to $100 means adding $50, which is 100% of $50.
Formulas & references
- Percentage change = (new − original) ÷ original × 100.
- Increase by a percent = number × (1 + percent ÷ 100); decrease = number × (1 − percent ÷ 100).
- Percentage of a number = (percent ÷ 100) × number.
- X as a percentage of Y = (X ÷ Y) × 100.
- Sale price = price × (1 − percent ÷ 100); saving = price × percent ÷ 100.
- Stacked discounts multiply: a then b gives a net factor of (1 − a)(1 − b), not (1 − a − b).
- Percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100 — relative to the average, not the original.
- On "percentage points" vs "percent": Australian Bureau of Statistics and UK Office for National Statistics style guidance both reserve "percentage points" for the arithmetic difference between two percentages.
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Related
The calculation takes a second. Knowing which percentage you're actually looking at is the part that pays.