Percentages are everywhere in daily life, yet most people reach for a calculator every time a discount, a tip, a tax rate, or a year-over-year change comes up. This percentage calculator answers the three questions that actually matter: what is P percent of X, Y is what percent of X, and by what percent did a value grow or shrink from X to Y. Pick the mode at the top, type your numbers, and the answer updates instantly — no mental division required.
The whole idea of a percentage is "per hundred." Twenty percent means twenty out of every hundred. Once you hold that one idea, every percentage problem collapses into a small set of multiplication and division steps, which is exactly what this page automates for you.
How to Use
- Choose the Calculation Type that matches your question. There are three modes, and picking the right one is the only step where it is easy to go wrong.
- If you chose "What is P% of X?", enter the percentage in Percentage (P) and the whole value in Base Value (X). The calculator returns the part that P percent of X represents.
- If you chose "Y is what percent of X?", put the part in Second Value (Y) and the whole in Base Value (X). The calculator tells you what share of X Y occupies, as a percent.
- If you chose "Percent Change (X to Y)", put the starting value in Base Value (X) and the ending value in Second Value (Y). The calculator returns the percentage increase (positive) or decrease (negative).
- Read the result card. The highlighted Result is the answer to whichever question you picked: a quantity in "of" mode, a rate in "what percent" mode, or a signed percent change in "change" mode. The row below re-expresses that answer as a percentage, and the last row shows the plain difference between Y and X. In "of" mode the Y row is not used; in the other two modes the P row is not used — only the fields that match your mode matter.
A quick rule of thumb before you start: the "of" problem asks for a quantity, the "what percent" problem asks for a rate, and the "change" problem compares two states. If your answer looks wrong, double-check that you are in the right mode rather than re-typing the numbers.
The Three Percentage Formulas
Every percentage question is one of three relationships, all built from the idea of "per hundred":
1. What is P% of X?
part = (P / 100) × X
Example: 20% of 200 is (20 / 100) × 200 = 0.20 × 200 = 40. This is the discount, tip, or tax amount sitting inside a total.
2. Y is what percent of X?
percent = (Y / X) × 100
Example: 50 out of 200 is (50 / 200) × 100 = 0.25 × 100 = 25%. This tells you the share, the grade on a test, or the portion of a budget spent.
3. Percentage change from X to Y?
change% = ((Y − X) / X) × 100
Example: going from 200 to 250 is ((250 − 200) / 200) × 100 = (50 / 200) × 100 = 25% increase. Going the other way, from 250 to 200 is ((200 − 250) / 250) × 100 = (−50 / 250) × 100 = −20%. Notice the asymmetry: a 25% rise followed by a 20% fall returns you to the start, because each step is divided by a different base.
Two edge cases are handled automatically. If the base X is zero in the "what percent" or "change" modes, the division is undefined and the calculator shows an error rather than a meaningless number. If the result is exactly zero, the trend is reported as "no change."
Examples
Example 1 — A discount. A jacket costs $80 and is on sale for 30% off. In "What is P% of X?" mode, set P = 30 and X = 80. The result is 0.30 × 80 = $24 off, so you pay $56. Use the same mode for sales tax: 8% tax on a $56 shirt is 0.08 × 56 = $4.48.
Example 2 — A tip. Your restaurant bill is $64 and you want to tip 18%. P = 18, X = 64 gives 0.18 × 64 = $11.52. Total with tip: $75.52. Split the bill among friends by running the "what percent" mode on each person's share.
Example 3 — Share of a budget. You spent $120 of a $400 grocery budget this week. In "Y is what percent of X?" mode, Y = 120, X = 400 gives (120 / 400) × 100 = 30% of the budget used.
Example 4 — Pay raise. Your salary moves from $50,000 to $56,000. In "Percent Change" mode, X = 50,000 and Y = 56,000 gives ((6,000) / 50,000) × 100 = 12% increase. If instead it were cut to $46,000, the result would be (−4,000 / 50,000) × 100 = −8%, an 8% decrease.
Example 5 — A large number. A store's monthly revenue grows from $1,000,000 to $1,250,000. The change mode computes (250,000 / 1,000,000) × 100 = 25% growth, and the result-as-percent line confirms the new revenue is 125% of the old one.
FAQ
How do I calculate what is P percent of a number?
Use the "What is P% of X?" mode. Divide the percentage by 100 to turn it into a decimal (20% becomes 0.20), then multiply by the whole value. For example, 20% of 200 is 0.20 × 200 = 40. This is the same as asking for a discount amount, a tip, or a tax amount.
How do I find what percent one number is of another?
Use "Y is what percent of X?" mode. Divide the part Y by the whole X, then multiply by 100. For example, to find what percent 50 is of 200: 50 / 200 = 0.25, times 100 = 25%. This is how you compute a test score, a market share, or how much of a budget you have spent.
How do I calculate a percentage increase or decrease?
Use "Percent Change (X to Y)" mode. Subtract the old value X from the new value Y, divide by X, then multiply by 100. A positive result is an increase; a negative result is a decrease. For example, from 200 to 250: (250 − 200) / 200 × 100 = 25% increase.
Why is a 20% increase not undone by a 20% decrease?
Because each percentage step is based on a different number. A 20% rise on 100 adds 20, taking you to 120. A 20% cut on 120 removes 24, taking you to 96. To return exactly to the original value after a 20% rise, you need a 16.7% decrease, because the second calculation uses the larger base of 120, not 100.
How do I convert a percentage to a decimal or fraction?
Divide by 100. 45% becomes 0.45 as a decimal and 45/100 (which simplifies to 9/20) as a fraction. To go the other way, multiply a decimal by 100: 0.08 × 100 = 8%. This conversion is the first hidden step in almost every percentage problem.
Can the calculator handle zero or very large numbers?
Yes. Zero is handled safely: 0% of any number is 0, and 0 as a part gives 0%. The engine also supports large values well above one million, such as percentages of revenue or population figures. The only case that produces an error is dividing by a base of zero, since the result is mathematically undefined.
Related Calculators
- What Percentage Calculator — isolate the "Y is what percent of X?" question on its own page.
- Fraction to Percent Calculator — convert 3/8 into 37.5% and back.
- Decimal to Fraction Calculator — turn 0.45 into 9/20 for exact work.
- Average Calculator — find the mean before comparing percentages across groups.
Disclaimer
This percentage calculator is provided for informational purposes only and does not constitute financial, tax, accounting, or legal advice. All results are based on the inputs you enter and the standard percentage formulas (part = P/100 × X; percent = Y/X × 100; change = (Y−X)/X × 100). While the calculations are checked against standard educational references, they are approximations for everyday use and may not be appropriate for formal financial, statistical, or regulatory reporting. Always verify important figures independently and consult a qualified professional for decisions involving money, taxes, or official records.