Percentage Calculator
Need to calculate a percentage? Use our fast and accurate Percentage Calculator for discounts, taxes, profits, and more—simplifying your decision-making process.
Understanding Percentages
A percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". For example, 50% means 50 out of 100, or half of the total.
Common Percentage Calculations
Finding a percentage of a number: To find X% of Y, multiply Y by (X/100).
25% of 200 = (25/100) × 200 = 0.25 × 200 = 50
Finding what percentage one number is of another: To find what percentage X is of Y, divide X by Y and multiply by 100.
50 is (50/200) × 100 = 0.25 × 100 = 25% of 200
Finding percentage change: To find the percentage change from X to Y, calculate (Y - X) / X × 100.
[(75 - 50) / 50] × 100 = [25 / 50] × 100 = 0.5 × 100 = 50% increase
Increasing by a percentage: To increase X by Y%, multiply X by (1 + Y/100).
50 × (1 + 30/100) = 50 × 1.3 = 65
Decreasing by a percentage: To decrease X by Y%, multiply X by (1 - Y/100).
50 × (1 - 30/100) = 50 × 0.7 = 35
Percentage Calculator: How to Calculate Percentages the Easy Way
A percentage is simply a number expressed as a fraction of 100. The word "percent" means "per hundred," so 25% is the same as 25 out of 100, or the fraction 25/100 = 0.25. Percentages let you compare quantities of different sizes on a common scale, which is why they show up everywhere from shopping discounts and exam results to tax, tips and interest.
Our percentage calculator handles the three most common questions instantly, but it helps to understand the formulas behind each one. Once you know these three patterns, you can solve almost any everyday percentage problem by hand.
- X% of Y = (X / 100) × Y
- What percent A is of B = (A / B) × 100
- Percentage change = ((new − old) / old) × 100
The Three Core Formulas With Worked Examples
1. Finding X% of a number (X% of Y). Divide the percentage by 100, then multiply by the number. To find 20% of 150: (20 / 100) × 150 = 0.2 × 150 = 30. This is the formula you use for discounts, tips and tax.
2. Finding what percent one number is of another (A is what percent of B). Divide A by B, then multiply by 100. If you scored 45 marks out of 60: (45 / 60) × 100 = 0.75 × 100 = 75%. This is how exam percentages and "share of total" figures are worked out.
3. Percentage increase or decrease. Subtract the old value from the new value, divide by the old value, then multiply by 100. If a price rises from 80 to 100: ((100 − 80) / 80) × 100 = (20 / 80) × 100 = 25% increase. If it falls from 100 to 80: ((80 − 100) / 100) × 100 = −20%, a 20% decrease. A negative answer always means a decrease.
| Question | Formula | Result |
|---|---|---|
| 30% of 250 | (30/100) × 250 | 75 |
| 18 is what % of 90 | (18/90) × 100 | 20% |
| 40 → 50 change | ((50−40)/40) × 100 | +25% |
Everyday Uses: Discounts, Marks, Tips, Tax and Interest
Percentages are practical tools you use most days, often without a calculator. Here is how the formulas apply to real situations.
- Discounts and sales: For a 30% off sale on a $90 item, the discount is (30/100) × 90 = $27, so you pay 90 − 27 = $63. A quicker route: you pay 70% of the price, and (70/100) × 90 = $63.
- Exam marks: Marks percentage uses formula 2. If you got 540 out of 600 across all subjects: (540/600) × 100 = 90%.
- Tips: A 15% tip on a $40 bill is (15/100) × 40 = $6, making the total $46.
- GST / sales tax: To add 8% tax to a $200 purchase: (8/100) × 200 = $16, so the total is $216.
- Simple interest: 5% annual interest on $1,000 of savings earns (5/100) × 1000 = $50 in one year.
A handy mental shortcut: 10% of any number is found by moving the decimal point one place left (10% of 250 = 25), and 1% by moving it two places (1% of 250 = 2.5). You can build many percentages from these, for example 20% is double 10%, and 5% is half of 10%.
Tips for Getting Percentages Right Every Time
Most percentage mistakes come from mixing up which number is the "whole." In the formula (A / B) × 100, B is always the total or original amount you are comparing against. Choosing the wrong base is the single most common error, so identify the whole first.
- Percentage points are not percentages. If a rate goes from 5% to 7%, that is a rise of 2 percentage points but a 40% increase ((7−5)/5 × 100).
- Increases and decreases do not cancel out. A 50% rise followed by a 50% fall does not return you to the start: 100 → 150 → 75.
- Convert between forms freely. 0.5 = 50% = ½. To turn a decimal into a percentage, multiply by 100; to turn a percentage into a decimal, divide by 100.
When in doubt, plug your numbers into the calculator above to check your working in seconds.
Frequently Asked Questions
To find a percentage of a number, divide the percentage by 100 and multiply by the number: X% of Y = (X / 100) × Y. For example, 20% of 150 is (20 / 100) × 150 = 30. To find what percent one number is of another, divide and multiply by 100: (A / B) × 100.
Use the formula X% of Y = (X / 100) × Y. Divide the percentage by 100 to get a decimal, then multiply by the number. For instance, 30% of 250 is 0.30 × 250 = 75. A quick shortcut: 10% is the number with its decimal point moved one place left.
Use percentage change = ((new − old) / old) × 100. Subtract the old value from the new value, divide by the old value, then multiply by 100. If a price rises from 80 to 100, the increase is ((100 − 80) / 80) × 100 = 25%. A negative result means a decrease.
Divide the marks you scored by the total possible marks, then multiply by 100: (marks obtained / total marks) × 100. If you scored 540 out of 600, your percentage is (540 / 600) × 100 = 90%. For multiple subjects, add up all marks obtained and all total marks before dividing.
Find the discount amount with (discount% / 100) × original price, then subtract it. For 30% off a $90 item, the discount is 0.30 × 90 = $27, so you pay $63. Faster: pay (100 − discount%) of the price, which is 70% × $90 = $63.
A percentage point is the simple arithmetic difference between two percentages, while a percentage change measures that difference relative to the starting value. If an interest rate moves from 5% to 7%, that is a 2 percentage point rise, but a 40% increase because (7 − 5) / 5 × 100 = 40%.