The five percentage formulas
“Per cent” means per hundred, so every percentage calculation is a multiplication or division by 100 in disguise. These are the five forms the calculator handles.
- p% of a number: number × p ÷ 100. 15% of 80 = 12.
- A as a percentage of B: A ÷ B × 100. 30 of 120 = 25%.
- Percentage change: (new − old) ÷ old × 100. 80 → 100 = +25%.
- Add or subtract p%: number × (1 ± p ÷ 100). 200 + 22% = 244.
- Whole from a part: part ÷ p × 100. 45 is 15% of 300.
Which option answers your question
Most percentage questions are one of these five in everyday clothes. Match the wording, then pick the option in the menu above.
| The question | Option | Answer |
|---|---|---|
| What is a 15% tip on a 64.00 bill? | p% of a number | 9.60 |
| I scored 42 out of 60. What is that as a percentage? | What percent is A of B | 70% |
| Rent went from 1,200 to 1,290. How big a rise is that? | Percentage change | +7.5% |
| What is 49.99 with 8.25% sales tax added? | Add or subtract (add) | 54.114175 — 54.11 at the till |
| What does an 85.00 jacket cost at 30% off? | Add or subtract (subtract) | 59.50 |
| 18 students are 12% of a year group. How many are in it? | Whole from a part | 150 |
Undoing a percentage
A price of 150 that already includes a 25% increase was not 112.50 before it. Taking 25% off 150 gives 112.50, but the increase was worked out on the original price, not on 150. Divide by the multiplier instead: 150 ÷ 1.25 = 120, and 120 plus 25% is indeed 150.
On this page, use Whole from a part: the price you have is the part, and the percentage is 100 plus the increase — here 150 as 125% gives 120. The same works in the other direction. A sale price of 68 after 15% off is 85% of the original, so 68 at 85% gives 80.
Percentage change or percentage difference?
Percentage change needs a starting value: it asks how far something moved from where it began. When two figures are simply being compared — two shops’ prices, two survey results — some fields use a percentage difference instead, which measures the gap against the average of the two: |a − b| ÷ ((a + b) ÷ 2) × 100. For 80 and 100 that is 20 ÷ 90 × 100 ≈ 22.22%, whichever comes first. This calculator does not have a separate option for it; the formula is short enough to do with the basic-calculator method below.
Why percentage changes are not symmetrical
A percentage change is measured against the starting value. Going from 80 to 100 is a 25% rise, because the 20 is compared with 80; going back from 100 to 80 is a 20% fall, because the same 20 is now compared with 100. For the same reason a 10% increase followed by a 10% decrease leaves 99, not 100.
When the starting value is negative the change is measured against its size, so −50 rising to −25 is an increase of 50%. A change from zero has no percentage, because nothing can be divided by zero.
How to calculate a percentage on a basic calculator
A phone or desk calculator needs no % key for any of this; divide by 100 yourself and the order of keys is always the same.
- 15% of 80: press 80 × 15 ÷ 100 = and read 12.
- 30 out of 120 as a percentage: press 30 ÷ 120 × 100 = and read 25.
- Marks to a percentage: 438 out of 500 is 438 ÷ 500 × 100 = 87.6.
- Add 18% to 250: press 250 × 1.18 = and read 295.
The % key itself behaves differently between calculator brands — some add the percentage and show 295 for 250 + 18 %, others show only the 45 — so the explicit “÷ 100” sequence above is the one that works everywhere. For a full mark sheet with several subjects, the percentage calculator for marks adds up the totals for you.
Percent and percentage points
A rate that moves from 4% to 5% has risen by one percentage point, but by 25% in relative terms. Both statements are correct; they answer different questions. Use “Percentage change” with 4 and 5 to get the relative figure.
Worked example, step by step
A restaurant bill is 64.00 and you want to leave a 15% tip, then check what share of a 500 monthly food budget that whole meal used.
- Tip: choose “p% of a number”, enter 15 as the percentage and 64 as the number. 64 × 15 ÷ 100 = 9.60.
- Total paid: 64.00 + 9.60 = 73.60. That step is plain addition, not a mode on this page.
- Share of budget: choose “What percent is A of B”, enter 73.60 as the part and 500 as the whole. 73.60 ÷ 500 × 100 = 14.72%.
Chaining two modes like this — one answer typed into the next question — covers most real percentage problems, since they are rarely a single formula in practice.
Why some answers show a fraction
The calculator does its arithmetic with exact fractions rather than rounded decimals, using the same fraction engine as the fraction calculator. Most answers land on a terminating decimal and show as one: 15% of 80 is simply 12. Some do not — 1 as a percentage of 3 is 33.333…%, a decimal that never ends — and for those the result shows the exact fraction alongside a rounded decimal marked with ≈, so the precision lost by rounding is visible rather than hidden.
Edge cases
- A whole of zero. “What percent is A of B” and “Whole from a part” both refuse a zero in the divisor position — B in the first, the percentage in the second — because dividing by zero has no answer. The form explains which field to fix.
- A change from zero. “Percentage change” from a starting value of 0 is refused for the same reason: there is no base to measure the move against.
- Negative numbers. Percentage change is measured against the size of the starting value, not its sign, so a move from −50 to −25 is a 50% increase, not a decrease — the value moved closer to zero by half of its own size.
- A percentage over 100. Fully valid — 250% of 40 is 100 — but the part-of-a-whole bar under the result only draws for shares between nothing and all of it, so it stays hidden rather than showing a bar stretched past its own end.
- Very long numbers. Each field accepts up to 15 digits; longer input is rejected rather than silently truncated.
Common mistakes
- Subtracting a percentage to undo an increase. Removing 25% from a price that already has 25% added back does not return the original — see “Undoing a percentage” above.
- Treating a percentage-point move as a percentage move. A tax rate rising from 4% to 5% is one percentage point, not 1%; in relative terms it is a 25% rise. Naming the wrong one changes the number by a large margin whenever the base rate is small.
- Applying two percentage changes as if they add up. A 10% rise followed by a 10% fall does not cancel out, because the second percentage is taken of a different, larger number. Run the two steps through “Add or subtract a percentage” in sequence rather than adding +10 and −10 together.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. 15% of 80 is 80 × 15 ÷ 100 = 12.
How do I work out what percent one number is of another?
Divide the part by the whole and multiply by 100. 30 out of 120 is 30 ÷ 120 × 100 = 25%.
How is percentage change calculated?
Subtract the old value from the new one, divide by the old value and multiply by 100. From 80 to 100 is (100 − 80) ÷ 80 × 100 = +25%. From 100 to 80 is −20%, which is why a rise and a fall of the same size are not the same percentage.
If a price goes up 10% and then down 10%, is it back where it started?
No. 100 up 10% is 110, and 10% off 110 is 99. The second percentage is taken of a larger number. The calculator shows both steps if you run them one after the other.
How do I find the whole when I know a part and its percentage?
Divide the part by the percentage and multiply by 100. If 45 is 15% of something, the whole is 45 ÷ 15 × 100 = 300.
How do I find the price before a percentage was added?
Divide by 1 plus the percentage as a decimal, not subtract the percentage. 150 including a 25% increase was 150 ÷ 1.25 = 120. Taking 25% off 150 gives 112.50, which is wrong because the 25% was worked out on the original price.
Why does the answer sometimes show a fraction?
Some answers never end as decimals — 1 is 33.333…% of 3. The calculator shows the exact fraction alongside a rounded decimal so nothing is silently lost.