Percentage calculator
15% of 3,800 · 4,200 is what percent of 5,600 · what the change from 12,000 to 9,600 is — all on one screen.
There are four basic ways to ask a percentage question, and the hard part is remembering which number divides which. Those four, plus double discounts, unit-price comparison and bonus-pack deals, make seven cards side by side, so fill in the row you actually meant. Nothing to submit — the answer moves as you type.
The four questions
What you enter is saved in this browser, so it is still here next time
What is a given percent of a number
570
What percent of the whole is this
75%
How much did it change from one value to another
down 20%
What is it after rising or falling by that much
42,500
Two discounts in a row come to what
28%
20% off followed by 10% off comes to 28% off. Discounts multiply, they do not add.
Which is cheaper — price per unit
7.9 · B
A 9 13.92% more · B 7.9 cheapest
A bonus offer as a discount
33.33%
2+1 works out at 33.33% off per item. That is the figure to compare against "30% off".
A rate moving from 2% to 3% has risen one percentage point and 50% at the same time. Points subtract; percent divides.
The four basic questions are four divisions
"X% of a base" is base × rate ÷ 100, so 15% of 3,800 is 570. "What percent is this of that" is part ÷ whole × 100, so 4,200 ÷ 5,600 = 75%. "How much did it change" is (after − before) ÷ before × 100, so 12,000 to 9,600 is −2,400 ÷ 12,000 = −20%, a fall of 20%. "Apply this change" is base × (1 + rate ÷ 100), so 50,000 with −15% is 42,500. The third and fourth are the same formula run in opposite directions.
Discounts multiply; freebies divide
Two successive discounts combine as 1 − (1 − first)(1 − second). 20% then 10% is 1 − 0.8 × 0.9 = 0.28, or 28%. A freebie deal is free units ÷ total units: buy 2 get 1 is 1 ÷ 3 = 33.33%, buy 1 get 1 is 50%, buy 3 get 1 is 25%. When "2+1" and "30% off" sit side by side on a shelf, 2+1 is 3.33 points cheaper — provided you can use all three.
Unit price is just price divided by quantity
A at 4,500 for 500 g and B at 7,900 for 1,000 g gives 9 per gram for A and 7.9 for B, so B is cheaper and A costs 9 ÷ 7.9 − 1 = 13.92% more. The page picks the cheaper one and states how much dearer the other is. Both quantities must be in the same unit — grams on one side and pieces on the other still produces a number, but a meaningless one. Values keep two decimal places.
Division by zero shows as "—"
A ratio with a whole of 0, a change from 0, a unit price with quantity 0 and a freebie with no units at all cannot be divided, so a "—" stands in for the answer. Anything divided by a non-zero number is defined, so negatives are accepted. Entering −5,000 to −2,000 in the change row gives −60%; whether a shrinking deficit should read as "down" is for the reader to judge. The rate in the apply-change row does not go below −100%.
Common questions
QWhy are a rise and a fall of the same size not symmetrical?
They divide by different numbers. Going from 100 to 50 is a 50% fall, but getting back from 50 to 100 is a 100% rise, because the fall divides by 100 and the rise divides by 50. It is why a share that halves has to double just to break even.
QWhat is the difference between % and a percentage point?
A rate going from 2% to 3% has risen by one percentage point, and at the same time by 50%. Percentage points subtract two rates; percent divides them. That is how a headline can say rates rose 50% and another say they rose 0.5 points about the same event.
QIs 20% off then 10% off the same as 30% off?
No — it is 28% off. 10,000 less 20% is 8,000, and 10% off that is 7,200. The second discount applies to the already-reduced price, so discounts multiply rather than add: 0.8 × 0.9 = 0.72.
QHow much is buy-one-get-one as a discount?
50%. You get two for the price of one, so each costs half. Buy 2 get 1 is 33.33%, buy 3 get 1 is 25%, buy 4 get 1 is 20%. The free item is the same each time, but the more you have to buy, the smaller the discount. Enter the paid and free counts in the freebie row to see it.
QHow do I get the pre-tax price from 11,000 including 10% VAT?
Not with these four rows. Entering 11,000 and −10% in the apply-change row gives 9,900, but the pre-tax price is 11,000 ÷ 1.1 = 10,000. The 1.1 that was multiplied on has to be divided off, which is not the same as taking 10% away. The VAT calculator does that sum.