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Percentage Calculator

Get three percentage answers on one screen: X% of Y, X as a percent of Y, and the change between two numbers.

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%X% of YX is ?% of YFrom → To

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Quick answer

This percentage calculator answers the three questions people usually ask, on one screen: what is X% of Y, X is what percent of Y, and the percentage increase or decrease from one number to another. Type your numbers and each answer updates as you go, with increases in green and decreases in red. The arithmetic is exact and happens in your browser, so the numbers you type never leave your device.

  • 3question types
  • 2decimals shown
  • Liveupdates as you type
  • 0numbers sent anywhere

What the Percentage Calculator does

Percentages turn up in discounts, tips, test scores and price changes, and the sum you need flips depending on the question. The three common forms sit side by side here, so you don't have to remember which formula goes with which question.

Each section works on its own: fill in the one you need and read the answer. The change row also colours the result, green for a rise and red for a fall, so one glance gives you the direction as well as the size.

How it works

The first answer multiplies: X% of Y is (X ÷ 100) × Y. The second divides: X as a percent of Y is (X ÷ Y) × 100. The third measures relative change: (To − From) ÷ From × 100, which comes out positive for an increase and negative for a decrease.

Every box recalculates as soon as you change a number, so you can try what-if values without pressing a button.

Methodology

  1. Step 1. Pick the section that matches your question. The three work independently.
  2. Step 2. For X% of Y, the tool computes (X ÷ 100) × Y.
  3. Step 3. For X is what % of Y, it computes (X ÷ Y) × 100.
  4. Step 4. For a change, it computes (To − From) ÷ From × 100 and shows the sign.
  5. Step 5. Results update as you type and are rounded to two decimals for display.

The three percentage formulas

X% of Y = (X ÷ 100) × Y X is what % of Y = (X ÷ Y) × 100 Change (From → To) = (To − From) ÷ From × 100
Worked examples
15% of 200 = 30
50 is 25% of 200
100 → 125 = +25% (and 125 → 100 = −20%)

Percentage change is measured against the From value, so a rise and a fall of the same size don't mirror each other: 100 to 125 is +25%, but the way back from 125 to 100 is −20%.

The three questions, worked

15% of 200 = 3030of 20050 is 25% of 20050 = 25%of 200100 → 125 = +25%+25125 → 100 = −20%−2525 of 10025 of 125
A rise and a fall of the same size don't mirror each other, because change is measured against the starting value.

Assumptions

  • Percentage change is measured against the starting (From) value. The same absolute change gives a different percentage from a different starting point.
  • Results are exact. Only the two-decimal display is rounded.
  • A percentage needs a non-zero denominator. If Y or the From value is 0, the percentage is undefined.

Technical details

ModesX% of Y · X is what % of Y · % change
OutputsEach answer live; change shows sign + colour
RoundingDisplay rounded to two decimals
InputsPlain numbers (no currency assumed)
ComputeYour browser does the arithmetic as you type

Standards and references

  • Relative (percentage) change: the standard definition used for the change box: (final − initial) ÷ initial × 100, positive for a rise and negative for a fall.
  • Per cent (per hundred): a percentage is a fraction of 100, which is why X% of Y multiplies by X ÷ 100.

Accuracy and limits

The results are exact arithmetic, not estimates. The only rounding is in the two-decimal display, so a repeating value such as a third of a percent shows as 0.33.

Percentage change is lopsided: a rise from 100 to 125 is +25%, but the drop back from 125 to 100 is −20%, because each direction starts from a different base. A 50% loss needs a 100% gain to get back to where you started.

Percentages applied one after another don't simply add. Two successive 10% increases give 21%, not 20%, because the second 10% is taken on the larger amount.

If a denominator is zero (Y in the first two sections, or the From value in the change) the percentage can't be defined, since it would mean dividing by zero.

Real-world uses

Discounts and tips

Find 15% of a bill, or 20% off a price, in one step.

Scores and shares

Turn X out of Y into a percentage for a grade or a proportion.

Price and metric changes

See how much a value rose or fell between two points.

Quick what-ifs

Change one number and watch all three answers move.

When it fits, and when it doesn't

Good for

  • Everyday percentage maths
  • Discounts, tips, scores and proportions
  • Percentage increase or decrease between two numbers
  • Trying a few what-if numbers quickly

Not the best choice for

  • Compound growth over many periods
  • Interest on a loan or savings
  • Percentile or statistical rank
  • Tax-inclusive or tax-exclusive splits

For growth that compounds each period, use a compound-interest calculator. For tax add-ons, use a GST calculator. For a loan, use the EMI calculator.

Frequently asked questions

How do I find X% of a number?
Multiply: X% of Y is (X ÷ 100) × Y. For instance, 15% of 200 is 0.15 × 200 = 30. The first box does this for you.
How do I work out what percent one number is of another?
Divide, then multiply by 100: X is (X ÷ Y) × 100 percent of Y. For example, 50 is (50 ÷ 200) × 100 = 25% of 200.
How is percentage increase or decrease calculated?
It is the relative change: (To − From) ÷ From × 100. From 100 to 125 is +25%; from 125 to 100 is −20%. A positive result is an increase and a negative one is a decrease.
Why is a 25% rise not cancelled by a 25% fall?
Because the base changes. A 25% rise from 100 gives 125, and a 25% fall from 125 gives 93.75, not 100. Each percentage is taken on a different starting number.
Do two 10% increases make 20%?
No, they make 21%. The second 10% applies to the already-increased amount (110), which adds 11 for a total of 121. Percentages applied in sequence compound.
What if I divide by zero?
A percentage of zero, or a change from zero, is undefined, since there is no meaningful percent of nothing. Make sure the Y or From value isn't 0.
How precise are the answers?
The maths is exact. Only the display is rounded to two decimal places, so you see 33.33% rather than the full repeating decimal.
Can it handle negative numbers?
The arithmetic works with negatives, but percentage change from a negative starting value can be confusing to read. Check those results carefully.
Is anything I type sent anywhere?
No. Your browser does every calculation as you type, and the page keeps no record of your numbers.

References

This page covers all three modes the tool runs, including the fact that a 25% rise and a 25% fall don't cancel out.

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