Percentage Calculator
This percentage calculator answers the three questions that come up whenever numbers are compared in hundredths: what is a given percent of a number, one value is what percent of another, and how much did a value change from one reading to the next. It then adds the two ways people actually apply a percent — adding it on (tips, tax, markups, raises) and taking it off (discounts, markdowns, deductions) — so five modes live behind a single dropdown instead of five separate pages. The page opens with a worked example already on screen, and every mode shows the result, the equation and a four-row breakdown of the working, so the answer can be checked without redoing the arithmetic by hand.
Settings
Result
P% of XResult
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What a Percentage Calculator Answers
A percent is a fraction with 100 on the bottom: P% means P ÷ 100, so 15% is the same quantity as the decimal 0.15. That single idea covers every mode here. When the rate is known, one multiplication finds the part; when the part and the whole are known, one division finds the rate; and when two readings of the same quantity are known, the gap between them is measured against the reading you started from. The five modes are the five shapes of that arithmetic.
| Mode in the dropdown | Question it answers | Equation it runs |
|---|---|---|
| What is P% of X? | What is 15% of 200? | X × P ÷ 100 |
| X is what percent of Y? | 30 is what percent of 200? | X ÷ Y × 100 |
| Percentage change from X to Y | What is the percentage change from 200 to 250? | (Y − X) ÷ X × 100 |
| X increased by P% | What is 200 increased by 15%? | X + X × P ÷ 100 |
| X decreased by P% | What is 200 decreased by 15%? | X − X × P ÷ 100 |
Read the table as one family: the first two modes are the percent of calculator in both directions, the third is the percentage change calculator, and the last two are the percentage increase calculator and the percentage decrease calculator. All five take the same two numbers, and the dropdown decides which equation those numbers feed.
Percentages show up in a handful of everyday places, and each one maps onto a mode. Shopping is the decrease reading — a 15% discount on a $200 item is the tool’s own default pair, and 200 − 200 × 15 ÷ 100 = 170, so the price you pay is 170 rather than 200. Tipping, sales tax, a markup or a raise is the same sum in the other direction: 200 + 200 × 15 ÷ 100 = 230, with 30 as the amount added. Grade scores and survey answers are “what percent of” questions — if 30 of 200 responses carry one answer, that is 15% of the sample, and the remainder row flips the reading around when you need the other side. Prices, salaries and follower counts move between two readings, which is the percentage change case: from 200 to 250 is a 25% increase.
The tool is unitless, and that is deliberate. A base of 200 can be 200 dollars, 200 students, 200 cm of fabric or 200 inches of pipe, and the percentage comes out the same; the only requirement is that both fields describe the same quantity, so the numbers mean something together. Whether you are working in metric or imperial, in currency or in counts, the arithmetic is unchanged.
Percentage Formulas and Conventions
Every mode is one line of arithmetic, and the whole set fits in six symbols. The table below names them, and the formulas that follow are the ones the tool evaluates, in the order they appear in the dropdown.
| Symbol | Meaning | Where it is used |
|---|---|---|
| P | the percentage rate, the number with the % sign | divided by 100 to become the decimal form of the rate |
| X | the base, starting value or first field | the base value in mode 1, the part in mode 2, the starting value in mode 3, the value being changed in modes 4 and 5 |
| Y | the second field in the ratio and change modes | the whole in mode 2 and the ending value in mode 3 |
| P ÷ 100 | the rate as a decimal | the multiplier a base is scaled by, and the first breakdown row of mode 1 |
| Y − X | the absolute change | the difference the change mode divides by the starting value |
| 1 ± P ÷ 100 | the combined multiplier | the last breakdown row of the increase and decrease modes |
Percent of a number. To find a part when the rate is known, multiply and divide by one hundred. The percent of calculator in the first mode does it in this order:
\[ \text{Part} = \frac{P}{100} \times X \]
What percent of. When the part and the whole are known, the same relationship is solved for the rate instead:
\[ \text{Percentage} = \frac{X}{Y} \times 100 \]
The percent change formula. The third mode divides the difference by the starting value, which is what makes the reading a change relative to where you began rather than a plain ratio:
\[ \text{Percentage change} = \frac{Y – X}{X} \times 100 \]
Increase and decrease. The last two modes keep the change amount as a visible quantity instead of folding it into a multiplier, so the breakdown can show both the amount and the one-step shortcut:
\[ \text{Increased value} = X + \frac{X \times P}{100} = X \left(1 + \frac{P}{100}\right) \]
\[ \text{Decreased value} = X – \frac{X \times P}{100} = X \left(1 – \frac{P}{100}\right) \]
Percentage difference is a different reading. If you are looking for a percentage difference calculator, note the distinction: percentage difference measures the gap relative to the average of the two values, so it is symmetric and has no direction, while percentage change measures it relative to the starting value. The equation for the average-based version is shown here only to name it — the third mode of this page runs the starting-value form above:
\[ \text{Percentage difference} = \frac{|Y – X|}{(X + Y) \div 2} \times 100 \]
The multiplier rows in modes 4 and 5 are the bridge between the two readings: adding 15% is a multiplier of 1.15 and subtracting 15% is a multiplier of 0.85, and both are printed as the last row of their breakdown. That row is also the sanity check on direction — a multiplier above 1 means the value grew, a multiplier below 1 means it shrank, and a change in the opposite direction carries a negative percentage on the main reading.
Precision and boundaries. Results are rounded to at most six decimal places and trailing zeros are trimmed, so an arithmetic artefact such as 229.99999999999997 cannot reach the screen — the card prints 230, and whole numbers are printed without a decimal point. Very large readings switch to exponential notation: at or above 1e15 the card prints a short form such as 1e15, and a number the size of 1.2346e20 keeps four decimals in the mantissa, so the result stays readable instead of running off the card. Any number is accepted — greater than zero, negative, or a decimal — with exactly two exceptions, both divisions by zero, and each names itself: “The whole value (Y) cannot be zero — dividing by zero is undefined.” in the “X is what percent of Y” mode, and “The starting value (X) cannot be zero — percentage change is undefined.” in the percentage change mode. An empty or non-numeric field is answered with “Please enter a valid number in both fields.” and a calculation that overflows the largest representable number is answered with “The result is out of range for these inputs.” rather than an Infinity on the card.
How to Use the Percentage Calculator
- Pick the question you are asking in the Calculation Mode dropdown. Only the two input fields for that mode stay on screen, and they are labelled with what they mean in that mode — a base and a rate, a part and a whole, or a starting value and an ending value.
- Type the numbers. The result recomputes as you type, and pressing Enter or the Calculate button refreshes it explicitly.
- Read the result card: the headline number, the question it answers in words, the equation, and the four-row breakdown of the working — the intermediate quantities of whichever mode is running, so the rate as a decimal, the whole value, the change amount and the multiplier are all visible instead of being folded into the final number.
- Copy what you need. Copy Result puts the headline number on the clipboard by itself; Copy Summary copies the sentence and the equation together, which is the form to paste into a message or a note.
- Use Reset to return all five modes to their defaults — 15% of 200, 30 of 200, 200 to 250, 200 increased by 15%, and 200 decreased by 15% — and recalculate.
If a field is empty or holds something that is not a number, the last good result stays on screen and the reason appears under the form; the card is never wiped back to a dash, because a cleared card makes it hard to tell a rejected input from a calculation that has not run yet. Switch modes and the tool recalculates immediately with that mode’s own defaults, so you can compare the five readings without retyping the same pair of numbers.
Worked Examples
The five pairs below are the calculator’s own defaults, so every line can be reproduced by opening the page and switching the dropdown. Each table lists what the card shows: the question, the equation, the result and the four breakdown rows, followed by the summary sentence.
Example 1 — What is 15% of 200?
The first mode is the everyday percent of calculator: a rate of 15% applied to a base of 200. The equation is one multiplication, 15% × 200 = 30, and the breakdown repeats the same step from both ends — 0.15 is the rate written as a decimal, which is the number actually multiplied, and 30 is the result row. The reverse check closes the loop by dividing the result by the base and multiplying by 100, which returns the rate you started with, 15%.
| Line on the card | Value |
|---|---|
| Question | What is 15% of 200? |
| Equation | 15% × 200 = 30 |
| Result | 30 |
| Percentage as a decimal (P ÷ 100) | 0.15 |
| Base value (X) | 200 |
| Result (X × P ÷ 100) | 30 |
| Reverse check (result ÷ X × 100) | 15% |
| Summary | 15% of 200 is 30 |
Example 2 — 30 is what percent of 200?
Turn the question around and the tool divides instead of multiplies. The fraction row is 0.15 — the part divided by the whole before it is scaled to hundredths — and the percentage row is 15%, which is that fraction times 100. The third row is the complement: 85% is what remains to reach a full 100%, the figure you want when the part you entered is the smaller side of the comparison. The whole is repeated unchanged at 200, which confirms which field was treated as the denominator.
| Line on the card | Value |
|---|---|
| Question | 30 is what percent of 200? |
| Equation | 30 ÷ 200 × 100 = 15% |
| Result | 15% |
| Fraction (X ÷ Y) | 0.15 |
| As a percentage (fraction × 100) | 15% |
| Remainder to reach 100% | 85% |
| Whole (Y) | 200 |
| Summary | 30 is 15% of 200 |
Example 3 — percentage change from 200 to 250
This is the percentage change calculator at work on two readings of the same quantity. The absolute change is 50, and the relative change is 0.25 — the same 50 measured against the value it grew from rather than against a raw total. Scaling that ratio to hundredths gives the headline reading, 25%, and because the ending value is larger than the starting value the Direction row reads Increase. The starting value is repeated as the last row, which is the number the tool divided by; a move in the other direction would keep the same four rows but print the direction as Decrease, and two equal readings would print No change.
| Line on the card | Value |
|---|---|
| Question | What is the percentage change from 200 to 250? |
| Equation | (250 − 200) ÷ 200 × 100 = 25% |
| Result | 25% |
| Absolute change (Y − X) | 50 |
| Relative change (Y − X) ÷ X | 0.25 |
| Direction | Increase |
| Starting value (X) | 200 |
| Summary | From 200 to 250 is a 25% increase |
Example 4 — 200 increased by 15%
Adding a percentage on top of a value is the percentage increase calculator mode, and it is the shape of a tip, a sales tax, or a raise. The increase amount is 30, the final value is 230, and the multiplier row is 1.15 — the shortcut form of the same sum, the number the starting value is scaled by when the amount of the change is not needed separately. Keeping the amount and the multiplier on separate rows is the point of the mode: one tells you how much was added, the other tells you how the final value was reached.
| Line on the card | Value |
|---|---|
| Question | What is 200 increased by 15%? |
| Equation | 200 + 200 × 15 ÷ 100 = 230 |
| Result | 230 |
| Increase amount (X × P ÷ 100) | 30 |
| Starting value (X) | 200 |
| Final value (X + change) | 230 |
| Multiplier (1 + P ÷ 100) | 1.15 |
| Summary | Increasing 200 by 15% gives 230 |
Example 5 — 200 decreased by 15%
The discount case, and the reason the decrease mode exists rather than asking you to enter a negative rate: the decrease amount is 30, the final value is 170, and the multiplier is 0.85. The arithmetic mirrors mode 4 exactly — the change amount was already computed by the time the multiplier is printed, which is why the two rows always agree. If you are checking a markdown by hand, the multiplier row is the fastest route: it is the number the original price is multiplied by to land on the sale price in a single step.
| Line on the card | Value |
|---|---|
| Question | What is 200 decreased by 15%? |
| Equation | 200 − 200 × 15 ÷ 100 = 170 |
| Result | 170 |
| Decrease amount (X × P ÷ 100) | 30 |
| Starting value (X) | 200 |
| Final value (X − change) | 170 |
| Multiplier (1 − P ÷ 100) | 0.85 |
| Summary | Decreasing 200 by 15% gives 170 |
Percentage Calculator FAQ
How do I calculate percentage of a number?
Multiply the number by the percentage and divide by 100. The first mode does exactly that: with a rate of 15 and a base of 200 the card reads 15% × 200 = 30, and the breakdown shows the same step twice — once as the rate in decimal form, 0.15, and once as the result row, 30. The reverse check then divides the result by the base and multiplies by 100, confirming the rate you started with.
What is the difference between percentage change and percentage difference?
Percentage change divides the difference by the starting value; percentage difference divides it by the average of the two values. That is why a move from 200 to 250 is a 25% increase — the equation is (250 − 200) ÷ 200 × 100 — while the average-based reading of the same pair would be symmetric and would carry no direction at all. The third mode here gives the percentage change, and its Direction row says the direction in words: Increase, Decrease or No change.
How do I work out a discount?
Use the last mode, the percentage decrease calculator: enter the original price and the percent off, and the card shows the amount taken off, the final price and the multiplier. The default pair, 200 decreased by 15%, gives a decrease amount of 30, a final value of 170 and a multiplier of 0.85. The final-value row is the price you would pay; the multiplier is the same answer in one-step form.
How do I add a tip or sales tax?
Switch to the fourth mode, the percentage increase calculator, and enter the amount and the rate. With the defaults, 200 increased by 15% gives 230, and the breakdown separates the increase amount, 30, from the final value, 230, so you can see how much was added before you round it. The multiplier row, 1.15, is the same sum written as a single multiplication.
Can I enter negative numbers and decimals?
Yes. Any number is accepted — greater than zero, negative, or a decimal such as 7.5 — and the sign is carried through the arithmetic, so a value that falls produces a negative percentage rather than an error. The only rejected values are the two zeros that would sit in a divisor: the whole value (Y) in the second mode, and the starting value (X) in the change mode. Each of those is answered with its own message instead of an Infinity.
What do the four rows under the result mean?
They are the intermediate steps of the same calculation, so you can check the reading without redoing the arithmetic. Each mode labels its own four rows with the quantities that formula passes through: the rate written as a decimal, the base or whole value, the change amount, the ratio, the direction of a change, or the multiplier — which is 1.15 for an increase of 15% and 0.85 for a decrease of 15%. The labels name the formula that produced each number, which makes the card usable as a worked solution rather than a black box.
Why does it say the result is out of range?
Because the calculation overflowed the largest number the page can represent, and the tool refuses to print Infinity. Results this large are normally still readable — at or above 1e15 the card switches to exponential notation, so a number the size of 1.2346e20 prints in a short form — and “The result is out of range for these inputs.” appears only when even that representation is impossible.
Is this percent calculator online free?
Yes. It is a free percent calculator online with no sign-up, no download and no usage limit: the arithmetic runs in your browser as you type, and switching the dropdown recalculates for the new mode immediately. Nothing about the calculation needs an account or a connection to a server.
Related Tools
This page belongs to the Math cluster on BunTool, where every tool follows the same structure: definition, formulas, worked examples, FAQ. If the arithmetic you need is more than one percentage, the basic calculator handles the rest of the running sum, including a percent key for amounts like 200 + 15%. If the two numbers you are comparing are not measurements but draws from a range, the random number generator produces them in a batch between any bounds. And if the quantity behind the percentage has to be measured from a shape first — an area, a length, an angle — the triangle calculator supplies the numbers before you bring them here.
