To calculate the percentage increase between two numbers, subtract the old value from the new value, divide by the old value, then multiply by 100 — written as (new − old) ÷ old × 100. A positive answer means the number went up; a negative answer means it went down; equal values give exactly 0%. For example, a price that rises from 200 to 250 is a +25% increase because (250 − 200) ÷ 200 × 100 = 50 ÷ 200 × 100 = 25. This single formula covers price changes, salary raises, weight loss progress, investment returns, traffic growth, grade improvements, and any other before-and-after comparison you can think of, because every such comparison reduces to "how big was the change, measured against the starting point." The reason the starting point matters is that a 50-unit move looks very different against a base of 200 than against a base of 250, which is exactly why the same 50-unit gap produces a +25% in one direction and a −20% in the other.
The Percentage Increase Formula in Plain English
The formula has three moving parts:
(new − old) ÷ old × 100
- New is the value you ended up with — the "after" number.
- Old is where you started — the "before" number, also called the base.
- The subtraction gives the absolute change, the division by old converts that change into a fraction of the base, and multiplying by 100 turns the fraction into a percentage.
If old is zero, the change is mathematically undefined — you cannot divide by zero — and any honest calculator should refuse to give a percentage rather than invent one. This is the case behind phrases like "infinite growth," which is why a well-built percent-change tool flags a zero starting value instead of returning a number.
Negative numbers are allowed wherever they make sense: −10% of 200 is −20, and a starting value of 250 falling to 200 produces a negative percentage naturally. Results are rounded for display but computed at full precision, so you never see floating-point noise like 25.000000000004, and the formula is echoed back alongside the answer so you can check the working or learn how it was done.
Worked Example: Going From 200 to 250
Take a $200 item whose price rises to $250. Plug the numbers into the formula directly:
(new − old) ÷ old × 100 = (250 − 200) ÷ 200 × 100 = 50 ÷ 200 × 100 = 0.25 × 100 = +25%
So the price went up 25%. The plus sign is just a sign convention — the result reads as an "increase" because the new value is larger than the old.
Now suppose the price drops from $250 back to $200:
(new − old) ÷ old × 100 = (200 − 250) ÷ 250 × 100 = −50 ÷ 250 × 100 = −0.20 × 100 = −20%
That is a 20% decrease, not −25%. The same 50-unit gap shows up as very different percentages, and that asymmetry is one of the most common sources of confusion with percent-change problems.
How to Calculate Percentage Increase Between Two Numbers
- Open the Percentage Calculator and pick the "% change" mode from the mode selector at the top.
- Type the old (starting) value into the first field and the new (ending) value into the second field — the field labels update to match the mode as soon as you select it.
- Read the answer below the fields: a positive number is an increase, a negative number is a decrease, and a result of exactly 0% means nothing changed.
- Glance at the worked formula the calculator echoes back so you can check the working or learn the steps.
- If either value is negative, type it with the minus sign — the tool accepts negative numbers wherever they make sense, so a drop that crosses zero produces a negative percentage automatically.
- If your starting value is 0, the tool shows a clear message instead of a misleading percentage, because dividing by zero has no defined answer.
There is no button to press and nothing sent to a server — the answer and the worked formula update the moment you finish typing, and every calculation runs entirely in your browser.
Why the Two Directions Aren't Mirrors
It surprises most people the first time: going from 200 up to 250 is +25%, but going from 250 back down to 200 is only −20%. The percentages do not match even though the absolute change (50 units) is identical in both directions. The reason is that percentage change is always measured against the starting value, and the two trips have different bases.
| Direction | Starting value | Ending value | Absolute change | Percentage change |
|---|---|---|---|---|
| Up | 200 | 250 | +50 | +25% |
| Down | 250 | 200 | −50 | −20% |
A 50-unit gain is 25% of a 200 base, but a 50-unit loss is 20% of a 250 base. Once you internalize that percentage change is "the change relative to where you began," the asymmetry stops feeling like a contradiction and starts feeling accurate.
When Percentage Change Is the Right Metric
Percentage change is the natural metric whenever you want to know how big a movement was relative to its starting point, regardless of the size of the numbers involved. It shows up across everyday decisions:
- Price changes — a $5 increase on a $20 item is a 25% jump, while the same $5 on a $200 item is a 2.5% nudge; the percentage makes the difference obvious at a glance.
- Salary raises — moving from $50,000 to $55,000 is a 10% raise, useful for comparing raises across very different base salaries.
- Investment returns — a portfolio that grows from $10,000 to $11,500 has returned 15% for the period.
- Traffic, sales, or user growth — when comparing this month to last, the absolute numbers become less informative as the base grows, and the percentage change captures the actual rate.
- Weight change — losing 5 pounds from 200 is a 2.5% change; the same loss from 150 is roughly 3.3%, which helps compare progress for people at different starting weights.
The qualitative values above show how the formula behaves across very different scales; for your exact figure, plug your numbers into the Percentage Calculator's "% change" mode.
If your goal is to combine several percentage changes into a single figure — for instance, the average growth rate across six months — see the guide on how to calculate the average of percentages.
Related Questions the Same Tool Handles
The Percentage Calculator covers all three questions people typically ask about percentages in one place, so you do not need a different tool for each scenario:
- X% of Y finds a part of a whole using (X ÷ 100) × Y. Use it for discounts (20% off a $60 jacket saves $12), tips (18% of a $45 bill is $8.10), sales tax, commission, or simple interest for a single period.
- X is what % of Y turns two raw numbers into a proportion using X ÷ Y × 100. Use it for test scores (42 out of 50 is 84%), completion rates, or how much of a budget you have spent. The whole (the second number) cannot be zero — the tool shows a clear error in that case.
- % change is the mode covered in this article, using (new − old) ÷ old × 100.
Pick a mode, type two numbers, and the answer plus the worked formula appear the moment you finish typing. Everything runs locally in your browser, so the numbers you enter never leave your device.