Percentage Calculator
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Result
Answer
- Working
- 15% of 200 = (15 ÷ 100) × 200 = 30
How do you calculate a percentage?
To calculate a percentage of a number, divide the percentage by 100 and multiply by that number: 15% of 200 is (15 ÷ 100) × 200 = 30. To find what percent one number is of another, divide the first by the second and multiply by 100.
part = (percent ÷ 100) × whole percent = (part ÷ whole) × 100- percent
- The rate, as a number out of 100
- whole
- The base value the percentage is taken of
- part
- The resulting amount
Every percentage question is one equation rearranged. Given any two of the three quantities you can solve for the third: multiply to find the part, divide to find the percent, and divide the part by the rate to recover the whole. Percentage change introduces a fourth form, (new − old) ÷ old × 100, and the detail that matters is the denominator — the change is always measured against the starting value, which is why increases and decreases of the same size do not cancel. A 50% rise from 100 gives 150; a 50% fall from 150 gives 75, not 100. Reversing a 50% increase takes a 33.3% decrease. The same asymmetry is behind the difference between percentage points and percent: a rate moving from 4% to 6% has risen by two percentage points and by 50%, and news reports routinely conflate the two.
- Decide which quantity is the whole and which is the part.
- To find a part, divide the percentage by 100 and multiply by the whole.
- To find a percentage, divide the part by the whole and multiply by 100.
- For a change, subtract the old value from the new one.
- Divide that difference by the old value, then multiply by 100.
Worked example: 15% of 200, then the percentage change from 200 to 230
15% of 200, then the percentage change from 200 to 230
For 15% of 200, divide 15 by 100 to get 0.15, then multiply by 200 to get 30. The mental shortcut is to work from 10%: moving the decimal point one place gives 10% of 200 = 20, half of that is 5% = 10, and 20 + 10 = 30. For percentage change from 200 to 230, the difference is 30, and 30 ÷ 200 = 0.15, so the increase is 15%. Note that going back the other way is not 15%: from 230 down to 200 is 30 ÷ 230 = 13.04%, because the base is now larger. That asymmetry is the most common error in percentage work. Reverse percentages follow the same logic — if a price is $230 after a 15% increase, the original was 230 ÷ 1.15 = $200, not 230 minus 15%.
What each percentage input means
- What do you want to work out?
- Pick the question you are answering. The two inputs below mean different things in each mode.
- First value (X)
- In 'percent of' mode this is the percentage. In the others it is the first number.
- Second value (Y)
- The base value the percentage applies to, or the second number in a comparison.
What this percentage does not account for
- Percentage change from zero is undefined, because there is no base to measure against. Any increase from zero is infinite in percentage terms.
- Percentage increases and decreases do not cancel. Reversing a 50% increase needs a 33.3% decrease, and reversing a 50% decrease needs a 100% increase.
- Percentage points and percent are different. A rate rising from 4% to 6% is a two percentage point rise and a 50% rise; using the wrong one changes the meaning entirely.
- Discounts applied in sequence do not add. 20% off then a further 10% off is 28% off in total, not 30%, because the second discount applies to the already-reduced price.
- Negative bases make percentage change ambiguous. This calculator divides by the absolute value, which keeps the sign of the change meaningful, but conventions differ.
Frequently asked questions
How do you calculate a percentage of a number?
Divide the percentage by 100, then multiply by the number. For 15% of 200: 15 ÷ 100 = 0.15, and 0.15 × 200 = 30. A quick mental route is to find 10% by shifting the decimal, then scale.
How do you work out percentage increase?
Subtract the old value from the new one, divide by the old value, then multiply by 100. From 200 to 230 the difference is 30, and 30 ÷ 200 × 100 = 15% increase.
Why isn't a 50% increase cancelled by a 50% decrease?
Because the base changes between the two steps. 100 plus 50% is 150, and 150 minus 50% is 75, not 100. Undoing a 50% increase requires a 33.3% decrease instead.
What is the difference between percentage points and percent?
If a rate moves from 4% to 6%, that is a 2 percentage point increase but a 50% increase. Percentage points measure the absolute gap between two percentages; percent measures relative change.
How do you calculate a reverse percentage?
Divide by one plus the rate as a decimal. If a price is $230 after a 15% increase, the original was 230 ÷ 1.15 = $200. Subtracting 15% from $230 gives the wrong answer.
How do you calculate a discount?
Multiply the price by the discount rate to get the saving, then subtract it. For 30% off $80: 0.30 × 80 = $24 saved, leaving $56. Equivalently, multiply by 0.70 directly.
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