Audited 25 May 2026·Last updated 27 Jul 2026·6 citations·Tier 1·0 uses

Percentage Calculator

Free percentage calculator: find a percent of a number, calculate percent change between two values, or work out what percent one number is of another.

Percentage Calculator

What do you want to calculate?
The percentage you want to take of the value. Used only in the "percent of a number" mode.
%
The base number you're taking a percent of. Used only in the "percent of a number" mode.
The original or earlier value. Used only in the "percent change" mode.
The new or later value. Used only in the "percent change" mode.
The portion or subset you're measuring. Used only in the "what percent" mode.
The total the part belongs to. Used only in the "what percent" mode.
Result
50
In "percent of a number" mode the result is a plain number. In "percent change" and "what percent" modes the result is a percentage value (e.g. 25 means 25%).

Background.

The Quanta percentage calculator handles the three percentage questions that account for nearly every real-world use of the symbol: what is X percent of a number, how much did a value change in percent from one figure to another, and what percent of a whole a part represents. Pick the mode that matches your question, type in two numbers, and the answer updates as you type — no formulas to memorize, no decimal slips, no fighting with a phone keyboard.

The same engine powers tip splits at restaurants, sale prices in shopping carts, grade calculations on exams, sales-tax add-ons at checkout, growth rates in spreadsheets, body-fat changes between weigh-ins, and the dozens of other places where someone says "figure out the percent." Under the hood it uses arbitrary-precision decimal arithmetic so that 10% of $19.99 returns exactly $1.999 rather than the $1.9989999999999999 that naive JavaScript would give you.

Percentages look trivial until you have to do twenty of them in a row, or until the difference between a 4-percentage-point move in a tax bracket and a 4-percent move in income costs you real money. This page also walks through the underlying formula so that the next time you face one of these problems with only a napkin and a pen, you know exactly which operation to reach for.

Whether you're a student double-checking homework, a small-business owner pricing a markup, a personal-finance hobbyist tracking a portfolio, or just trying to figure out how much to leave the server, the calculator and the explainer below it cover every variant you're likely to encounter, including the common traps — percent of versus percent off, percent change versus percentage-point change, negative percent change, and division-by-zero when the starting value is itself zero. Bookmark this page; we built it as a permanent reference, not a one-off widget.

What is percentage calculator?

A percentage is a ratio expressed as a fraction of 100 — the word literally comes from the Latin per centum, "per hundred." Saying "25%" is shorthand for the fraction 25/100, the decimal 0.25, and the ratio 1:4 all at once. The notation became standardized in European commercial mathematics in the 15th and 16th centuries because merchants needed a consistent way to express interest rates, taxes, and trade margins across currencies and units, and 100 is a convenient common denominator. Today percentages do three distinct jobs: they scale a quantity (35% of a paycheck goes to taxes), they describe relative change (sales grew 12% year-over-year), and they describe composition (oxygen makes up 21% of the atmosphere). Each of those jobs has its own arithmetic, which is why this calculator exposes three modes rather than one. Crucially, a percentage is dimensionless — it's a pure number that only has meaning when you know what whole it refers to. "50% more" of a $10 item is $5; "50% more" of a $1,000 item is $500. That dependency on a reference value is the single biggest source of percentage mistakes in the wild, and the explainer sections below show you how to keep them straight.

How to use this calculator.

  1. Choose the mode at the top that matches your question. "What is X% of a number" covers tips, taxes, discounts, and any time you're scaling a value down or up by a percentage.
  2. If you picked "percent of a number", enter the percent (e.g. 18 for an 18% tip) and the base value (e.g. 64.50 for a restaurant bill). The result updates instantly.
  3. If you picked "percent change", enter the starting value in the From field and the ending value in the To field. The calculator returns a positive percent for growth and a negative percent for a decline.
  4. If you picked "what percent", enter the Part (the subset) and the Whole (the total). The result is the percentage the part represents of the whole — for example, 18 correct answers out of 20 questions returns 90.
  5. Read the result, then copy it into your spreadsheet, receipt, homework, or message. The result respects the sign of your inputs: negative starting values and decreases are handled correctly.
  6. If you change your mind about which question you're asking, switch modes — the calculator keeps your other inputs so you can experiment without retyping everything.

The formula.

R = V × (P ⁄ 100)
R · resultV · valueP · percent

Each mode runs a distinct formula. Mode 1, percent of a number, is `result = value × (percent ÷ 100)`. So 20% of 250 is 250 × 0.20 = 50. Mode 2, percent change, is `result = ((to − from) ÷ from) × 100`. This is the standard relative-difference formula recognized by NIST and used in every economics, finance, and science context where growth is reported. If from is zero the formula is undefined (division by zero), and the calculator returns 0 rather than infinity so your downstream spreadsheet doesn't blow up. Mode 3, what percent, is `result = (part ÷ whole) × 100`. It's the same arithmetic as mode 2 with different labels, and it also returns 0 if the whole is zero. All three formulas operate on decimal-precision numbers internally, which matters for repeated chained calculations where rounding errors otherwise accumulate. To go the other direction — converting a percentage back to a decimal — divide by 100; to a fraction, write the percentage over 100 and reduce. 75% is 0.75 is 3/4. Knowing all three representations of the same value makes mental math much faster than reaching for a calculator every time.

A worked example.

Example

A side-project's monthly recurring revenue grew from $80 to $100 between January and February. Selecting the "percent change" mode and entering 80 in the From field and 100 in the To field returns a result of 25 — meaning the revenue grew by 25%. The arithmetic: (100 − 80) ÷ 80 × 100 = 20 ÷ 80 × 100 = 0.25 × 100 = 25%. Note that if the figures were reversed — revenue fell from 100 to 80 — the result would be −20%, not −25%, because the denominator changed. This asymmetry is the most-missed feature of percent change and the reason you should always identify which number is the baseline before reaching for a formula.

modepercentChange
from80
to100

Frequently asked questions.

What's the difference between percent and percentage points?
A percentage point is the arithmetic difference between two percentages, while a percent is the relative difference between two values. If a tax rate rises from 20% to 24%, that's a 4 percentage-point increase but a 20% relative increase (4 ÷ 20 × 100). News headlines routinely confuse the two, especially when reporting on central-bank rates and election polls, and the difference can be material — a 1 percentage-point cut to a 5% mortgage rate is a 20% reduction in interest, not a 1% one.
How do I calculate a percent increase versus a percent decrease?
Both use the same formula — (new − old) ÷ old × 100 — and the sign of the result tells you which one occurred. A positive number is an increase; a negative number is a decrease. The calculator's "percent change" mode handles both automatically. The trap to avoid is asymmetry: an item that goes from $100 to $80 dropped 20%, but to get back from $80 to $100 it needs to rise 25%, not 20%. The denominator changed when the baseline changed.
How do I take a percentage off a price?
There are two equivalent paths. The literal one: compute the discount (use "percent of a number" mode with the discount percent and the price) and subtract it from the original. The shortcut: multiply the price by (100 − discount) ÷ 100. A 25% discount on a $48 jacket is either $48 × 0.25 = $12 off, leaving $36, or $48 × 0.75 = $36 directly. The shortcut is faster and avoids one subtraction step, which is why retail point-of-sale systems use it internally.
How do I add a percentage, like sales tax?
Multiply the pre-tax amount by (100 + tax rate) ÷ 100. A 7.25% sales tax on $40 is $40 × 1.0725 = $42.90. If you want to back the tax out of a tax-inclusive price, divide rather than subtract: $42.90 ÷ 1.0725 = $40. The naive trick of subtracting 7.25% from $42.90 gives the wrong answer ($39.79) because that 7.25% is being taken off the larger, tax-inclusive base instead of the smaller pre-tax base.
What is 20% of 250?
Fifty. The arithmetic is 250 × 20 ÷ 100, or equivalently 250 × 0.20. For mental math, 10% of any number is just the number with the decimal shifted left by one digit — 10% of 250 is 25 — and 20% is double that. The same shortcut works in reverse for tips: 20% of any bill is twice 10% of the bill, which is the easiest mental tip calculation in the world.
How do I work out what percentage one number is of another?
Divide the part by the whole and multiply by 100. If you got 45 out of 60 on a quiz, that's 45 ÷ 60 × 100 = 75%. The "what percent" mode in this calculator runs that arithmetic for you and handles the edge case where the whole is zero (it returns 0 instead of attempting an undefined division). This is the formula behind every test score, batting average, and conversion-rate report you've ever seen.
Why does the calculator return 0 when I enter a starting value of 0 for percent change?
Mathematically, percent change is undefined when the starting value is zero, because the formula divides by that starting value. Different tools handle this differently — some return Infinity, some return NaN, some throw an error. Quanta returns 0 because it's the value least likely to break a downstream spreadsheet or trigger an exception in a chained calculation. If you genuinely need to express "appeared from nothing" growth, percent change isn't the right tool; report the raw values or use a logarithmic measure instead.
What is the formula for percentage in maths?
There isn't one formula — there are three, and choosing the right one is the whole skill. For "percent of a number": result = value × percent ÷ 100. For "percent change": result = (new − old) ÷ old × 100. For "what percent is X of Y": result = X ÷ Y × 100. Every percentage problem reduces to one of these three patterns. Get fluent at recognizing which one a word problem maps to and the arithmetic itself becomes trivial.
Can a percentage be greater than 100?
Yes. Anything that's larger than its reference value is more than 100% of it. A stock that doubles is 200% of its starting price, or equivalently has risen 100% — those mean the same thing said two different ways. The distinction matters most in finance writing, where "is 200%" and "rose 200%" mean entirely different things (the second implies a starting position of 100% and an ending position of 300%). When in doubt, restate the sentence with raw numbers to confirm the meaning.
What's the most common percentage mistake people make?
Reversing the base. If sales drop 20% and then recover 20%, you don't end up where you started — you end up 4% below. (100 → 80 → 96.) The recovery percentage is calculated against the new, smaller base, so it produces a smaller absolute gain than the absolute loss it's trying to undo. This bias is why investment returns are usually reported as compound annual growth rates rather than simple percentages, and why "break-even" after a loss always requires a larger percentage gain than the percentage of the original loss.

References& sources.

  1. [1]NIST Guide to the SI, §7.10.2 — guidance on expressing relative differences as dimensionless percentages.
  2. [2]Khan Academy — Percent word problems and the three canonical percentage operations.
  3. [3]Investopedia — Percentage Change: definition, formula, and uses in finance and economics.
  4. [4]BBC Bitesize (KS3 Maths) — Percentages, percentage change, and reverse percentages explained for a pedagogical audience.
  5. [5]International Bureau of Weights and Measures (BIPM) — SI Brochure, 9th edition, §5.4.7 on the use of the percent symbol with dimensionless quantities.
  6. [6]Federal Reserve Board — explanatory note on the distinction between basis points, percentage points, and percent change when describing interest rate moves.
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