How to Calculate Percentages: Every Type with Worked Examples

Percentages show up in almost every decision that involves numbers — sales tax, restaurant tips, test scores, investment returns, pay raises, discounts, and interest rates. Understanding how to calculate them isn't just a school skill. It's something you'll use every day.

The good news: every percentage problem is a variation of the same three relationships. Once you understand those, you can handle any percentage question that comes up. Our percentage calculator handles all of them instantly, but knowing the math makes you faster and more confident when you're working without a screen.

The three core percentage relationships

Every percentage problem asks you to find one of three things: the percentage itself, the part, or the whole. The formula connecting them is:

Part = (Percentage / 100) x Whole

Rearranged:

• Percentage = (Part / Whole) x 100
• Whole = Part / (Percentage / 100)

Every worked example below is one of these three forms.

Type 1: What is X% of Y?

This is the most common type — finding the part when you know the whole and the percentage.

Formula: Part = (Percentage / 100) x Whole

Worked example: Sales tax

A laptop costs $849. Sales tax is 8.25%. What is the tax amount?

Tax = (8.25 / 100) x 849 = 0.0825 x 849 = $70.04

Total price: $849 + $70.04 = $919.04

Worked example: Tip at a restaurant

Your bill is $67.50. You want to leave 20%.

Tip = 0.20 x 67.50 = $13.50

Total: $81.00

The mental math shortcut for 10% and 20%

To find 10% of any number, move the decimal point one place left. $67.50 becomes $6.75. For 20%, double that: $13.50. For 15%, take 10% and add half: $6.75 + $3.38 = $10.13.

Type 2: X is what percent of Y?

Here you know both numbers and need to find the percentage relationship between them.

Formula: Percentage = (Part / Whole) x 100

Worked example: Test score

You got 43 out of 52 questions right. What is your score?

Percentage = (43 / 52) x 100 = 0.8269 x 100 = 82.7%

Worked example: Discount rate

A jacket was $120. It is now $89. What percent off is it?

Savings = $120 - $89 = $31

Discount = (31 / 120) x 100 = 25.8% off

Worked example: Budget used

You have spent $1,340 of a $2,000 monthly budget. What percentage have you used?

Percentage = (1,340 / 2,000) x 100 = 67%

Type 3: X is Y% of what?

This is the reverse problem — you know the part and the percentage, and you need the whole.

Formula: Whole = Part / (Percentage / 100)

Worked example: Finding original price after discount

A shirt is on sale for $35 after a 30% discount. What was the original price?

The sale price is 70% of the original (100% - 30% = 70%).

Original = 35 / 0.70 = $50

Worked example: Working backward from tip

You tipped $12, which was 18% of the bill. What was the bill?

Bill = 12 / 0.18 = $66.67

Percentage change: increases and decreases

Percentage change tells you how much a value has gone up or down relative to its starting point.

Formula: Percentage Change = ((New - Old) / Old) x 100

A positive result is an increase. A negative result is a decrease.

Worked example: Pay raise

Your salary went from $58,000 to $63,500. What percentage raise did you get?

Change = (63,500 - 58,000) / 58,000 x 100 = 5,500 / 58,000 x 100 = 9.48%

Worked example: Portfolio drop

Your investment account went from $24,000 to $19,200. What was the percentage loss?

Change = (19,200 - 24,000) / 24,000 x 100 = -4,800 / 24,000 x 100 = -20%

The asymmetry trap

If something drops 20% and then rises 20%, you do not break even. Start with $100. Drop 20% gives $80. Rise 20% gives $96. You are still down 4%. The percentage is calculated from the current value each time, so losses and gains are not symmetric.

Percentage point vs percentage change

A percentage point is an absolute difference between two percentages. If your savings rate goes from 8% to 12%, it increased by 4 percentage points.

A percentage change is relative. That same move from 8% to 12% is a 50% increase in your savings rate, because 4 / 8 x 100 = 50%.

Both statements are mathematically true. Knowing the difference lets you see through misleading headlines.

Compound percentage: stacking discounts and taxes

When two percentages are applied sequentially, you cannot simply add them. The second percentage applies to the already-modified value.

Worked example: Two discounts stacked

A store takes 20% off, then takes an additional 15% off the sale price. What is the total discount?

Start with $100. After 20% off: $80. After 15% off $80: $80 x 0.85 = $68.

Total discount: $32 off $100 = 32% off, not 35%.

Quick reference: common percentage calculations

What you want to find	Formula	Example
X% of Y	(X / 100) x Y	15% of 80 = 12
What % is X of Y	(X / Y) x 100	12 is 15% of 80
X is Y% of what	X / (Y / 100)	12 / 0.15 = 80
% increase from A to B	((B - A) / A) x 100	80 to 92 = +15%
% decrease from A to B	((A - B) / A) x 100	80 to 68 = -15%
Value after X% increase	Value x (1 + X/100)	80 x 1.15 = 92
Value after X% decrease	Value x (1 - X/100)	80 x 0.85 = 68

The one mistake everyone makes

When someone says prices went up 10% and then came back down 10%, most people assume you are back to the starting price. A $100 item that increases 10% becomes $110. A 10% decrease from $110 is $11, bringing it to $99 — still down 1%.

This is why investment recoveries take longer than the initial drop. A 50% loss requires a 100% gain to return to breakeven. The compound interest calculator shows this effect clearly when you model positive and negative growth years side by side.