Percentage Calculator

Pick the question, type two numbers into the sentence, and get the answer with the working written out — plus the mental-math shortcut for next time.

Fraction	Percent	Decimal	Everyday example
1/100	1%	0.01	1p in £1
1/20	5%	0.05	typical card cashback cap
1/10 ★	10%	0.10	move the decimal one place
1/8	12.5%	0.125	half of a quarter
1/6	16.67%	0.1667	service charge on some bills
1/5 ★	20%	0.20	UK VAT · common tip
1/4 ★	25%	0.25	quarter off in a sale
1/3	33.33%	0.3333	"a third off"
1/2 ★	50%	0.50	half price
3/4	75%	0.75	battery at three-quarters
1/1	100%	1.00	the whole thing
3/2	150%	1.50	one-and-a-half times

Six percentage problems, one calculator

Almost every percentage question you'll ever meet is one of six shapes. Pick the shape from the dropdown, type your two numbers into the sentence, and the answer appears with the working written out — the same working you'd show in an exam or an email to your boss.

The formulas

What is X% of Y? → Y × (X ÷ 100) X is what % of Y? → (X ÷ Y) × 100 % change from X to Y → ((Y − X) ÷ X) × 100 Increase Y by X% → Y × (1 + X ÷ 100) Decrease Y by X% → Y × (1 − X ÷ 100) X is Y% of what? → X ÷ (Y ÷ 100)

Worked examples

Sale price. A £120 jacket is 30% off. Decrease 120 by 30%: 120 × 0.70 = £84. (Tip: "30% off" means you pay 70% — multiplying once by 0.70 is faster than finding 30% and subtracting.)
Test score. You scored 30 out of 200. 30 ÷ 200 × 100 = 15%.
Pay rise. Salary moved from £250 to £300 per day. Change = (300 − 250) ÷ 250 × 100 = +20%. Note the divisor is the old value — that trips people up constantly.
Reverse VAT. A receipt shows £45 which already includes 20% VAT — so £45 is 120% of the pre-tax price. 45 ÷ 1.20 = £37.50 before tax. (Use "X is Y% of what?" with 45 and 120.)

Mental-math tricks worth stealing

The 10% anchor. 10% just moves the decimal point: 10% of 348 is 34.8. From there, 5% is half of that (17.4), 20% is double (69.6), 1% is a tenth (3.48). Nearly any percentage can be assembled from these blocks.
The swap trick. X% of Y always equals Y% of X. Struggling with 8% of 25? Flip it: 25% of 8 = 2. Same answer, no effort. The calculator shows this check under every "percent of" answer.
Chaining discounts. 20% off then another 10% off is not 30% off. Multiply the "you pay" factors: 0.80 × 0.90 = 0.72, so it's 28% off. This is also why a 50% loss needs a 100% gain to break even.

Percent vs. percentage points

If an interest rate rises from 4% to 6%, it went up 2 percentage points — but 50 percent (because 2 is half of 4). News reports mix these up daily. Use "points" when subtracting two percentages, and "% change" when comparing them relative to the starting value. Our percentage-change mode always gives you the relative version.

The asymmetry that costs people money

Percentage changes don't undo each other. A £100 share that drops 25% is worth £75; gaining 25% back only reaches £93.75. To recover a P% fall you need a rise of P ÷ (1 − P/100) percent — after a 50% fall, that's 100%. Try it in the increase/decrease modes and watch the numbers refuse to meet. This single idea explains why volatile investments can grind downward even when average gains and losses look balanced.

Using the export tools

The CSV button downloads your inputs, formula and result in one row — handy for pasting evidence into spreadsheets. PDF report prints a clean page with the working shown. Share image renders your calculation as a picture, and Copy link gives you a URL that reopens this exact calculation for anyone you send it to.

Frequently asked questions

How do I calculate a percentage of a number?

Divide the percentage by 100 and multiply. 15% of 200 is 0.15 x 200 = 30. Equivalently, find 1% (divide by 100) and scale up: 1% of 200 is 2, so 15% is 30. The calculator's first mode does this and shows the working.

How do I work out what percent one number is of another?

Divide the part by the whole and multiply by 100. Scoring 30 out of 200: 30 / 200 x 100 = 15%. Order matters — the number after 'of' is always the divisor.

What's the difference between percent and percentage points?

Points measure the simple gap between two percentages; percent measures relative change. A rate going from 4% to 6% rose 2 percentage points, but 50 percent, since 2 is half of the starting 4. Use points when subtracting percentages directly.

Why doesn't a 20% increase then a 20% decrease get back to the start?

Because the second change applies to a new, larger base. 100 up 20% is 120; 120 down 20% is 96, not 100. The bigger the swings, the bigger the gap — a 50% loss needs a 100% gain to break even.

How do I calculate a discount price quickly?

Multiply by what you PAY, not what you save. 30% off means you pay 70%: price x 0.70. For 25% off, x 0.75. One multiplication, no subtraction step, and it chains correctly for stacked discounts (20% then 10% off = x 0.80 x 0.90 = 28% off total).

What is the percentage swap trick?

X% of Y always equals Y% of X, because both are X x Y / 100. So 8% of 25 (awkward) equals 25% of 8 (easy) = 2. Whenever a percentage looks hard, flip it and it often becomes trivial.

What do you want to work out?

Fraction ↔ percent ↔ decimal reference