AllFreeCalculator

Percentage Calculator

Four percentage modes in one tool. Pick the question that matches yours and the answer updates as you type.

%

Result

50

Formula: (X ÷ 100) × Y

The all-in-one percentage calculator

The percentage calculator handles the four percentage questions that come up in everyday life: "what is X% of Y", "X is what percent of Y", "what is the percent change from one number to another", and "add or subtract a percent from a number". Tips, taxes, discounts, grades, growth rates and statistics all reduce to one of those four. Pick the mode that matches your question, type in your two numbers, and the answer (with the formula behind it) appears instantly.

What "percent" actually means

"Percent" literally means "per hundred", so a percentage is just a fraction with 100 as the denominator. 25% is 25/100, or 0.25. That single idea is the entire engine of percentage maths: every formula below is a rearrangement of percent = part ÷ whole × 100.

The four modes in detail

  • X% of Y: tips, sales tax, commission, "what's 30% of $150?". Formula: (X ÷ 100) × Y.
  • X is what % of Y: exam scores, market share, "47 out of 60 is what percent?". Formula: (X ÷ Y) × 100.
  • Percent change: price rises, weight changes, growth rates. Formula: (new − old) ÷ |old| × 100.
  • Add or subtract a percent: sale prices, after-tax totals, raises. Formula: N × (1 ± P ÷ 100).

Why percent change is asymmetric

If a stock goes from $100 to $120 that is a 20% increase, but if it goes from $120 back to $100 that is a 16.67% decrease — not 20%. The reason is the denominator: percent change is always measured against the starting value, so changes in opposite directions have different bases. The calculator handles this correctly by using |from| in the denominator.

Mental-math shortcuts worth knowing

10% of any number is just that number with the decimal moved one place left. 1% moves it two places. Build the rest from there: a 15% tip is 10% + half of that; a 30% discount is 10% × 3. The calculator gives you the exact figure, but the mental tricks are useful for sanity checks and fast estimates.

Use with the other tools

For shopping discounts with stacking and tax, use the percent off calculator. For tax brackets, the federal income tax percentage calculator applies the marginal-vs-effective rate split. For credit-weighted school averages, the GPA calculator is purpose-built.

Frequently asked questions

How do you calculate a percentage?

A percentage is a fraction out of 100. To find X% of Y, multiply: (X ÷ 100) × Y. To find what percent X is of Y, divide: (X ÷ Y) × 100. Every other percentage question is a rearrangement of those two ideas.

What is the difference between "X% of Y" and "X is what % of Y"?

They are inverse questions. "X% of Y" gives the part: 25% of 60 = 15. "X is what % of Y" gives the ratio: 15 is 25% of 60. Pick the mode that matches what you already know.

How do I work out percentage change?

Percent change = (new − old) ÷ |old| × 100. Positive means an increase, negative means a decrease. A jump from 120 to 150 is +25%, while a drop from 150 to 120 is −20% (the base value matters).

Why does percent change look different depending on direction?

Because the base value changes. Going from 100 to 120 is +20%, but going back from 120 to 100 is −16.67%. The denominator (the starting number) is what flips. That is why discounts and stock price moves can be misleading without the base.

How do I add tax or a tip with this calculator?

Use "Add a percentage". Set N to the bill, choose +, and enter the tax or tip percentage. The result is your new total. For a discount, choose − instead.

What happens if I divide by zero?

Percent of 0 and percent change from 0 are mathematically undefined. The calculator detects this and shows "Undefined" instead of an infinity or NaN.

Worked example

One example per mode:

  • X% of Y: 18% tip on a $42 dinner → 0.18 × 42 = $7.56
  • X is what % of Y: scored 47/60 on a test → (47 ÷ 60) × 100 = 78.33%
  • % change: rent rose from $1,800 to $2,025 → (2,025 − 1,800) ÷ 1,800 × 100 = +12.5%
  • Add a percent: $129 jacket + 8.25% sales tax → 129 × 1.0825 = $139.64

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