Percentages made easy: the four formulas and the Percentage Calculator

Percentages appear in marks, discounts, interest rates, taxes, tips, statistics and every news report. Most people can find 10% of a number, but get stuck when the question is slightly different: "What percentage is 30 out of 120?" or "By what percent did the price go up?" The free Percentage Calculator has one row for each of the four everyday questions, so you pick the one that matches, type two numbers and read the answer as a sentence. This guide explains the formulas behind those rows, with examples, and the mistakes that make people wrong even when the arithmetic is right.

What "percent" means

Per cent means "per hundred". 25% means 25 out of every 100, which is the fraction 25/100, or the decimal 0.25. Every percentage problem is a conversion between these three forms. To convert a percentage to a decimal, divide by 100. To convert a decimal back, multiply by 100.

The four formulas

1. X% of Y

Answer = X ÷ 100 × Y

What is 15% of 200? 0.15 × 200 = 30. Use it for discounts, tips, commission and taxes: a 12% tip on ₹850 is 0.12 × 850 = ₹102.

2. X is what percent of Y

Answer = X ÷ Y × 100

30 out of 120 is 30 ÷ 120 × 100 = 25%. Use it for marks (what percent did I score?), shares (what part of the budget is rent?) and rates (what percent of visitors bought?). The number you are measuring goes on top and the whole goes on the bottom, which is the order people most often reverse.

3. Percentage change from A to B

Answer = (B − A) ÷ A × 100

A price rises from ₹80 to ₹100: (100 − 80) ÷ 80 × 100 = +25%. A negative answer is a fall. Always divide by the starting value A. Use it for price changes, growth in sales, salary revisions and exam improvement.

4. Adding or removing a percentage

Increase by X%: Y × (1 + X ÷ 100). Decrease by X%: Y × (1 − X ÷ 100).

A ₹500 item with a 10% discount costs 500 × 0.9 = ₹450. The same item with 10% added is 500 × 1.1 = ₹550. One multiplication does the whole job, and the multiplier is simply 1.10 for "10% more" or 0.90 for "10% less".

Examples from daily life

Question	Calculation	Answer
15% of ₹200	0.15 × 200	₹30
30 out of 120 is what percent	30 ÷ 120 × 100	25%
Price from ₹80 to ₹100	(100 − 80) ÷ 80 × 100	+25%
Price from ₹100 to ₹80	(80 − 100) ÷ 100 × 100	−20%
₹500 plus 10%	500 × 1.1	₹550
₹500 minus 10%	500 × 0.9	₹450
Score 42 out of 60	42 ÷ 60 × 100	70%
Rate from 5% to 6%	(6 − 5) ÷ 5 × 100	+20% in the rate

Why 25% up is not the same as 25% down

Look at the third and fourth rows. Going from 80 to 100 is a 25% rise, but going back from 100 to 80 is a 20% fall, not 25%. The reason is the starting value: the first change is measured against 80, the second against 100. The same effect explains the famous puzzle: if a price rises 20% and then falls 20%, it does not return to where it began. ₹100 rises to ₹120, and 20% of 120 is 24, so the final price is ₹96. Percentages are not symmetrical, and you can't undo an increase by subtracting the same percentage.

To reverse a percentage, divide by the same multiplier. If a price went up by 25% (multiplier 1.25), the fall needed to return it is 1 − 1 ÷ 1.25 = 20%. The same logic is the reason you remove GST by dividing by 1.18, not by subtracting 18%. The GST Calculator does this correctly and the GST guide explains it.

Percent and percentage points

When a rate moves, two different statements are possible. If a loan rate goes from 5% to 6%, it rose by 1 percentage point, but the rate itself increased by 20%. Newspapers mix these up all the time. Use "percentage points" for the plain difference between two percentages and "percent" for relative change. If a party's support goes from 30% to 33% of voters, that is 3 percentage points, or a 10% relative rise.

Using the calculator

1. Open the Percentage Calculator.
2. Find the row that matches your question: a percentage of a number, what percent one number is of another, the change between two numbers, or add or remove a percentage.
3. Type your two numbers into that row.
4. Read the answer below the row. It appears as you type and is written as a sentence, so you can check that it answers the question you meant.

Nothing is sent anywhere; the sums are done in your browser.

Common mistakes

• Dividing by the wrong number in percentage change. Divide by the starting value.
• Adding stacked discounts. Two discounts of 20% and 10% make 28%, not 30%, because the second applies to the reduced price. The Discount & Profit Margin Calculator handles stacks.
• Mixing percent and percentage points.
• Subtracting a percentage to reverse an addition, as with tax.
• Using a percentage of a different base, for example comparing "10% of last year's sales" with "10% of this year's".
• Rounding too early, which compounds errors across steps.
• Percentages above 100. They are fine: a price that doubles has risen 100%, and one that triples has risen 200%.

Where percentages matter next

• Money: interest and returns use repeated percentages; see compound interest and the EMI guide.
• Shopping: discounts, margins and markups. Margin and markup are different percentages of the same profit, and mixing them up is a common pricing mistake.
• Study: marks, grades and weightings are percentages of totals.
• Health: a BMI is a ratio, not a percentage, but changes in weight are often expressed in percent.
• Data: conversion rates, bounce rates and growth rates are percentages, and a small base can make a big percentage out of a tiny change.
• Code: a progress bar, a CSS width of 50% or a PHP grade script all use these formulas, as the PHP numbers and math lesson shows, and the CSS units lesson shows how percentage widths relate to a parent.

Quick mental tricks

• 10%: move the decimal one place left. 10% of 450 is 45.
• 5%: half of 10%. 5% of 450 is 22.5.
• 1%: move it two places left.
• 15%: 10% plus 5%. 15% of 200 is 20 + 10 = 30.
• 25%: a quarter. 50%: a half. 75%: three quarters.
• X% of Y equals Y% of X. 8% of 50 is the same as 50% of 8, which is 4. Use whichever is easier.

Quick answers

How do I calculate a percentage of a number? Divide the percentage by 100 and multiply by the number.

How do I find the percentage increase? Subtract the old value from the new, divide by the old value, and multiply by 100.

Why does +20% then −20% not equal zero? The second change is taken from the larger number.

What is the difference between percent and percentage points? Percentage points are the plain difference between two percentages. Percent describes the relative change.

Can a percentage be more than 100? Yes, for example a value that has more than doubled.