Percentage Calculator
Percentages show up everywhere — discounts at checkout, exam scores, tips at a restaurant, interest rates, tax, and year-over-year growth. This calculator covers all five situations people actually search for: finding a percentage of a number, finding what percent one number is of another, percentage increase or decrease, adding or subtracting a percentage, and working backwards to find an original value.
Percentage change = ((New − Old) ÷ Old) × 100 → e.g. 50 to 65 = +30%
Pick the calculation you need in the tool below — each tab uses a different formula, explained underneath.
How Percentages Work
The word "percent" literally means "per hundred" — a percentage is just a fraction with a denominator of 100. So 30% is the same as 30/100, or 0.30 as a decimal. Every percentage calculation on this page comes down to one relationship: part = percentage × whole. Depending on which two of those three values you already know, you rearrange the same formula to solve for the missing one.
- To convert a percentage to a decimal, divide by 100 (20% → 0.20)
- To convert a decimal to a percentage, multiply by 100 (0.20 → 20%)
- "Percentage of" always means multiply the whole by the decimal form
- "Percentage change" always compares a new value against an old (starting) value, never the new value against itself
Finding a Percentage of a Number
Example: What is 20% of 150?
(20 ÷ 100) × 150 = 0.20 × 150 = 30
This is the most common percentage question — used for tips, taxes, commissions, and discounts. Once you have the decimal form of the percentage, the rest is a single multiplication.
Finding What Percent One Number Is of Another
Example: 42 out of 60 questions correct — what percent is that?
(42 ÷ 60) × 100 = 0.70 × 100 = 70%
This is the reverse of the previous calculation — instead of knowing the percentage and finding the part, you know the part and the whole and need to find the percentage. It's the formula behind test scores, completion rates, and "market share" style statistics.
Percentage Increase and Decrease
Example (increase): Price rises from 50 to 65
((65 − 50) ÷ 50) × 100 = (15 ÷ 50) × 100 = +30%
Example (decrease): Price falls from 80 to 60
((60 − 80) ÷ 80) × 100 = (−20 ÷ 80) × 100 = −25%
A positive result means an increase; a negative result means a decrease. The "old" (starting) value is always the denominator — this is the detail most people get wrong when calculating by hand.
Adding or Subtracting a Percentage
FORMULA — decrease New value = Old value × (1 − Percentage ÷ 100)
Example: $80 item with a 25% discount
$80 × (1 − 0.25) = $80 × 0.75 = $60 (you save $20)
Example: $80 with 8% sales tax added
$80 × (1 + 0.08) = $80 × 1.08 = $86.40
This is the formula behind every discount, markup, tip, and tax calculation — you're scaling the original number up or down by a fixed proportion.
Reverse Percentage
(use a negative percentage for a decrease)
Example: After a 20% price increase, an item costs $120 — what was the original price?
$120 ÷ (1 + 0.20) = $120 ÷ 1.20 = $100
Example: After a 20% discount, an item costs $80 — what was the original price?
$80 ÷ (1 − 0.20) = $80 ÷ 0.80 = $100
This is useful when you're shown a final, "after" price or value and need to work out what it started as — for example, checking whether a "was/now" discount sign is showing the real original price.
The Trap: Why 20% Up Then 20% Down Isn't Zero
$100 increased by 20% = $100 × 1.20 = $120
$120 decreased by 20% = $120 × 0.80 = $96 — not back to $100!
This happens because each percentage change is calculated on a different base number — the increase is 20% of $100, but the decrease is 20% of $120, which is a larger amount (20% of $120 = $24, versus 20% of $100 = $20). This asymmetry is why a stock that drops 50% needs a 100% gain (not 50%) just to break even, and why "50% off, then an extra 50% off" is not the same as "75% off."
Real-Life Uses
- Shopping discounts — calculating a sale price, or checking whether an advertised discount is accurate
- Tips and service charges — quickly working out 15%, 18%, or 20% of a restaurant bill
- Sales tax — adding a tax percentage to a purchase price at checkout
- Test scores and grades — converting "correct out of total" into a percentage grade
- Salary raises and inflation — measuring how much a wage, price, or budget has grown or shrunk
- Investment returns — tracking gains and losses as a percentage of the amount invested
- Body composition and nutrition — percentage of daily calorie or macronutrient targets
Glossary
- Percentage
- A way of expressing a number as a fraction of 100; 25% means 25 out of every 100.
- Percentage Point
- A unit used when comparing two percentages directly — e.g. going from 40% to 45% is a rise of 5 percentage points, but a 12.5% relative increase.
- Percent Change
- The relative difference between an old and a new value, expressed as a percentage of the old value.
- Base Value
- The starting or reference number that a percentage is calculated against; also called the "whole" or "old value."
- Markup
- A percentage added to a cost price to determine a selling price.
- Discount Rate
- The percentage subtracted from an original price to determine a sale price.
Frequently Asked Questions
Q: How do you calculate a percentage of a number?
A: Divide the percentage by 100, then multiply by the number: (X ÷ 100) × Y. For example, 20% of 150 = 0.2 × 150 = 30.
Q: How do you find what percent one number is of another?
A: Divide the part by the whole and multiply by 100: (Part ÷ Whole) × 100. For example, 42 out of 60 = (42 ÷ 60) × 100 = 70%.
Q: What is the formula for percentage increase or decrease?
A: ((New − Old) ÷ Old) × 100. A positive result is an increase, a negative result is a decrease.
Q: How do you calculate a discount using percentages?
A: Multiply the original price by (1 − discount rate). For a 25% discount on $80: $80 × 0.75 = $60.
Q: What is a reverse percentage calculation?
A: Finding the original value before a percentage change, using Original = Final ÷ (1 + % change ÷ 100). For a final value of $120 after a 20% increase: $120 ÷ 1.20 = $100.
Q: Why do percentages sometimes not add up the way people expect?
A: Because each percentage change is calculated on a different base value — increasing then decreasing by the same percentage does not return you to the original number.