Percentage increase between two numbers
Subtract the number you started from, divide the difference by that starting number, then multiply by 100. Going from 40 to 50 the difference is 10, and 10 divided by 40 is 0.25, so it is a 25% increase. The order matters: divide by where you started, never by where you ended up, or 25% comes out as 20%.
The same base at common percentages
| 1.00% | 0.4 | 40.4 | 39.6 |
| 2.00% | 0.8 | 40.8 | 39.2 |
| 5.00% | 2 | 42 | 38 |
| 10.00% | 4 | 44 | 36 |
| 12.50% | 5 | 45 | 35 |
| 15.00% | 6 | 46 | 34 |
| 20.00% | 8 | 48 | 32 |
| 25.00% | 10 | 50 | 30 |
| 30.00% | 12 | 52 | 28 |
| 40.00% | 16 | 56 | 24 |
Results are provided as-is, with no warranty of accuracy. The method and its sources are published below so you can check the working.
Dividing by the ending value instead of the starting value turns a 25% increase into a 20% one. It is the most common mistake with this calculation.
A rise and a fall of the same percentage do not cancel out. 40 up 25% is 50, but 50 down 25% is 37.50 rather than 40.
If the starting number is zero there is no answer at all. Any increase from nothing is infinitely large, so the tool shows a dash rather than a figure.
How it works
The formula
Every percentage question is the same four quantities:
base the number the percentage is measured against
percent the rate
amount base x percent / 100
after base + amount
Each mode fixes two of them and the other two follow:
A% of B base = B, percent = A
A is what % of B base = B, amount = A, percent = amount / base x 100
From A to B base = A, amount = B - A, percent = amount / base x 100
A increased by B% base = A, percent = B
A decreased by B% base = A, percent = -B
after = base + amount, in every mode, including the ones where the amount
is negative.
When base = 0 the percentage is undefined and the tool says so rather than
dividing.
What it assumes
- Percentage change is measured against where you started, never where you ended. From 40 to 50 is a 25% rise; the same 10 over 50 would be 20%, and the two are different answers to different questions.
- With a negative starting value the sign follows the textbook formula rather than the direction of travel. From -40 to -50 reads as a 25% increase, because the size of the figure grew by a quarter.
- A base of zero has no percentage, so the answer is a dash. An infinite figure on a page somebody is checking a bill against is worse than no figure at all.
- Arithmetic is decimal, not binary floating point. 10% of 1.15 comes out as 0.115 rather than 0.11499999999999999, which is what the same sum gives in a double.
- Figures are carried to ten decimal places and displayed to two. The sentence beside the answer rounds to four, because a repeating decimal written out in full is unreadable in prose.
- Nothing is rounded to a currency. The tool does not know whether the numbers are pounds, kilograms or exam marks, so it will not silently turn 0.435 into 0.44.
Common questions
Which number goes on the bottom?
The one you started from. An increase from 40 to 50 is 10/40 = 25%; the same pair described as a decrease from 50 to 40 is 10/50 = 20%. Same two numbers, different question, different answer — and swapping them by accident is the most common mistake in this arithmetic.
What if the starting number is zero or negative?
A percentage increase from zero is undefined — there is nothing for the change to be a proportion of — so the tool shows a dash rather than infinity. From a negative start the formula still computes, but the sign is genuinely ambiguous, so report the absolute change instead.
Sources
Method written and checked by Tessalor on Jul 30, 2026.
The full method, worked example and every assumption behind this figure are on Percentage Calculator.