How to Calculate Percentages (Formulas)

You can calculate any percentage with one of three simple formulas: to find X% of a number, multiply the number by X and divide by 100; to find what percentage one number is of another, divide the first number by the second and multiply by 100; and to find a percentage change, subtract the old value from the new value, divide by the old value, and multiply by 100. Once you know these three, tips, discounts, grades, and price increases all become the same quick calculation.

Percentages show up everywhere — on price tags, in tip jars, on exam results, and in your bank statements. Yet most people reach for a calculator because they were never taught the shortcuts. This guide covers the three formulas you actually need, shows you how to use them with real numbers, and teaches you mental-math tricks that make common percentages instant.

The Three Percentage Formulas

Nearly every percentage problem you will ever meet is one of these three types. Learn to spot which one you are dealing with, and the rest is simple arithmetic.

Let's put each one to work.

Formula 1: Finding X% of a Number

This is the most common percentage calculation. A 20% tip, a 30% sale, a 15% tax — all of them ask "what is X% of this amount?"

Example: What is 25% of 200?

• Step 1: Divide the percentage by 100: 25 ÷ 100 = 0.25.
• Step 2: Multiply by the number: 0.25 × 200 = 50.
• Answer: 25% of 200 is 50.

Example: A jacket costs $80 and is 30% off. How much do you save?

• 30 ÷ 100 = 0.30, then 0.30 × 80 = 24.
• You save $24, so you pay $80 − $24 = $56.

Want the final price in one step instead? Multiply the price by (1 − discount). For 30% off, that is 0.70 × $80 = $56. Same answer, one less step.

Formula 2: Finding What Percentage One Number Is of Another

This formula answers "out of" questions: test scores, completion rates, and budget shares all use it.

Example: You scored 42 out of 50 on a test. What is your percentage?

• Divide the part by the whole: 42 ÷ 50 = 0.84.
• Multiply by 100: 0.84 × 100 = 84%.
• Answer: 84%.

Example: Your rent is $1,200 and your monthly income is $4,000. What share of your income goes to rent?

• 1,200 ÷ 4,000 = 0.30, × 100 = 30%.
• Rent takes 30% of your income — right at the common affordability guideline of 30%.

Formula 3: Percentage Increase and Decrease

Percentage change tells you how big a rise or fall is relative to where it started. The key detail: you always divide by the original value, not the new one.

Example: A gym membership rises from $40 a month to $50. What is the percentage increase?

• Change: 50 − 40 = 10.
• Divide by the original: 10 ÷ 40 = 0.25.
• Multiply by 100: 25%. The membership went up by 25%.

Example: A laptop drops from $900 to $720. What is the percentage decrease?

• Change: 900 − 720 = 180.
• 180 ÷ 900 = 0.20, × 100 = 20%. A 20% price drop.

A common trap: if a price rises 50% and then falls 50%, it does not return to the original price. $100 rises 50% to $150, then falls 50% to $75 — you end up 25% below where you started, because the second percentage is taken from a bigger number.

Reverse Percentages: Finding the Original Number

Sometimes you know the result and need to work backwards. A phone costs $68 after a 15% discount — what was the original price?

The sale price is 85% of the original (100% − 15%), so divide by 0.85:

• $68 ÷ 0.85 = $80. The original price was $80.

Similarly, if you know that $45 is 20% of some number, divide by 0.20: $45 ÷ 0.20 = $225. Dividing by the decimal form of the percentage always recovers the whole.

Percentage Shortcuts for Mental Math

You don't need a calculator for the percentages you meet daily. These tricks handle most of them:

• 10%: Move the decimal point one place left. 10% of 250 is 25.
• 1%: Move the decimal point two places left. 1% of 250 is 2.50.
• 5%: Half of 10%. 5% of 250 is 12.50.
• 20%: Double 10%. 20% of 250 is 50.
• 15%: Add 10% + 5%. 15% of 250 is 25 + 12.50 = 37.50.
• 25%: Divide by 4. 25% of 250 is 62.50.
• 50%: Halve the number. 50% of 250 is 125.

Another handy trick: percentages are reversible. 16% of 50 is the same as 50% of 16 — and 50% of 16 (which is 8) is much easier to work out in your head.

Percentages in Everyday Life

If you want to skip the arithmetic entirely, try our free Percentage Calculator — it handles all three formulas, plus percentage increase, decrease, and reverse percentages, in seconds.

Frequently Asked Questions

How do I calculate a percentage of a number?

Multiply the number by the percentage and divide by 100. For example, 20% of 150 is (20 ÷ 100) × 150 = 30. For a quick mental version, find 10% by moving the decimal point one place left, then double it for 20%.

How do I find what percentage one number is of another?

Divide the first number by the second and multiply by 100. For example, 30 out of 120 is (30 ÷ 120) × 100 = 25%. This is the formula behind test scores, completion rates, and budget shares.

How do I calculate percentage increase or decrease?

Subtract the old value from the new value, divide the result by the old value, and multiply by 100. If the result is positive it is an increase; if negative, a decrease. Always divide by the original value, not the new one.

What is a reverse percentage?

A reverse percentage recovers the original number when you only know the result after a percentage was applied. If a price is $68 after a 15% discount, the original price is $68 ÷ 0.85 = $80, because the sale price is 85% of the original.