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Percentage Calculator

Calculate percentages, percent of a number, percentage increase or decrease. Free online Percentage Calculator for math — instant, accurate results, no signup.

%
Result
30

Derivation

  1. ├── 01Givenpercent = 20%, of X = 150
  2. ├── 02Formularesult = (percent / 100) × X
  3. ├── 03Substitute(20/100) × 150 = 0.2 × 150
  4. └── 04Result30
Did you know?

The word "percent" comes from the Latin "per centum" — "by the hundred" — used by Italian merchants in the 15th century.

§01What is

Understanding the Percentage Calculator

A percentage calculator finds the unknown in a percent equation. It answers the three classic questions — "What is P% of X?", "Y is what percent of X?", and "P% of what is Y?" — and handles percentage change, increase, and decrease in one place.

We see percentages everywhere: shopping discounts, exam scores, interest rates, tips, statistics, even food labels. Percentages let us compare ratios fairly when the totals are different sizes, so a 25% test score means the same thing whether the test was out of 20 or 200 points. A percentage is part of a whole, expressed as a fraction of 100 and written with the % symbol. If you see 25%, it means 25 out of 100 — a quarter. If you see 50%, it means 50 out of 100 — half. That scale-free comparison is why percentages are the default language of discounts, statistics, and finance.

§02The Formula

How it’s calculated

(X / Y) × 100 = P%

Where

X
The part you’re comparing
Y
The whole (the total or base)
P%
The resulting percentage
§03Practical Example

Step-by-step walkthrough

Scenario

A $45 shirt is on sale for 20% off — what do you save?

  1. 01Plug the numbers in: save = 20% × 45
  2. 02Convert 20% to a decimal: 20 / 100 = 0.20
  3. 03Multiply: 0.20 × 45 = 9
  4. 04You save $9, sale price = $45 − $9 = $36.
§04Variants

Common Percentage Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

What is P percent of X?

Y = (P / 100) × X

Calculate a 15% tip on a bill of $45.

  1. 01Formula: Y = 15% × 45
  2. 02Convert: 15 / 100 = 0.15
  3. 03Multiply: 0.15 × 45 = 6.75
  4. 04A 15% tip on $45 is $6.75.
02 · PATTERN

Y is what percent of X?

P% = (Y / X) × 100

Your chickens laid 40 eggs; 12 are brown. What percent?

  1. 01Divide: 12 / 40 = 0.30
  2. 02Convert to percent: 0.30 × 100 = 30%
  3. 0312 is 30% of 40 — so 30% of the eggs are brown.
03 · PATTERN

Y is P percent of what?

X = Y / (P / 100)

You need 9 vanilla cupcakes, which is 60% of the batch. How many total?

  1. 01Convert 60%: 60 / 100 = 0.60
  2. 02Divide: 9 / 0.60 = 15
  3. 03You need 15 cupcakes so that 9 of them is 60%.
04 · PATTERN

Percentage change

Δ% = ((new − old) / old) × 100

A stock went from $50 to $65. What is the % change?

  1. 01Subtract: 65 − 50 = 15
  2. 02Divide by the original: 15 / 50 = 0.30
  3. 03Convert: 0.30 × 100 = 30% increase.
§05FAQ

Frequently asked questions

Increase = ((new − old) / old) × 100. Example: 50 → 65 is an increase of (65 − 50) / 50 × 100 = 30%.
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