Percentage Calculator

Verified 2026-04-29 Report an error

%
Result
50.00
On this page
  1. Overview
  2. Key takeaway
  3. How it's calculated
  4. Quick tricks
  5. Examples
  6. FAQ
  7. Embed
  8. Related calculators
  9. Popular tools

A percentage calculator answers the most common question in everyday math: what is X% of Y? Enter the percentage and the value, the result appears instantly. Useful for tip math, sales tax, discounts, grade calculations, and any time you need to take a slice of a number.

The formula is straightforward: (percent / 100) × value. The mental tricks in the section below make most everyday percentages doable in your head, no calculator needed.

When you'll use a percentage calculator

Percentages show up in nearly every domain that involves comparison or proportion. The most common everyday uses:

  • Tipping, 15%, 18%, or 20% of a restaurant bill.
  • Sales tax, adding state and local tax to a pre-tax price.
  • Discounts, figuring out the price after "30% off."
  • Grade calculations, converting "82 out of 110 on the test" into a percentage you can compare against a grading curve.
  • Tip-share calculations, splitting a 20% tip evenly across a group.
  • Commissions and bonuses, calculating a 3% real estate commission or a 10% performance bonus on a base salary.
  • Percent change, measuring growth or decline ("revenue is up 12% year-over-year").
  • Body composition and nutrition, "carbs as 40% of total calories."

For more complex percentage workflows you may want our specialized percentage change, percentage increase, or percentage decrease calculators, but the core arithmetic is identical to what's here.

The three classic percentage problems

Almost every percentage question is one of three forms, and they're all rearrangements of the same equation:

  1. What is X% of Y? → result = X × Y ÷ 100 (this calculator)
  2. X is what percent of Y? → percent = X ÷ Y × 100
  3. X is Y% of what? → value = X ÷ Y × 100

If you internalize the relationship part = (percent ÷ 100) × whole, you can always solve for whichever variable is missing, no need to memorize three separate formulas.

Common mistakes with percentages

Three errors come up constantly and are worth flagging.

Confusing percentage points with percent change. If a mortgage rate moves from 5% to 7%, that's a 2 percentage point increase, but a 40% percentage increase (because 7 is 40% greater than 5). News headlines routinely conflate these, which makes a small change sound dramatic or vice versa.

Assuming "+X% then −X%" returns to the original. It doesn't. If a stock rises 20% then falls 20%, you don't end up where you started, you end up at 96% of the original. The reason: the +20% was applied to the starting value, but the −20% is applied to the higher value. Asymmetry in the base means the two operations don't cancel.

Adding percentages of different bases. A 10% raise followed by a 5% raise is not a 15% raise; it's a 1.10 × 1.05 = 1.155 total, or 15.5%. Small enough to seem like a rounding issue, but it compounds quickly over longer chains.

Key takeaway

A percentage is just a fraction with 100 as the denominator. "20% of 250" really means "20 out of every 100, applied to 250", which is the same as 0.20 × 250. Once you see the percent sign as "÷ 100," every percentage problem becomes a multiplication problem, and most of them collapse to mental shortcuts.

How it's calculated

The core equation is result = (percent / 100) × value. The "÷ 100" is the work of the percent sign itself: a percentage is just a fraction with 100 as the denominator, so 25% is 25 / 100 = 0.25. Multiplying by 0.25 then says "take a quarter of."

Percent change

"What's the percent change from 80 to 100?" follows a closely related formula: ((new − old) / old) × 100. The change is (100 − 80) / 80 = 0.25, so the percent change is 25% increase. Going the other way, 100 to 80, uses the same formula and gives (80 − 100) / 100 = −0.20, a 20% decrease. The asymmetry between "up 25%" and "down 20%" describing the same two values is the source of a lot of confusion.

Percent off (discount math)

A 30% discount on a $80 item costs $80 × (1 − 0.30) = $80 × 0.70 = $56. The shortcut: instead of computing the discount and subtracting, multiply by (1 − discount fraction) directly. For sales tax, the same idea multiplied by (1 + tax fraction): $56 × 1.0875 = $60.90 for an 8.75% sales tax.

Reversing a discount

If a sale price is $56 after 30% off, what was the original? Divide by (1 − 0.30): $56 / 0.70 = $80. The same logic backs out a pre-tax price from a post-tax total: divide the total by (1 + tax rate). This trips people up, adding the discount percentage back to the sale price gives the wrong answer because you'd be applying the percentage to a smaller base.

Source: Elementary arithmetic, percent × value ÷ 100

Examples

  1. 20% of 250

    Result 50.00

    20% of 250 is 50. Mental shortcut: 10% of 250 is 25, double it for 20% → 50. This is the math behind a 20% restaurant tip on a $250 dinner check.

  2. 15% of 86.40

    Result 12.96

    15% of $86.40 is about $12.96. Mental shortcut: 10% is $8.64, half of that is $4.32, sum to $12.96. Useful for budgeting category percentages or estimating a 15% tip without a phone.

  3. 30% off a $80 item (calculating the discount)

    Result 24.00

    A 30% discount on an $80 item is $24 off, leaving a sale price of $56. To get the sale price directly, multiply by (1 − 0.30) = 0.70: $80 × 0.70 = $56. Mental shortcut: 30% is 3 × 10%, so 30% of $80 is 3 × $8 = $24.

  4. 8.75% sales tax on $56

    Result 4.90

    8.75% sales tax on a $56 purchase adds $4.90, for a total of $60.90. To compute the after-tax total directly, multiply by (1 + 0.0875): $56 × 1.0875 = $60.90. Useful for any state-and-local sales tax math.

  5. 7% commission on a $450,000 sale

    Result 31,500.00

    A 7% commission on a $450,000 home sale comes to $31,500. In the typical US real estate transaction this is split between the buyer's and seller's agents (often 3.5% each). Mental shortcut: 7% is "1% × 7"; 1% of $450,000 is $4,500, times 7 is $31,500.

  6. 40% carbs in a 2,200-calorie diet

    Result 880.00

    At a 2,200-calorie daily target with carbs at 40% of calories, that's 880 calories from carbs. Since carbs provide 4 calories per gram, that's 880 ÷ 4 = 220 grams of carbs per day. The same arithmetic powers our macro calculator, which handles all three macronutrients at once.

Frequently asked questions

How do I calculate a percentage of a number?

Multiply the number by the percentage, then divide by 100. So 20% of 250 is (20 × 250) ÷ 100 = 50. Equivalently, convert the percentage to a decimal first (20% = 0.20) and multiply: 0.20 × 250 = 50. Both routes give the same answer; pick whichever feels more natural.

How do I do percentages in my head?

Anchor on 10%, moving the decimal one place left. Once you have 10%, every other percentage is a small adjustment: double it for 20%, halve it for 5%, add 1% increments (decimal moved two places) for the rest. This single anchor handles 95% of everyday percentage math without a calculator.

What's the difference between percentage and percentage points?

A percentage is a relative measure (X out of 100). Percentage points are the difference between two percentages. If a mortgage rate goes from 5% to 7%, that's a 2 percentage point increase, but a 40% percentage increase (because 7 is 40% larger than 5). Mixing these up causes a lot of confusion in news headlines about interest rates and polling.

How do I convert a fraction to a percentage?

Divide the numerator by the denominator, then multiply by 100. So 3/8 becomes 3 ÷ 8 = 0.375, times 100 = 37.5%. Easy reference points: 1/2 = 50%, 1/4 = 25%, 1/3 ≈ 33.3%, 1/5 = 20%, 1/8 = 12.5%, 1/10 = 10%.

How do I calculate percent change?

Use the formula ((new − old) / old) × 100. If revenue went from $80,000 to $100,000, the percent change is ((100000 − 80000) / 80000) × 100 = 25% increase. Going the other direction (100,000 to 80,000) is ((80000 − 100000) / 100000) × 100 = −20%, a 20% decrease. Note that the same two numbers produce different percentages depending on which is the baseline, this asymmetry is what makes "up 25% then down 20%" return you to the original.

How do I find the original price after a discount?

Divide the sale price by (1 − discount as a decimal). If a shirt is on sale for $35 after 30% off, the original price was $35 ÷ (1 − 0.30) = $35 ÷ 0.70 = $50. The common mistake is to add 30% back to the sale price, that gives $35 × 1.30 = $45.50, which is wrong because the 30% discount was applied to the higher original price, not the sale price.

What's the difference between markup and margin?

Markup is the percentage added to cost to get the selling price: (price − cost) / cost × 100. Margin is the same dollar amount expressed as a percentage of the selling price: (price − cost) / price × 100. A $10 cost sold for $15 has a 50% markup but only a 33% margin. Retailers usually quote markup; financial statements usually report margin. Confusing them is a common source of profitability errors in small-business pricing.

How do I calculate compound percentage changes?

Multiply the growth factors, don't add the percentages. A 10% raise followed by a 5% raise is 1.10 × 1.05 = 1.155, or 15.5%, not 15%. Same for compounded losses: a 20% drop followed by a 30% drop is 0.80 × 0.70 = 0.56, a 44% total decline (not 50%). For long chains, like decade-over-decade investment returns, small additive approximations drift far from the actual compounded result.

Why does "percent of percent" sometimes give weird answers?

Because percentages are always relative to a base, and applying multiple percentages can change the base implicitly. "30% of 50% of 200" is unambiguous (200 × 0.50 × 0.30 = 30), but "30% off, then 20% off" depends on whether the second discount is on the original price or the already-discounted price. In retail, sequential discounts almost always apply to the running price, so two 20% discounts equal 0.80 × 0.80 = 0.64, a 36% total discount, not 40%.

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