Percentage Calculations: Increase, Decrease and Percentage Difference
Avoid the base-value mistakes behind discounts, growth rates and percentage-point confusion.
Percent of a number
To find 15% of 80, convert 15% to 0.15 and multiply: 80×0.15=12.
Percentage increase
From 80 to 100, the change is 20 and the original base is 80, so the increase is 20/80=25%.
The reverse change is not symmetric
From 100 down to 80, the decrease is 20/100=20%. A +25% rise followed by −20% returns to the starting value because the bases differ.
Percentage points are different
A rate moving from 10% to 15% rises by 5 percentage points but by 50% relative to the original 10%.
Percentage difference needs a defined use
When neither value is clearly the original, some contexts use the absolute difference divided by the average of the two values. State the formula so readers know what “difference” means.
A task you can work through
A price from 80 to 100 rises by 20 on a base of 80, so the increase is 25%. A subsequent fall from 100 to 80 is a fall of 20 on a base of 100, so the decrease is 20%. The site’s Percentage Calculator has separate inputs for “X% of Y”, “X is what percent of Y” and change from one number to another. Choose the question first; the same two numbers can yield different answers depending on their roles.
Where this approach fails
Percentage points are different from relative percentage change. If a rate goes from 5% to 7%, that is a two-point increase and a 40% relative increase. A reduction of 100% takes a positive amount to zero; an increase of 100% doubles it. Percentage change is undefined when the original base is zero, so a calculator should not present a finite percentage in that case.
Check the result before using it
Before calculating, write “base =” beside the starting value. For a discount, multiply the original price by the rate to find the discount amount, then subtract it. For a rise and fall, recompute using the new base rather than canceling identical percentages. Keep extra decimals until the final display when rounding could matter.
Check the denominator on every line
In the question “30 is what percent of 200?” the denominator is 200, giving 15%. In “200 is what percent of 30?” the denominator is 30, giving about 666.67%. A formula can be arithmetically correct while answering the wrong question. For a change from 50 to 75, use 50 as the base to get a 50% increase. Explain that base beside any percentage you publish so another person can reproduce it.
Try the related tool
Three common percentage questions, answered instantly. The tool page explains its implementation and limitations. Keep your original and inspect any important result.
Percentage Calculator →