Percentage Calculator
Use this percentage calculator to work out percent of a value, percent change between two figures, increases, decreases, basis points, and the original prices behind discounts or markups. Every card refreshes as you type and the whole page runs inside your browser, so no numbers leave your machine. The change card turns any pair of figures into a signed difference, a percent change with a direction word, basis points, and a percent difference side by side.
Percentage of a value
What percent is A of B?
Change, increase and decrease
Add or subtract a percentage
Original price before discount / after markup
How percentage calculations work
Each card on this page runs one small formula, and the same six expressions cover almost every percent question that shows up at work. Written in plain text, they look like this.
- Percent of a value = percent ÷ 100 × value. Fifteen percent of 80 is 0.15 × 80 = 12.
- What percent is A of B = A ÷ B × 100, which has no defined answer when B is zero.
- Percent change = (to − from) ÷ |from| × 100. The bars around the starting figure keep a drop from flipping the sign rule when from is negative.
- Percent difference = |A − B| ÷ ((|A| + |B|) ÷ 2) × 100, which uses the average of the two magnitudes instead of either one alone.
- Basis points = percent × 100. A figure of 1.25% is 125 basis points, and 25 basis points is a quarter of a percent.
- Discount: original = final ÷ (1 − rate). Markup: original = final ÷ (1 + rate), where rate is the percent written as a decimal.
- Zero base rule: when the starting figure is zero, percent change is undefined rather than 0%. Both figures being zero is the single case where 0% is the right answer, and the cards print a dash with a short reason for every other undefined output.
Examples
| Case | Work | Result |
|---|---|---|
| Percent of a value | 15% of 80 | 12 |
| Percent increase | From 40 to 50 | +25% increase |
| Percent decrease | From 200 to 180 | −10% decrease |
| Part of a whole | 80 is what percent of 200 | 40% |
| Discounted price | 250 after 20% off | Original 312.50 |
| Budget growth | From 12,500 to 13,750 | +10% increase, 1,000 bp |
When to use this tool
- Discount price checking. The tag says 250 after 20% off, and the before-discount card gives 312.50 so you can see the size of the cut.
- KPI and month-over-month deltas. Signups moved from 4,000 to 4,600, and the change card turns that pair into a signed percent for the weekly report.
- Grade curves. A raw score of 72 against a top score of 80 reads as 90% of the top, which is the percent-of-a-value card in one line.
- Tip and bill splits. Add 18% to a dinner total or take 10% off a shared cost with the add-or-subtract card, then split the printed figure.
- Growth reports. A budget of 12,500 growing to 13,750 reads as a 10% increase and 1,000 basis points, both of which appear together on the change card.
- Comparing two independent measurements. Two instruments reading 98.2 and 101.6 have no natural starting point, so the percent difference row is the right form to quote.
- Finance quotes. Bond yields and fee schedules move in basis points, and the change card converts any percent figure for you.
Best practices
- Keep full precision through the arithmetic and round only at the display stage, so a chain of rounded percentages does not drift away from the true figure.
- Use percent change when both figures describe the same thing at two points in time, such as last month against this month.
- Use percent difference when the two figures are independent measurements with no agreed starting point.
- State the base whenever a percentage is presented. Twenty percent of the smaller group and twenty percent of the total lead to different readings.
Common mistakes
- Mixing up percent change with percentage-point change. A rate that moves from 30% to 40% rises by 10 percentage points, while the relative change is 33.3%.
- Dividing by the wrong base. Percent change divides by the starting figure, and percent difference divides by the average of the two magnitudes.
- Adding a percent to a total that already contains it. A tip calculated on a bill that includes tax shares the base with the tax, which inflates the tip.
- Treating a zero starting value as a 0% change. Moving from 0 to 40 has no defined percent, so the raw difference of 40 is the reading that still holds.
- Rounding too early. Dropping decimals on each step of a multi-step calculation shifts the final figure more than people expect.
- Sign errors on decreases. Writing the formula as (from − to) and then reporting the answer as a rise turns a 10% drop into a claimed +10% gain.
Frequently Asked Questions
How do I calculate percent change?
Subtract the starting figure from the ending figure, divide that difference by the starting figure, and multiply by 100. Moving from 40 to 50 gives a difference of 10, and 10 ÷ 40 × 100 = 25%, so the change is a 25% increase. When the starting figure is zero the answer is undefined, which is why the main card shows a dash with a short reason in that case.
What is the difference between percent change and percentage-point change?
Percent change measures movement relative to the starting figure with the formula (to − from) ÷ |from| × 100. A percentage-point change is plain subtraction of two percentages, so a rate that moves from 30% to 40% rises by 10 percentage points while the relative change is 33.3%. Reports mix the two constantly, so name the one you mean whenever both could apply.
How do I find the original price before a discount?
Divide the sale price by 1 minus the discount rate. A price of 250 after 20% off works out as 250 ÷ 0.80 = 312.50, which means the discount itself was 62.50. The price card on this page runs that direction and the markup direction as well, where original = final ÷ (1 + rate).
What are basis points?
One basis point is one hundredth of one percent, so 0.01%. Multiply a percent figure by 100 to get basis points: 1.25% equals 125 basis points. Bond yields, central bank rates, and fee schedules are quoted this way because a quarter of a percent is easier to pass around as 25 basis points.
Why is percent change undefined when the starting value is zero?
The formula divides by the starting figure, and division by zero has no finite answer. Moving from 0 to 40 is an unbounded relative rise, so the honest output is undefined rather than 0 or some invented figure. The raw difference of 40 still appears on the card, and a dash with a short reason replaces the percent.
How do I add 15% to a number?
Multiply by 1.15, which is the same as computing value + value × 15 ÷ 100. The add-or-subtract card does both sides at once: for 200 you get 230 after adding 15% and 170 after taking 15% away. The reduction side works the same way with the factor 0.85.
What formulas do percent increase and percent decrease use?
One formula covers both cases: (to − from) ÷ |from| × 100. A positive result is an increase and a negative result is a decrease. Some people write the decrease form as (from − to) ÷ from × 100 and drop the minus sign; the signed form keeps the direction visible and avoids reporting a drop as a gain.
Related Tools
How to calculate percentage change
- Enter the starting and ending figures
Type the starting figure into the from field and the ending figure into the to field of the change card. The outputs refresh on every keystroke.
- Read the percent change and direction
The card reports the signed difference, the percent change with a direction word, basis points, each figure as a percent of the other, and the percent difference.
- Check the zero-base case
When the from field is zero, percent change and basis points have no defined answer, so the page shows an em dash with a short reason instead of a number.