Skip to tool
ecech.
Finance Developer Text & SEO Network Time E-commerce Math Design Health Converters
📊 Math & Statistics

Percentage Increase and Decrease Calculator

Four related questions in one place — change between two numbers, apply a percentage, find the original, and see the working written out so you can check it.

Result

—

Working

Advertisement

How the calculation works

Percentage change (new − old) ÷ old × 100 250 → 325  =  +30% 325 → 250  =  −23.1% Not symmetric — the divisor changes. Percentage points new% − old% 4% → 6%  =  +2 points … which is also +50% relative Use points when both values are already rates. Reporting "interest rose 2%" when it rose 2 points is the most common numerical error in business writing.

How to Use This Tool

Percentage questions come in four shapes and people routinely reach for the wrong one. This tool separates them explicitly, because the difference between "increased by 50%" and "increased by 50 percentage points" is the difference between a rounding error and a scandal.

Change between two numbers

Use this when you have a before and an after: last month's revenue and this month's, an old price and a new one. The formula is (new − old) ÷ old × 100, and the crucial detail is that you divide by the original. This makes percentage change asymmetric, which surprises people constantly. Going from 250 to 325 is a 30% increase; going back from 325 to 250 is a 23.1% decrease. The absolute movement is identical and the percentages differ, because the number you divide by has changed. This is why a stock that falls 50% needs to rise 100% to recover.

Applying a percentage

Use this for discounts, markups, tips and tax. Note the sequencing trap: applying −20% then +20% does not return you to where you started, it leaves you 4% down. Successive percentages multiply rather than add, and the tool shows the multiplier explicitly so this is visible rather than surprising.

Finding the original

This is the one most people get wrong. If a price is 92 after a 15% discount, the original is not 92 plus 15%. It is 92 ÷ 0.85 = 108.24. Adding the percentage back gives 105.80, which is wrong by more than two units, and the error grows with the percentage. Any time you need to strip out VAT, recover a pre-discount price or work back from a post-commission payout, this is the mode you need.

Percent versus percentage points

When both of your numbers are already percentages, saying one "rose by 2%" is ambiguous and usually wrong. A rate moving from 4% to 6% has risen by 2 percentage points, and by 50% in relative terms. Both statements are true and they sound wildly different, which is precisely why headlines pick whichever one suits the argument. This tab shows both figures side by side so you can label yours correctly.

Edge cases the tool handles

  • Zero as the original value. Percentage change from zero is mathematically undefined, not infinite. The tool says so rather than displaying a meaningless number.
  • Negative starting values. Going from −50 to −25 is an improvement, but the naive formula reports it as a decrease. The working notes when the sign makes the result misleading.
  • Very small bases. A change from 1 to 3 is +200%, which is technically correct and usually not what you want to report. The tool flags when the base is small enough for the percentage to mislead.
Advertisement

Frequently Asked Questions

Why is a 30% increase not reversed by a 30% decrease?
Because each percentage is taken from a different base. Adding 30% to 100 gives 130; taking 30% off 130 removes 39, leaving 91. The increase was calculated on 100 and the decrease on 130. To reverse a 30% increase you need a 23.08% decrease, which the reverse mode calculates for you.
How do I find the original price before a discount?
Divide rather than add. If the discounted price is 92 after 15% off, the original is 92 divided by 0.85, which is 108.24. Adding 15% back to 92 gives 105.80 and is wrong. The same logic applies to removing VAT or sales tax from a gross figure.
What is the difference between percent and percentage points?
Percentage points measure the absolute gap between two rates; percent measures the relative change. A rate moving from 4% to 6% has risen 2 percentage points and 50% relatively. Both are correct, they mean very different things, and mixing them up is the most common numerical error in business and news writing.
What happens if the starting value is zero?
Percentage change is undefined, because the formula divides by the original value. It is not infinite and it is not 100%. The correct thing to report is the absolute change, or to describe it in words as new activity from a zero base. The tool says undefined rather than inventing a number.
Can percentage change be more than 100%?
Increases can be any size: going from 10 to 40 is a 300% increase. Decreases cannot exceed 100% for positive quantities, because that would mean going below zero. If you see a reported decrease over 100%, either the underlying value went negative or somebody has divided by the wrong number.
Which formula should I use for percentage difference?
If one value is clearly a baseline, use percentage change and divide by that baseline. If neither is a baseline, for example comparing two measurements of the same thing, use percentage difference, which divides by the average of the two so the answer is the same whichever order you compare them in.
Why does applying two discounts not add up?
Because they compound. A 20% discount followed by a 10% discount gives 0.8 times 0.9, which is 0.72, so 28% off in total rather than 30%. The tool shows the multiplier for each step so the compounding is visible rather than something you discover at the till.

Related tools in Math & Statistics

🛒Amazon FBA Fee and Net Profit CalculatorReferral fee, fulfilment fee by size tier, monthly storage, returns and ad spend — subtracted in the order Amazon actually applies them, down to profit per unit. 💰Foreign Transaction Fee Currency ConverterLive mid-market rates, then your card's foreign transaction fee and the issuer's conversion margin added on top — so you see the number that actually hits your statement. 💻JSON Formatter and Validator with Error Line NumbersPaste broken JSON and get the exact line and column that failed, with a human explanation of what the parser expected. Format, minify, sort keys and copy out.
#percentage #math #everyday #analytics
Browse all Math & Statistics tools