Percentages show up everywhere. Discounts, tips, taxes, raises, interest rates. Yet plenty of people still hesitate when doing the math in their head. It’s really just three formulas, each solving a slightly different question. Here’s how to tell them apart.
Formula 1: Finding a Percentage of a Number
This is the most common calculation. “What is X% of Y?”
Result = (Percentage ÷ 100) × Number
Example: What is 20% of $80?
$80 × (20 ÷ 100) = $16
Formula 2: Finding What Percentage One Number Is of Another
This flips the question. “X is what percent of Y?”
Percentage = (Part ÷ Whole) × 100
Example: 15 is what percent of 60?
(15 ÷ 60) × 100 = 25%
Formula 3: Percentage Increase or Decrease
This one calculates change over time. “How much did this go up or down, in percentage terms?”
Percentage Change = [(New Value − Old Value) ÷ Old Value] × 100
Example: A $50 item increases to $65. What’s the percentage increase?
[($65 − $50) ÷ $50] × 100 = 30% increase
A negative result here simply indicates a decrease instead. The formula itself doesn’t change.
Real-Life Example: Calculating a Discount
Let’s use Formula 1 for a real shopping scenario. A $120 jacket is 25% off.
Discount amount: $120 × (25 ÷ 100) = $30
Final price: $120 − $30 = $90
NerdWallet’s guide to shopping math covers a few quick mental-math shortcuts for common discount percentages like 10%, 20%, and 25%.
Real-Life Example: Calculating a Tip
Tipping uses the same Formula 1 logic. A $45 restaurant bill, tipping 18%:
Tip: $45 × (18 ÷ 100) = $8.10
Total: $45 + $8.10 = $53.10
A quick mental shortcut: calculate 10% first (move the decimal one place), then adjust. For 18%, find 10% ($4.50), then add roughly 80% of that again to approximate 18% quickly without a calculator. The Emily Post Institute’s tipping guidance covers standard percentages across different service scenarios.
Real-Life Example: Reversing a Percentage (Finding the Original Price)
Sometimes you know the final, tax-included price and need to find the original amount. This uses a variation of Formula 1, solved in reverse:
Original Price = Final Price ÷ (1 + Tax Rate as a decimal)
Example: A receipt shows $107 total, including 7% sales tax.
$107 ÷ 1.07 = $100 original price
This same reverse logic works for removing VAT, GST, or any percentage-based markup from a final number, as covered in our GST/VAT calculator guide.
Common Percentage Mistakes
- Confusing percentage points with percentage change — going from 10% to 15% is a 5 percentage point increase, but a 50% relative increase; these two descriptions aren’t interchangeable
- Forgetting the base can change — a 50% increase followed by a 50% decrease doesn’t return you to the original number, since the second calculation applies to a new, larger base
- Applying the formula to the wrong number — mixing up which figure is the “part” and which is the “whole” is the most common source of percentage errors
Khan Academy’s percentage lessons work through these common trap scenarios with additional worked examples.
Calculate any percentage instantly. Use the Percentage Calculator →
Frequently Asked Questions
How do you calculate a percentage increase?
Subtract the old value from the new value, divide that difference by the old value, then multiply by 100. For example, going from 50 to 65 is a [(65-50)/50] × 100 = 30% increase.
What is 15% of 200?
15% of 200 is 30, calculated as 200 × (15 ÷ 100). This same formula applies to any “percentage of a number” question by substituting your own values.
How do you find the original price before a discount?
Divide the discounted (final) price by (1 minus the discount rate as a decimal). For example, a $75 sale price after a 25% discount means the original price was $75 ÷ 0.75 = $100.
What is the difference between percentage and percentage points?
Percentage points measure the raw difference between two percentages (10% to 15% is 5 percentage points), while percentage change measures the relative difference (10% to 15% is a 50% relative increase). These describe the same shift very differently.
How do you calculate a 10% tip quickly?
Move the decimal point of the bill one place to the left. A $45 bill becomes $4.50 for a 10% tip, which can then be doubled, halved, or adjusted to estimate other tip percentages quickly without a calculator.
Can a percentage be greater than 100%?
Yes. Percentages greater than 100% simply indicate the new or resulting value is more than double the original reference value, which is common when describing growth, returns, or increases rather than simple proportions of a whole.