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Free percentage calculator for X% of Y, X is what percent of Y, and percent increase/decrease.
Last updated 7 October 2026
On 16 September 2026 the Federal Open Market Committee said it “decided to raise the target range for the federal funds rate by 1/4 percentage point to 3-3/4 to 4 percent”. The range it was raising had stood at 3-1/2 to 3-3/4 percent since 30 July. So the top of the range moved from 3.75% to 4.00%, and that one move can be reported two ways, both of them correct:
The second number is roughly twenty-seven times the first. Nothing has been exaggerated and neither figure is spin; they are answers to two different questions. A dispute about a percentage is very often one party answering the first question while the other hears the second.
That distinction, and the base a percentage is taken of, are where almost all real errors live. The three rows the panel above returns are the easy part.
Enter a Value A and a Value B and you get three results at once, because “work out the percentage” is three different requests that share a word.
A ÷ 100 × B. With A = 25 and B = 200 that is 50.
This row is the tip, the commission, the deposit, the sales tax line.
A ÷ B × 100. 25 out of 200 is 12.5%. This row is
the test score, the market share, the conversion rate.
(A − B) ÷ B × 100. From 200 down to 25 is
−87.5%. B is the starting figure, and the starting figure belongs on the
bottom.
Notice that all three rows use the same two inputs and none of them agrees with the others. Reading the wrong row is the commonest way to leave this kind of page with a wrong number.
The metrology guidance is blunter about this than most textbooks. NIST’s Guide for the Use of the International System of Units points out that “because the symbol % represents simply the number 0.01, it is incorrect to write, for example, ‘where the resistances R1 and R2 differ by 0.05 %,’ or ‘where the resistance R1 exceeds the resistance R2 by 0.05 %.’” Its remedy is to name the base out loud: “Instead, one should write, for example, ‘where R1 = R2 (1 + 0.05 %),’ or define a quantity Δ via the relation Δ = (R1 − R2) / R2 and write ‘where Δ = 0.05 %.’”
Translated out of the lab: “A is 5% more than B” is not a finished sentence until you say what the 5% is 5% of. Take A = 210 and B = 200. The difference is 10 either way. Against B, that 10 is 5%. Against A, the same 10 is 4.76%, because it is now being measured against 210. Both are right, they are not interchangeable, and quietly swapping them is how a 5% markup gets described as a 5% discount when it is really 4.76%.
This matters most when a percentage travels. A figure computed against last year’s revenue and then quoted against this year’s, or a margin computed on cost and then quoted on price, has not been rounded; it has been changed.
Start at 100. A 50% fall takes you to 50. A 50% rise on 50 adds 25, so you finish at 75. The rise was measured against the smaller number, and the smaller number is a smaller base. To climb from 50 back to 100 you need a rise of 100%.
The general rules are short. To undo a fall of d you need a rise of
d ÷ (1 − d). To undo a rise of d you need a fall of
d ÷ (1 + d). Working those through:
The asymmetry compounds, and that has a consequence worth sitting with. A gain of 10% followed by a loss of 10% is not flat: the multipliers are 1.10 and 0.90, and 1.10 × 0.90 = 0.99. One percent has gone. Run that same pair of moves ten times over and 100 becomes 90.44, with the quoted percentages having averaged exactly zero throughout. Averaging percentage changes and averaging the thing they happened to are not the same operation.
“30% off, and a further 20% off at the till” is not 50% off. The multipliers are 0.70 and 0.80, and 0.70 × 0.80 = 0.56, so you pay 56% of the original and the real discount is 44%. The order does not matter, because multiplication does not care, which is also why a shop can apply them in whichever sequence it likes without changing your bill.
The same arithmetic run backwards recovers a pre-discount price, and this is where people
lose money. If you paid $56 and the total discount was 44%, the original price
was 56 ÷ (1 − 0.44) = 56 ÷ 0.56 = $100. Adding 44% back onto
$56 instead gives $80.64, understating the original by $19.36. Divide to go
back; never add the percentage on again.
Which base you meant. Both ratio rows divide by Value B. If the figure you actually want is measured against Value A, that row is not on the panel, and the fix is to swap the two inputs rather than to reinterpret the answer.
Whether you wanted percentage points. Nothing here subtracts one percentage from another. If you hold two rates and you want the distance between them, that is plain subtraction and the result is in percentage points. No calculator can tell which of the two you came for, because that depends on the sentence you are about to write.
Division by zero is not a big number. A percentage is a ratio to a base, and zero is not a base you can measure against, so when Value B is zero there is no percentage to report. That is different from a very large answer and different again from zero. When both values are zero the ratio is indeterminate rather than infinite: every number k satisfies 0 = k × 0, so none of them is the answer.
How many digits your figures deserve. All three rows are reported to ten significant figures whatever you type. If the inputs came from counting 200 people, the fourth decimal place of a percentage is noise wearing the clothes of precision. Precision in the output is not evidence of precision in the input.
Anything about money past the arithmetic. An interest rate, a fee and an annual percentage rate are three different quantities, and whether a quoted percentage compounds, and how often, changes what you pay. This page multiplies and divides. It has not read your contract.
The BIPM’s SI Brochure records that “The internationally recognized
symbol % (per cent) may be used with the SI. When it is used, a space separates the number and
the symbol %”, and that “The symbol % should be used rather than the name ‘per
cent’.” So 25 %, with a space, in a specification or a lab report.
The same section rules out two abbreviations that look harmless: “The terms ‘parts per billion’ and ‘parts per trillion’ and their respective abbreviations ‘ppb’ and ‘ppt’ are also used, but their meanings are language dependent. For this reason the abbreviations ppb and ppt should be avoided.” A billion is not the same number in every language. A hundred is, which is most of why per cent has lasted.
This page sets its percentages tight against the number, in the ordinary web style rather than the metrological one. That is a deliberate inconsistency with the source above, noted here rather than hidden.
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Both, and they answer different questions. The gap between the two rates is 0.25 percentage points. Measured against where the rate started, the move is 0.25 ÷ 3.75 = 6.67 percent. The Federal Open Market Committee described its own 16 September 2026 decision in the first form: “by 1/4 percentage point to 3-3/4 to 4 percent”.
No, you are at 75% of where you began. 100 falls to 50, and a 50% rise on 50 is 25, not 50, because the rise is measured against the smaller figure. Climbing from 50 back to 100 takes a rise of 100%. In general, undoing a fall of d needs a rise of d ÷ (1 − d).
Value B, in both of the ratio rows. “A is what % of B” is A ÷ B × 100, and “Change from B to A” is (A − B) ÷ B × 100. If the figure you want is measured against A instead, swap the two inputs. With A = 210 and B = 200, A is 5% above B, but B is only 4.76% below A: the same difference of 10 against two different bases.
No. The multipliers are 0.70 and 0.80, and 0.70 × 0.80 = 0.56, so you pay 56% of the original price and the discount is 44%, not 50%. Successive percentages multiply; they never add.
Divide, do not add the percentage back. If you paid $56 after a 44% discount, the original was 56 ÷ (1 − 0.44) = 56 ÷ 0.56 = $100. Adding 44% to $56 gives $80.64, which is wrong by $19.36.
There is no percentage to report. A percentage is a ratio to a base, and zero cannot be a base, so the answer is not a very large number and it is not zero either. When both values are zero the ratio is indeterminate rather than infinite: every number satisfies 0 = k × 0, so no number is the answer.
For ordinary web and business writing, 25%. The BIPM’s SI Brochure asks for a space in technical work: “When it is used, a space separates the number and the symbol %.” NIST adds that % “represents simply the number 0.01”, so nothing may be attached to it: write “the mass fraction is 10 %”, never “10 % (m/m)”. This page uses the tight web form throughout.