Percentages are the arithmetic of everyday money: discounts, taxes, tips, raises, interest and statistics all speak in them. This tool handles the three questions that cover nearly every case: what is X% of a number, what percent is one number of another, and by what percent did a value change.
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%
20% of 35070
Value as % of comparison70%
% change to comparison42.86%
Value increased by percent420
The three core calculations
Percent of a number: multiply by the rate over 100. Twenty percent of 350 is 70. This answers discount, tax and tip questions directly.
One number as a percent of another: divide and multiply by 100. 350 of 500 is 70%. This answers scores, progress toward targets and market shares. Percentage change: the difference divided by the original. Going from 350 to 500 is a 42.9% increase, while going from 500 to 350 is a 30% decrease, and the asymmetry is not a mistake, it follows from the different starting points.
The traps worth knowing
Percentage changes do not cancel. A 50% loss needs a 100% gain to recover, which is why volatile investments punish more than symmetric-sounding numbers suggest.
Percentage points and percent are different things. A rate moving from 4% to 6% rose two percentage points, but that is a 50% increase in the rate. Headlines regularly blur the two in whichever direction is more dramatic.
Frequently asked questions
How do I calculate a percentage increase?
New value minus old value, divided by old value, times 100. From 400 to 460 is (60 ÷ 400) × 100 = 15%.
Why do a 50% drop and 50% rise not cancel out?
Because the base changes. 100 falling 50% is 50; rising 50% from there reaches only 75. Recovery percentages are always larger than the loss that caused them.
What is the difference between percent and percentage points?
Points measure absolute difference between rates; percent measures relative change. From 4% to 6% is two points but a 50% relative increase.
How do I work backwards from a total that includes a percentage?
Divide by 1 plus the rate. If 120 includes 20% tax, the base is 120 ÷ 1.2 = 100. Subtracting 20% from 120 gives the wrong answer.
How do I add successive percentages?
Multiply the factors instead of adding rates. A 20% discount followed by 10% off is 0.8 × 0.9 = 0.72, an effective 28% discount, not 30%.
Does this work for amounts of money?
Yes, percentages are unit-free. The math is identical for rupees, dollars, scores or anything else.