Percentage Increase Calculator

The denominator is the original value, and that is the whole difficulty

Every figure on this page comes from those three lines, and the first one contains the only genuinely hard idea in the subject: a percentage increase is always measured against the value you started with. Going from 50 to 80 is a rise of 30, and 30 out of the original 50 is 60%. Divide the same 30 by the new value of 80 instead and you get 37.5%, which is a real number answering a different question — what fraction of the final figure the growth accounts for. Both calculations are arithmetic anyone can do; only one of them is the percentage increase, and picking the wrong denominator is far and away the most common way to get this wrong.

The multiplier is the same fact said more compactly. Growing by 60% means ending on 1.6 times what you began with, because 80 ÷ 50 = 1.6. Read that number and you can skip the three steps entirely: anything above 1 is growth, anything below it is a fall, and 2 is a doubling. It is also what makes the third card work — if an increase multiplies, then undoing one has to divide, which is why subtracting the percentage back off the final value does not return you to where you began.

No authority is cited for any of this because none exists to cite: percentage increase is elementary arithmetic, set out in full in the cards above rather than asserted. What a particular pay award, price list, syllabus, or tax rule means by its percentage — which base it is measured against, and over what period — comes from that document, not from mathematics.

Three steps, in the order you write them down

The calculator shows this working for whatever numbers you enter; here it is once in full for the example above, a value rising from 50 to 80.

Step two is where the answer is won or lost, and it is worth saying the rule out loud as you write it: divide by the original. The third step does nothing mathematically — 0.6 and 60% are the same quantity, since per cent simply means “per hundred” — it only changes the units the answer is expressed in. If you are working in a spreadsheet with cells formatted as percentages, that multiplication is already done for you, and doing it again is the mistake described further down this page.

One habit makes the result much harder to misread: name the base in the sentence. “Up 60%” on its own is ambiguous in a way “up 60% on 50” is not, and the same discipline is what keeps a pay rise, a price change, and a growth figure comparable when they appear side by side in the same report.

Doubling is a 100% increase; a third more is 33.33%

A few of these are worth recognising on sight, because they come up constantly and each one is a single division. Doubling is a 100% increase, not 200% — the new value is 200% of the old one, which is a different sentence. Adding a half is 50%, adding a quarter is 25%, and going up by a third is the awkward 33.3333% that never quite lands on a round number. Every row below is computed by the same engine as the calculator above:

The last row is the one to look at twice. It runs the same calculation in reverse — 80 down to 50 — and the answer is not the 60% that took 50 up to 80, but 37.5%. The two directions are never mirror images of each other, because the base changes: going up, you divide by 50; coming back down, you divide by 80. That asymmetry is why a 50% fall needs a 100% rise to undo it, and it is the single most useful thing to know about percentage change once the formula itself is secure.

Increasing 350 by 20% is 420, and the increase itself is 70

The second mode answers the question from the other end: you know where you are starting and by how much it goes up, and you want the new figure. Find the increase, then add it on. For 350 raised by 20%: 350 × 0.2 = 70, and 350 + 70 = 420. The one-step version multiplies by 1.2 instead and lands on the same number, which is faster once the idea is secure but hides the increase itself — and the increase is usually the figure you actually need to quote.

Applying the same percentage more than once is a different calculation again, and this page does not model it: three annual rises of 5% do not come to 15%, because each one is applied to a total the previous one already moved. Our Percentage of a Percentage Calculator combines successive changes into the single change they really come to, and that is the tool to use for a multi-year pay scale, a stacked discount, or an escalating rent.

A price is 420 after a 20% rise — it was 350, not 336

Going backwards is the question people get wrong most reliably, and the wrong method is seductive because it feels symmetrical: the price went up 20%, so take 20% back off. That gives 420 − 84 = 336, and it is wrong by 14. The reason is that the 20% was a percentage of the original — it was 20% of 350, which is 70 — while the 20% you just subtracted was 20% of 420, a larger number entirely. The percentages are measured against different bases, so they are not the same amount of money.

The reliable method is to divide by the multiplier. A 20% increase multiplies by 1.2, so undoing it divides by 1.2: 420 ÷ 1.2 = 350. The calculator’s third mode does this and then multiplies the answer back out as a check, because a reversal you can verify in one line is a reversal you can trust. The same method handles a reduction: a value of 60 after a 25% fall was 60 ÷ 0.75 = 80.

Two ordinary cases have no answer at all, and the tool says so rather than returning a number. A 100% decrease multiplies by zero, and nothing that has been reduced to nothing carries any information about where it started. An original value of zero is the same problem from the other side: there is no percentage of zero, so a rise from nothing cannot be expressed as one — the amount of the change is the only honest figure to quote there.

When the answer comes out negative, it was a decrease

The same three steps calculate a percentage decrease; nothing about the method changes. Subtract, divide by the original, multiply by 100 — and if the new value is the smaller of the two, the difference is negative and so is the answer. From 80 to 50 the calculation gives -37.5%, which is a decrease of 37.5%. The calculator names it that way rather than quietly dropping the minus sign, because “a 37.5% increase” and “a 37.5% decrease” describe opposite events and the sign is the only thing separating them.

One case needs care rather than a rule. When the original value is negative — a loss narrowing from −50 to −25, say — the arithmetic still runs, but the sign of the result stops meaning what a reader expects: the figure improved, and the formula reports −50%. Dividing by a negative base inverts the direction of the answer, and there is no convention that fixes it, which is why the tool flags the case and points you at the amount of the change instead. A narrowing loss is best reported as exactly that, in currency.

If what you have is not two values but a rate that moved — an interest rate from 5% to 6%, a conversion rate, a tax rate — then there are two correct answers and they differ by a factor of twenty here: a rise of one percentage point, and a relative rise of 20%. That distinction is not modelled on this page. Our Percentage Change Calculator has a Percentage Points mode built for it, alongside the growth-rate work this page also leaves alone — compound annual growth, period-by-period tracking, and comparing many outcomes against one starting value.

Six questions, with the working rather than just the answers

Each answer below is produced by the same engine that runs the calculator, so what you see here and what the tool returns for the same numbers cannot drift apart. Try each one first, then check the working — the third and fifth are the two that catch people out.

1. 1. A price rises from 50 to 80. What is the percentage increase?

   Answer: 60%

   80 − 50 = 30; 30 ÷ 50 = 0.6; × 100 = 60%.

2. 2. Increase 350 by 20%. What is the new value?

   Answer: 420

   350 × 0.2 = 70; 350 + 70 = 420.

3. 3. After a 20% rise a price is 420. What was it before?

   Answer: 350

   1 + 0.2 = 1.2; 420 ÷ 1.2 = 350. Taking 20% off 420 gives 336, which is the wrong answer.

4. 4. A class grows from 120 to 150 pupils. By what percentage did it grow?

   Answer: 25%

   150 − 120 = 30; 30 ÷ 120 = 0.25; × 100 = 25%.

5. 5. A value goes from 80 to 50. What is the percentage increase?

   Answer: -37.5% — a decrease of 37.5%

   50 − 80 = -30; -30 ÷ 80 = -0.375; × 100 = -37.5%. A negative answer means there was no increase.

6. 6. A 19.99 subscription rises by 8%. What is the new price?

   Answer: 21.59

   19.99 × 0.08 = 1.6; 19.99 + 1.6 = 21.59.

Question five is the one worth dwelling on. It asks for a percentage increase where none took place, and the honest answer is a negative number with the word “decrease” attached — not a positive 37.5% with the sign quietly discarded. Question three is the divide-versus-subtract trap from the section above, and it is worth doing on paper at least once, because recognising it later depends on having got it wrong deliberately now.

In a spreadsheet, the trap is a stray ×100

Each calculation is one short formula. The mistake to avoid in all of them is multiplying by 100 in a cell that is already formatted as a percentage, which inflates the answer a hundredfold — Excel and Google Sheets both apply the ×100 as part of the display format, so doing it in the formula as well means it happens twice:

• Percentage increase between an original in A1 and a new value in B1: =(B1-A1)/A1, with the result cell formatted as Percentage. If you want the raw number 60 instead of 60%, use =(B1-A1)/A1*100 and leave the cell formatted as a number.
• Increase a value by a percentage, with the start in A1 and the rate in B1 as a real percentage: =A1*(1+B1). If B1 holds the plain number 20 rather than 20%, it is =A1*(1+B1/100).
• Undo an increase, with the final value in A1 and the rate in B1 as a real percentage: =A1/(1+B1) — divide, never =A1*(1-B1), which is the 336-instead-of-350 error in spreadsheet form.

There is nothing to download for any of this and no account to create: the calculator above is a free web page that runs entirely in your browser, on desktop or mobile, and the numbers you type are never sent anywhere.

Read the guide

The asymmetry in the reference table above — that 50 up to 80 is a 60% rise while 80 back down to 50 is a fall of only 37.5%, because the base changes underneath you — has a guide of its own: Why a Percentage Loss and an Equal Percentage Gain Don’t Cancel Out. It works the same arithmetic through in prose and carries the recovery figures this calculator does not model — what a given loss needs as a gain just to get back to level, and why that number grows so much faster than the loss that caused it.

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Sources and methodology

The arithmetic on this page cites no authority because none exists to cite — percentage increase is elementary mathematics, and it is written out in full above rather than asserted. What is cited below is the part that is somebody else’s behaviour rather than mathematics: what a spreadsheet actually does with the formulas in the section above, which is the one place a correct method still returns a wrong number.

• Microsoft Support — format numbers as percentages in Excel
• Microsoft Support — calculate percentages in Excel
• Google Docs Editors Help — TO_PERCENT (Sheets)
• How we calculate — methodology

Method. Every figure here — the calculator, the step-by-step working, both reference tables, and the practice answers — is produced in your browser by one engine, src/lib/percentage-increase.ts, so nothing on the page can disagree with the tool above it. That engine is checked on every change against 89 hand-written assertions, including the cases most likely to be got wrong: that the original value is the denominator and not the new one, that undoing a 20% rise on 420 divides to 350 rather than subtracting to 336, that a fall is reported as a negative percentage rather than made absolute, that an original of zero has no percentage answer at all, and that applying a percentage and then reversing it returns the value you started from. The count and the per-case breakdown are published on the formula verification page.