★ MATH · PERCENTAGES · INCREASE & DECREASE
From 80 to 100 is a 25.00% increase — a change of $20.00. Work out a percentage increase or decrease, find a percent of a value, or reverse a percent change to find the original. This one is the PERCENTAGE INCREASE tool — change, percent-of and reverse — the percentage-calculator page is the PERCENTAGE tool — what percent one number is of another, and percent-of — not the change between two values; the reverse-percentage-calculator page is the REVERSE PERCENTAGE tool — the original from a final value and a percent — not the increase itself; and the percentage-increase-and-decrease guide is the GUIDE — the method in words — not a calculator. No percentage-increase calculator exists on this site — this one is the first.
Work out a percentage increase or decrease from two values, find a percent of a value, or reverse a percent change to find the original. On the defaults it is 80 to 100 — a 25.00% increase and a change of $20.00. The percentage is always measured against the starting value, so 100 to 80 is a 20.00% decrease, not 25%.
It means the new value is a quarter bigger than the old one: 80 grew by $20.00 to reach 100, and $20.00 is a quarter of $80.00. The percentage is always measured against the starting value, never the new one — that is the whole idea, and it is also the most common mistake. The change in dollars is the same whichever way you read it, but the percentage is not: 80 to 100 is +25.00%, and 100 to 80 is −20.00%, because the second change is measured against 100, not 80.
The starting value decides the percentage. A rise of $20 is 25% of 80 and 20% of 100 — the same dollars, different percentages, because the base moved. Whenever a percentage looks wrong, check what it was measured against first.
A rise and a fall of the same dollars are never the same percent. 80 to 100 is +25.00% and 100 to 80 is −20.00%. A price that rises 25% and then falls 25% does not come back to where it started — it ends at 93.75, because the 25% fall is taken from the higher price.
Percentage points are not percentages. A rate that moves from 10% to 12% rose by 2 percentage points — but that is a 20% increase in the rate itself (2 ÷ 10). News reports mix the two up constantly; the calculator keeps them apart.
On the defaults: old 80, new 100, dollars.
And the other way: 100 after a 25% increase started at 80, because 100 ÷ 1.25 is 80. And 80 after a 20% decrease started at 100, because 80 ÷ 0.8 is 100. And 25% of 80 is $20.00, because 25 ÷ 100 × 80 is 20.
The defaults are an old value of 80 and a new value of 100, in dollars — chosen because the arithmetic is clean and the answer, +25.00%, is the textbook case. They are a starting point, not a lesson: type any two values and the calculator works out the increase or decrease, or switch the mode to find a percent of a value, or to reverse a change and find the original. The starting value must be more than 0 — a percentage change from nothing, or from a negative number, does not mean what it looks like — and a 100% decrease leaves nothing to reverse. Plain-number mode shows the same answers without the dollar sign.
These notes repeat in every explainer section because this page is built to be read start to finish: the starting value decides the percentage; a rise and a fall of the same dollars are never the same percent; and percentage points are not percentages.
| Output | Formula | What it means |
|---|---|---|
| Result | formula | +25.00%. |
| Detail | step by step | 80 → 100: +25.00% (increase, change $20.00). |
| Formula | by mode | (new − old) ÷ old × 100. |
| Breakdown | step by step | (100 − 80) ÷ 80 × 100 = 25.00%. |
| Verdict | in words | From 80 to 100 is a 25.00% increase. |
| Reverse: New value from 80 with a percentage increase of 25% or more | step | 100: 80 → 100: +25.00% (increase, change $20.00). |
| Reverse: Percent that takes 80 to 100 or more | step | 25: 80 → 100: +25.00% (increase, change $20.00). |
| Reverse: Original value that after a 25% increase reaches 100 or more | step | 80: 100 after a 25.00% increase started at $80.00 — it reaches $100.00. |
| Decrease: 100 → 80 | same model | 100 → 80: −20.00% (decrease, change −$20.00). |
| Percent of: 25% of 80 | same model | 25.00% of 80 = $20.00. |
| Reverse: 100 after +25% | same model | 100 after a 25.00% increase started at $80.00. |
| Reverse: 80 after −20% | same model | 80 after a 20.00% decrease started at $100.00. |
| Increase: 50 → 75 | same model | 50 → 75: +50.00% (increase, change $25.00). |
| No change: 100 → 100 | same model | 100 → 100: 0.00% (no change, change $0.00). |
| Percent of: 15% of 200 | same model | 15.00% of 200 = $30.00. |
| Increase: 25 → 200 | same model | 25 → 200: +700.00% (increase, change $175.00). |
| Decrease to zero: 100 → 0 | same model | 100 → 0: −100.00% (decrease, change −$100.00). |
| Percent of: 10% of 50 | same model | 10.00% of 50 = 5.00. |
| Starting value 0 | same model | The starting value cannot be 0 — a percentage change needs something to change from.. |
| Negative starting value | same model | The starting value must be more than 0 — a percentage change from a negative start does not mean what it looks like.. |
| Non-numeric starting value | same model | Enter a number for the starting value.. |
| Reverse of a 100% decrease | same model | A 100% decrease leaves nothing — there is no original value to find.. |
| Percent of: 0% of 80 | same model | 0.00% of 80 = $0.00. |
| Increase of 0%: 100 → 100 | same model | 100 → 100: 0.00% (no change, change $0.00). |
Results are exact for the numbers you type; displays round to 2 decimal places. The arithmetic is the textbook formula — (new − old) ÷ old × 100 — with nothing hidden: the change, the starting value and the percentage are all shown, so any answer can be checked by hand. The calculator refuses a starting value of 0 or less, because a percentage change from nothing is undefined and a change from a negative start does not mean what it looks like. It also refuses to reverse a 100% decrease, which leaves nothing to find, and a decrease of more than 100%, which would leave a negative value. Plain-number mode is for counts and measurements; money mode is for prices and pay.
From 80 to 100 is a 25.00% increase — a change of $20.00. From 100 to 80 is a 20.00% decrease — a change of −$20.00. 25% of 80 is $20.00; 100 after a 25.00% increase started at $80.00; 80 after a 20.00% decrease started at $100.00. 50 → 75 is +50.00%; 25 → 200 is +700.00%; 100 → 0 is −100.00%. New value from 80 with a percentage increase of 25% or more: 100. Percent that takes 80 to 100 or more: 25. Original value that after a 25% increase reaches 100 or more: 80. Source: Bright Side Kit, brightoolbox.com.
Subtract the old value from the new one, divide by the old value, and multiply by 100 — from 80 to 100 that is (100 − 80) ÷ 80 × 100 = 25.00%. The change is $20.00 and the starting value is 80.
The same formula, with the sign doing the work — from 100 to 80 that is (80 − 100) ÷ 100 × 100 = −20.00%. The change is −$20.00, measured against the starting value of 100.
25% of 80 is $20.00 — take 25 ÷ 100 × 80. Percent-of is the forward direction: the percentage of the value is the part.
Divide the final value by 1 plus the percentage as a decimal — 100 after a 25% increase started at 80, because 100 ÷ 1.25 is 80. For a decrease, divide by 1 minus the percentage: 80 after a 20% decrease started at 100, because 80 ÷ 0.8 is 100.
Because the percentage is always measured against the starting value — $20 is a quarter of 80 but a fifth of 100. A rise and a fall of the same dollars are never the same percent.
A percentage point is the plain difference between two percentages — a rate moving from 10% to 12% rose 2 percentage points, which is a 20% increase in the rate itself. The guide percentage-vs-percentage-points works it through.
From 50 to 75 is +50.00% — the change is $25.00, which is half of the starting value of 50.
No — losing everything is a 100% decrease, and there is nothing left to lose after that. A decrease of more than 100% would leave a negative value, so the calculator refuses it.