What is the Percentage Calculator?
Percentages express a proportion out of a hundred, which makes quantities of very different sizes directly comparable. They appear constantly — discounts, interest, tax, exam marks, tips, statistics — and they are also among the most commonly miscalculated everyday arithmetic.
This calculator handles the five everyday versions: a percentage of a number, the change from one number to another, what share one number is of another, the original number behind a percentage, and a total with a percentage removed.
What each input means
- What do you want to work out?
- Picks the question: a percentage of a number, the percentage change between two numbers, what share one number is of another, the original number behind a percentage, or a total with a percentage taken out.
- Value A
- The first number. Depending on the question it is the percentage, the starting value or the part.
- Value B
- The second number: the base the percentage applies to, the new value, the whole, or the total.
How this calculation works
A percentage of a number is the number multiplied by the percentage and divided by a hundred. Twenty percent of 250 is 250 × 20 ÷ 100, which is 50.
Two related operations cause most confusion. Percentage change is the difference divided by the original value, so which value counts as the original matters. And reversing a percentage requires division rather than subtraction — removing twenty percent from a total means dividing by 1.2, not multiplying by 0.8.
Formula: Result = value × percentage ÷ 100
Getting the most out of the result
- For percentage change, always divide by the original value, not the new one.
- Percentage increases and decreases do not cancel. Up ten percent then down ten percent leaves you below where you started.
- To find what percentage one number is of another, divide the first by the second and multiply by a hundred.
- Successive percentages multiply rather than add — two consecutive ten percent discounts total nineteen percent, not twenty.
- Distinguish percentage points from percent. A rate moving from four to six percent is a two point rise and a fifty percent increase.
Common mistakes to avoid
The most persistent error is assuming a percentage increase and an equal decrease cancel out — a hundred raised by fifty percent and then reduced by fifty percent gives seventy-five, not a hundred. Stacking discounts by adding them is similarly wrong, since each applies to a progressively smaller base. Reversing a percentage by subtracting rather than dividing is a routine invoicing mistake. And percentage change calculated against the new value instead of the original produces a subtly wrong answer every time.
Frequently asked questions
How do I calculate percentage increase or decrease?
Subtract the original value from the new one, divide by the original, then multiply by a hundred. Going from 80 to 100 is (100−80)÷80 × 100, a 25 percent increase. Dividing by the new value instead is the classic error.
How do I find what percentage one number is of another?
Divide the part by the whole and multiply by a hundred. If 45 out of 60 questions are correct, that is 45÷60 × 100, or 75 percent.
How do I remove a percentage from a total?
Divide rather than subtract. To find the pre-tax amount from a total that includes 18 percent tax, divide the total by 1.18. Multiplying by 0.82 gives a different and incorrect answer.
Why do a 50 percent rise and a 50 percent fall not cancel?
Because each applies to a different base. A hundred rising by half becomes 150; half of 150 is 75. The decrease operates on the larger number, so you end up below where you began.
Do stacked discounts add together?
No, they multiply. Twenty percent off followed by ten percent off the reduced price gives 0.8 × 0.9 = 0.72, a 28 percent total discount rather than 30.
What is the difference between percent and percentage points?
Percentage points measure the absolute gap between two percentages; percent measures relative change. A rise from 5 to 10 percent is 5 percentage points and a 100 percent increase. News reports frequently confuse the two.
Can a percentage exceed 100?
Yes. It simply means the part is larger than the reference value — growth of 250 percent means the quantity more than tripled. Only proportions of a fixed whole are naturally capped at a hundred.