Percentage Calculator
Find percentages, percentage change or difference, and increase or decrease a value by a percentage.
Results are provided as is, for general information. Check anything important before relying on it. See the Terms of Use.
About this tool
Find a percentage of a number, a part as a percentage of a total, directional change, an increase or decrease by a known percentage, symmetric percentage difference, or the original value before an increase or decrease. Each mode labels its inputs. Adjustment shows both the resulting value and the amount added or subtracted, without currency rounding. Difference compares nonnegative values against their mean, so swapping inputs leaves the answer unchanged. Results keep up to four decimal places and drop trailing zeros. Undefined divisions and results too large to represent show an error.
How it works
X% of Y = X ÷ 100 × Y X is what % of Y = X ÷ Y × 100 % change A → B = (B − A) ÷ A × 100 Increase V by P% = V × (1 + P ÷ 100) Decrease V by P% = V × (1 − P ÷ 100) Reverse increase = Final ÷ (1 + P ÷ 100) Reverse decrease = Final ÷ (1 − P ÷ 100), P < 100 % difference = |A − B| ÷ ((A + B) ÷ 2) × 100
For change, divide by the original value: a negative result means a decrease only when that baseline is positive. Adjustment applies a known rate to a nonnegative starting value and shows the amount added or subtracted. Symmetric difference instead divides the absolute difference by the mean of two nonnegative values; their order does not matter, and they cannot both be zero.
| Question | Working | Answer |
|---|---|---|
| What is 15% of 240? | 15 ÷ 100 × 240 | 36 |
| 30 is what percent of 200? | 30 ÷ 200 × 100 | 15% |
| A price went from 80 to 95. What is the percentage increase? | (95 − 80) ÷ 80 × 100 | 18.75% increase |
| Sales fell from 120 to 90. What is the percentage decrease? | (90 − 120) ÷ 120 × 100 | −25% (a 25% decrease) |
| Increase 72 by 12.5% | 72 × (1 + 12.5 ÷ 100); amount added = 9 | 81 (9 added) |
| Decrease 72 by 12.5% | 72 × (1 − 12.5 ÷ 100); amount subtracted = 9 | 63 (9 subtracted) |
| What is the symmetric difference between 72 and 90? | |90 − 72| ÷ ((72 + 90) ÷ 2) × 100 | 22.2222% |
| What is the signed percentage change from -100 to -50? | (-50 − (-100)) ÷ (-100) × 100 | −50% (negative baseline; numerically a rise) |
| What was the original value before a 25% increase to 75? | 75 ÷ 1.25 | 60 |
| What was the original price before 25% off left 60? | 60 ÷ 0.75 | 80 |
When to use it
Questions
Which percentage mode should I choose?
Use % change for two observed values, Increase / decrease to apply a known rate, and % difference for an order-independent comparison against their mean. Reverse percentage finds the original from a final value and known rate: 60 after a 25% decrease came from 80. A 100% decrease loses all information about the original, so it cannot be reversed.
What is the difference between percentage change and percentage points?
This tool reports percentage change: from 20 to 25 is a 25% increase, because the 5-unit rise is a quarter of the original 20. If the two numbers are themselves percentages — say a rate went from 20% to 25% — that is also a 5 percentage-point rise, which is a different statement. Use change here; add or subtract the raw numbers yourself for points.
Why is the percentage change from 0 an error?
Percentage change divides the difference by the starting value, so a zero starting value makes it undefined. Use a nonzero baseline or describe the absolute change. Adjustment by a known percentage can start at zero; the result is still zero.
How is a decrease shown?
For a positive starting value, a negative percentage means a decrease: from 250 to 200 is -20%. With a negative starting value, the signed formula reverses that relationship. From -100 to -50 is numerically a rise but gives -50% when divided by -100. The tool explains the signed result without labeling it a decrease.
How do I work out a tip or a discount with it?
Use '% of a number' for the amount alone, or 'Increase / decrease' for both the amount and the final value. Decreasing 80 by 25% subtracts 20 and gives 60. The Tip Calculator adds bill splitting, and the Discount Calculator provides sale-price and savings tasks.
Does it handle decimals and negative numbers?
All modes accept decimals. Reverse percentage requires nonnegative final values and rates; reverse decreases must be below 100%. Percent-of, part/total and change also accept negative inputs; a negative baseline in change receives a signed-formula explanation. Adjustment requires a nonnegative starting value and percentage. Symmetric difference requires nonnegative values with at least one positive value. Results display up to four decimal places.
How does percentage difference differ from percentage change?
Change uses the original value as its denominator: 72 to 90 is a 25% increase, while 90 to 72 is a 20% decrease. Symmetric difference uses the mean of the two values: |90 - 72| divided by 81 times 100 is 22.2222% in either order. It requires nonnegative inputs; two zeros are undefined, one zero and one positive value gives 200%, and equal positive values give 0%.
Can I decrease a value by more than 100%?
Yes. The generic adjustment mode does not cap the percentage: decreasing 72 by 150% subtracts 108 and gives -36. A decrease above 100% produces a negative result for a positive starting value; a zero starting value stays zero. For a retail discount bounded to 0–100%, use the Discount Calculator.
How do I reverse a percentage — find the original before the change?
Choose Reverse percentage, enter the final value and rate, then select Increase or Decrease. It divides by the original change factor. A price after a 25% markup is 125% of the original, so the price 75 came from 75 ÷ 1.25 = 60. The trap is subtracting 25% of 75: that gives 56.25, wrong because the 25% belonged to the smaller original, not the larger final figure. For markdowns the same rule applies with addition: a sale price of 60 after 25% off came from 60 ÷ 0.75 = 80.
Why does 20% off followed by 20% on not balance out?
Because each percentage applies to a different base. A 100 price falls to 80; the 20% rise is taken on 80, reaching 96 — factors multiply (0.8 × 1.2 = 0.96), a net 4% loss. The same logic is why stacked discounts never add: 20% then 10% is 0.8 × 0.9 = 0.72, a 28% total markdown. Chain percentage changes by multiplying their factors, never by summing percentages.
Why does the tool refuse a 25% discount in sale-price terms?
It does not refuse percentages — it refuses inputs that would confuse the result. The 'X is what % of Y' mode treats 60 against 75 as a share (80%), not as a discount, because that mode's job is share-of. Read percentages as questions, not commands: 60 is what percent of 75 (share), from 90 to 60 (change), and 25% of something (amount-of). Mixing the frames is the single most common percentage mistake.