Percentage Increase Calculator
Fill in the blanks and press Calculate. The direction is named rather than only signed, and a fall is handled the same way.
This percentage increase calculator does the two jobs that phrase actually covers. Give it a starting value and a final one and it tells you the rise between them; give it a number and a percentage and it tells you what that number becomes.
From 120 to 150 is a 25% increase. Increase 156 by 10% and you get 171.6. Percent increase and percentage increase are the same calculation under two spellings, and both are answered here. Both come with the working, and the direction is named in words rather than left as a minus sign for you to interpret.
How to Calculate Percentage Increase
For a rise from one value to another:
percentage increase = (new − original) ÷ |original| × 100
Three things happen in order. Subtract to get the change, divide by the value you started from, and multiply by 100 to turn the ratio into a percentage.
The middle step is the one that decides everything, and it is the one people reverse. Dividing by the original is what makes this a percentage increase; dividing by the new value gives you a different number entirely, and it answers a question nobody asked.
Why 120 to 150 and 150 to 120 Are Different Numbers
Take those two figures and go up: 150 − 120 = 30, and 30 out of 120 is a 25% increase.
Now go back down: 120 − 150 = −30, and 30 out of 150 is a 20% decrease.
The gap is the same 30 both times. The percentages are not, because the thing you divide by has changed. Twenty-five per cent up and twenty per cent down describe the exact same pair of numbers, travelled in opposite directions.
This is not a quirk to be memorised, it is the direct consequence of the denominator, and once you have seen it in these numbers you will spot it everywhere. A shop that raises a price by 25% and later advertises "25% off" has not put it back.
How to Increase a Number by a Percentage
The second job, and the one people bring a pay rise or a price rise to.
Turn the percentage into a multiplier and multiply once. A 10% rise means multiplying by 1.1, so 156 becomes 171.6. A 25% rise means ×1.25, so 80 becomes 100. A salary of 45,000 with an 8% rise is 45,000 × 1.08 = 48,600.
Nothing is added on afterwards. That is worth stressing because the alternative method — work out 10% of it, then add that on — gives the same answer for one step and falls apart the moment there are two.
The Multiplier Method Is Worth the Habit
Here is why. Suppose a price rises 10% one year and 10% again the next. Most people say 20%.
It is 21%. Multiply by 1.1 twice and you get ×1.21, because the second rise is 10% of a number that has already grown. Three years of it is ×1.331, a 33.1% rise rather than 30%.
The gap is small over one or two steps and enormous over many. That is the whole of compound interest, sitting inside a habit of arithmetic.
Anyone who converts to a multiplier first gets this right without thinking about it. Anyone who adds percentages together gets it wrong every time, and usually does not find out.
A Rise and a Fall of the Same Percentage Do Not Cancel
This is the most useful thing on the page, and the calculator points it out on every answer.
Increase 100 by 25% and you have 125. Now take 25% off that: 125 × 0.75 = 93.75. You are 6.25 short of where you began, and no arithmetic error was made.
The reason is the one from earlier. The rise was 25% of 100; the fall was 25% of 125 — bigger base, bigger cut, and you land below the start every single time, whatever the percentage.
| Up, then down the same | You land at | To actually undo it |
|---|---|---|
| 20% | 96 | a fall of 16.67% |
| 25% | 93.75 | a fall of 20% |
| 50% | 75 | a fall of 33.33% |
| 100% | 0 | a fall of 50% |
The version of this that costs people real money runs the other way round. An investment that falls 50% needs a 100% gain to get back to level, not another 50%. Halve something and you must double it to recover, and doubling is a great deal harder than halving.
Naming the Direction, Rather Than Signing It
A calculator that hands you "−20%" has told you the truth and left the last bit of work undone.
This page writes "a 20% decrease" instead, in words, because that is what belongs in a sentence, a report or an answer to a question. Minus signs get dropped when figures are copied between a screen and a page; the word does not.
If what you want is the bare signed figure — for a spreadsheet column, say, where the sign is doing useful work — the percent change calculator gives exactly that and leaves the labelling to you.
What the Calculator Does With Awkward Numbers
Three things, and each is a deliberate choice rather than an accident.
Whole numbers stay exact. From 2,400 to 2,436 is precisely 1.5%, and it says 1.5% rather than 1.50% or 1.5000000001. Nothing was measured, so nothing needs rounding.
Recurring decimals are named as such. From 3 to 7 is 133.333…%, and the page says the decimal runs on rather than pretending the number it shows is the whole of it. That is a small honesty and surprisingly rare.
A measurement gets rounded properly. Type a value with a decimal point and you are almost certainly reporting a measurement, so the tool offers a figure rounded to the significant figures your input actually justifies, and says how many that was.
Negative Numbers, and One Question With No Answer
Going from −10 to −5 is a rise. The value went up by 5, and 5 out of 10 is a 50% increase — which the calculator reports, because dividing by the absolute value of the start is what makes a rise between two negatives read as a rise.
Now the other one. What does "increase −200 by 10%" actually mean? The phrase sounds ordinary and does not survive being taken seriously.
Multiplying by 1.1 gives −220, which is a fall. Adding 10% of 200 gives −180, which is a rise. Two perfectly reasonable readings that disagree about which direction you just went. There is no correct answer to pick, so this page does not pick one — it says so and asks you to give both values instead. A calculator that quietly chooses is wrong half the time and never tells you which half.
Where the Other Percentage Tools Come In
Three related questions look like this one and are not.
If you want the plain signed movement without the words "increase" or "decrease" attached, that is the percent change calculator. If your question is a percentage of something rather than a change in it — what is 20% of 80, or 20 is 25% of what — the percentage calculator handles all three of those, including working backwards from a discounted price.
The other two compare rather than change. When your two numbers are equals with neither one a baseline — two lab measurements of the same thing, two supplier quotes — the percent difference calculator divides by their average, so swapping them changes nothing. When one number is a known accepted figure and the other is your own measurement, the percent error calculator divides by the truth and tells you how far off you were.
One question sorts all four: what is my answer supposed to be a percentage of? For this page it is the original value, every time.
Where Percentage Increases Turn Up
| Situation | Which mode |
|---|---|
| A salary went from 50,000 to 55,000 | between two numbers — a 10% rise |
| You were offered an 8% rise on 45,000 | increase by a percentage — 48,600 |
| Rent is going up 6% next year | increase by a percentage |
| Sales rose from 1,200 to 1,560 units | between two numbers — a 30% rise |
| A population grew 3% a year for five years | increase by a percentage, five times over |
That last row is the one worth pausing on, because percentage growth compounds rather than adding up. Five years at 3% is ×1.03 five times, which is ×1.159 — a rise of 15.9%, not 15%. The difference looks trivial and is the reason compound growth eventually outruns anyone's intuition.
How to Use This Percentage Increase Calculator
Choose which of the two questions you are asking. The sentence in the form changes to match, so you read what you are working out before typing anything, and the per cent sign moves to whichever box is actually a percentage.
Values can carry commas, a currency symbol or a unit — ₹50,000 and 65 kg both read cleanly — and decimals, fractions and scientific notation all parse. The working underneath shows the formula, your own numbers in it, and the round-trip warning whenever it applies. A fall is read correctly if you enter one, and named as a decrease — though when a reduction is what you set out to work out, the percentage decrease calculator is written around that question, with discounts and sale prices rather than pay rises.
Percentage Increase Calculator FAQ
How do you calculate percentage increase?
What is the percentage increase formula?
How do I increase a number by a percentage?
Why isn't 150 to 120 a 25% decrease?
If something rises 25% and then falls 25%, am I back where I started?
My investment fell 50%. How much do I need to gain to recover?
Is two 10% rises the same as one 20% rise?
Can percentage increase be more than 100%?
What if the value went down instead of up?
What is the difference between percentage increase and percent error?
Is this percentage increase calculator free?
Divide by where you started, convert the percentage to a multiplier before you use it, and remember that a rise and a fall of the same size never cancel. Those three habits cover almost every percentage increase you will meet, and the calculator at the top will hold you to all of them while doing the arithmetic instantly.
