Math & Science
Percentage Calculator
Six of the most common percentage questions, each with its own mode so you never have to remember which way round the formula goes.
Percentage Calculator
About the Percentage Calculator
Most percentage mistakes are not arithmetic mistakes. They happen because the formula gets used the wrong way round — dividing by the new value instead of the old, or subtracting a percentage that was added to a different base. This calculator avoids that by giving each question its own mode.
Six modes cover nearly everything people actually need: X% of Y, X is what percent of Y, percentage change from X to Y, X plus Y%, X minus Y%, and X is Y% of what number. Pick the sentence that matches your question and the formula follows automatically.
Each result shows the working, not just the answer. That matters when you are checking a discount, a tax figure or a test score, and you need to be able to see why the number came out the way it did.
How to use the Percentage Calculator
- Choose the mode that matches your question.
- The two field labels change to match — read them rather than assuming the order.
- Enter both numbers.
- Select Calculate.
- For percentage change, the direction tells you whether it rose or fell.
The six percentage formulas
X% of Y = (X ÷ 100) × Y
X is what % of Y = (X ÷ Y) × 100
Change X → Y = ((Y − X) ÷ X) × 100
X plus Y% = X + (X × Y ÷ 100)
X minus Y% = X − (X × Y ÷ 100)
X is Y% of what = (X ÷ Y) × 100
Worked example
A jacket is marked down from £80 to £56. What is the discount?
Change from 80 to 56: (56 − 80) ÷ 80 = −0.30.
−30% — a 30% discount
Now reverse it. If you only know the sale price is £56 after 30% off, the original was 56 ÷ 0.70 = £80. Notice you divide by 0.70, not multiply by 1.30 — that is the mistake that trips most people up.
Percentage change and percentage difference are not the same
They answer different questions, and mixing them up produces two different numbers from the same pair of values.
- Percentage change has a direction. It measures movement from a starting value, so it divides by the old value. Going from 40 to 50 is a 25% increase.
- Percentage difference has no direction. It compares two values neither of which came first, so it divides by their average. The difference between 40 and 50 is 22.2%.
Use change when something moved over time — prices, populations, scores. Use difference when comparing two independent measurements, such as results from two instruments.
Why a 50% rise then a 50% fall does not return you to the start
Because the two percentages apply to different bases. This surprises people constantly, and it is worth seeing laid out:
| Step | Calculation | Result |
|---|---|---|
| Start | — | 100 |
| Rise 50% | 100 + (100 × 0.50) | 150 |
| Fall 50% | 150 − (150 × 0.50) | 75 |
The rise was 50 points. The fall was 75 points, because it was taken from the larger figure. To reverse a 50% rise you need a 33.3% fall. This is the same reason a stock that drops 50% must gain 100% just to break even.
Working backwards from a discounted price
To find an original price, divide by the remaining fraction rather than adding the percentage back:
| Discount | Divide sale price by | £56 was originally |
|---|---|---|
| 10% off | 0.90 | £62.22 |
| 20% off | 0.80 | £70.00 |
| 25% off | 0.75 | £74.67 |
| 30% off | 0.70 | £80.00 |
| 40% off | 0.60 | £93.33 |
| 50% off | 0.50 | £112.00 |
The same logic removes VAT or sales tax. To strip 20% VAT from a gross price, divide by 1.20 — do not subtract 20%. Our VAT calculator handles that directly.
Percentages and percentage points
If an interest rate moves from 4% to 5%, that is a rise of one percentage point but a 25% increase. Both statements are true and they describe the same event. News reports mix them up regularly, so read carefully when the numbers matter.
Quick mental shortcuts
- 10% — move the decimal one place left. 10% of 340 is 34.
- 5% — take 10% and halve it.
- 15% — 10% plus half of that 10%. Handy for tips.
- Reversibility — X% of Y always equals Y% of X. 16% of 25 is awkward; 25% of 16 is obviously 4.
For tips specifically, the tip calculator splits the bill too. For marks and grades, try the marks percentage calculator.
Percent off calculator (discount calculator)
Choose X decreased by Y% above. Enter the price and the discount. Or do it by hand:
Sale price = original price × (1 − discount ÷ 100)
Amount saved = original price × discount ÷ 100
| Price | 10% off | 20% off | 25% off | 30% off | 50% off |
|---|---|---|---|---|---|
| $20 | $18.00 | $16.00 | $15.00 | $14.00 | $10.00 |
| $50 | $45.00 | $40.00 | $37.50 | $35.00 | $25.00 |
| $80 | $72.00 | $64.00 | $60.00 | $56.00 | $40.00 |
| $100 | $90.00 | $80.00 | $75.00 | $70.00 | $50.00 |
Stacked discounts multiply, they do not add. 20% off and then a further 10% off is 0.8 × 0.9 = 0.72 — a 28% discount, not 30%.
Percent difference formula: the difference between two numbers
Use percentage difference when neither number is the "starting" one — for example, comparing two shops' prices.
% difference = |A − B| ÷ ((A + B) ÷ 2) × 100
$40 and $50: difference 10, average 45. 10 ÷ 45 × 100 = 22.2%. If one value came first, use percentage change instead.
Weight loss percentage
Weight loss % = (starting weight − current weight) ÷ starting weight × 100
From 200 lb to 186 lb: 14 ÷ 200 × 100 = 7%. Pick Percentage change from X to Y above to do it in one step.
Percent yield, recovery and mass percent formula
Chemistry uses the same "part ÷ whole × 100" idea.
- Percent yield = actual yield ÷ theoretical yield × 100. Made 8.5 g when you expected 10 g? That is 85%.
- Percent recovery = mass recovered ÷ starting mass × 100. Common after recrystallisation.
- Mass percent = mass of the part ÷ total mass × 100. 5 g of salt in 100 g of solution is 5% by mass.
Percentage increase formula and percentage decrease
Percentage increase = (new − old) ÷ old × 100
Percentage decrease = (old − new) ÷ old × 100
How to calculate percentage increase: a rent rising from $1,200 to $1,350 is (1,350 − 1,200) ÷ 1,200 × 100 = 12.5%. A price falling from $80 to $60 is a 25% decrease. Always divide by the starting value.
How to find percentage: the three everyday questions
- How to calculate percentage of a number: change the percent to a decimal and multiply. 15% of 80 is 0.15 × 80 = 12.
- How to find a percentage of an amount you have: divide the part by the whole and multiply by 100. 12 out of 80 is 12 ÷ 80 × 100 = 15%.
- How to find percent change: (new − old) ÷ old × 100. A percent increase is positive; a decrease is negative.
For a percentage growth calculator over several years, the yearly rate is different: use (end ÷ start)1/years − 1, or the compound interest calculator.
How to find a percentage of a percentage
Convert both to decimals and multiply. 20% of 50% is 0.20 × 0.50 = 0.10, which is 10%. Stacked discounts work the same way: 20% off and then a further 10% off leaves you paying 0.8 × 0.9 = 72% — a 28% discount in total, not 30%.
Win percentage, margin percentage and average percentage
- Win percentage calculator: wins ÷ games played × 100. 18 wins from 25 games is 72%. Some leagues count a tie as half a win.
- Margin percentage: (price − cost) ÷ price × 100. Selling for $50 something that cost $30 is a 40% margin — but a 66.7% markup, because markup divides by cost.
- Average percentage: do not just average the percentages. Add up the parts and the totals separately. 9/10 and 30/50 average to 39/60 = 65%, not (90% + 60%) ÷ 2 = 75%.
Other ways to use this calculator
Six modes cover most percentage problems.
- Discount percentage calculator — use “X decreased by Y%” — or read how to calculate a discount.
- Pay raise and salary increase percentage calculator — use “Percentage change from X to Y” with old and new pay.
- Markup percentage calculator — markup % = (price − cost) ÷ cost × 100.
- Decimal to percent and percent to decimal — multiply or divide by 100.
- Attendance and food cost percentage — use “X is what percent of Y?”.
- Percent of a number — the first mode finds any percent of any number.
- How to calculate percent off — price × (1 − discount ÷ 100).
- Weight loss percentage calculator — use percentage change with your old and new weight.
Related guides
- How to Calculate Percent Yield, Percent Recovery and Mass Percent
- How to Calculate a Discount Percentage
- Percentage Difference vs Percentage Change
Frequently asked questions
Divide the percentage by 100, then multiply by the number. For 15% of 240: 15 ÷ 100 = 0.15, and 0.15 × 240 = 36. A useful shortcut is that X% of Y always equals Y% of X, so if one direction looks awkward, flip it. Working out 4% of 75 is fiddly, but 75% of 4 is obviously 3.
Percentage change has a direction and divides by the starting value — going from 40 to 50 is a 25% increase. Percentage difference has no direction and divides by the average of the two values, giving 22.2% for the same pair. Use change when something moved over time, and difference when comparing two independent measurements where neither came first.
Because each percentage applies to a different base. Starting at 100, a 50% rise adds 50 to reach 150. The 50% fall is then taken from 150, so it removes 75 and leaves you at 75. The fall was bigger in absolute terms. To undo a 50% rise you need a 33.3% fall — and a stock that halves must double just to break even.
Divide by the remaining fraction rather than adding the discount back. If an item costs £56 after 30% off, you paid 70% of the original, so the original was 56 ÷ 0.70 = £80. Adding 30% to £56 gives £72.80, which is wrong. The same rule strips VAT: divide by 1.20 for 20% VAT, do not subtract 20%.
Multiply the price by the discount and divide by 100 to get the saving, then subtract it. 25% off $80 is a $20 saving, so you pay $60. Or multiply by (1 − 0.25) directly: $80 × 0.75 = $60.
Divide the absolute difference by the average of the two numbers, then multiply by 100. For 40 and 50, that is 10 ÷ 45 × 100 = 22.2%.
Subtract the old value from the new value, divide by the old value and multiply by 100. Going from 1,200 to 1,350 is an increase of 150, and 150 divided by 1,200 is 12.5%.
Sources and further reading
- NIST — Guide for the Use of the International System of Units — correct usage of percent and percentage points
- BIPM — The International System of Units (SI Brochure) — the percent symbol as a dimensionless ratio
- Percentage — Encyclopaedia Britannica — definitions of percentage change and difference