How to Calculate Percentages, Discounts and Percent Change
Learn the simple formulas for percentages, percent change, sale prices and stacked discounts, plus common mistakes, with worked examples and free calculators.
Percentages show up everywhere: a store sign promises 30% off, your rent goes up by 4%, a report says sales fell 12%, and a recipe needs to scale to 150%. Most of us learned the math in school, but when you’re standing in a checkout line or checking a spreadsheet, it’s easy to forget which number goes where.
This guide walks through the handful of formulas that cover almost every everyday percentage question. Each one comes with a small worked example, so you can check your own numbers. We’ll also look at the traps that catch people most often, like stacked discounts and the difference between “percent” and “percentage points,” and show how to get quick answers with Deftivo’s free calculators.
What a percentage really means
“Percent” means “per hundred.” So 25% is 25 out of 100, which is the same as the fraction 25/100 or the decimal 0.25. Once you remember that, most percentage math is just multiplying or dividing.
A quick conversion habit helps a lot:
- To turn a percentage into a decimal, divide by 100 (move the decimal point two places left). 15% becomes 0.15.
- To turn a decimal into a percentage, multiply by 100. 0.4 becomes 40%.
The core formulas
Here are the four questions people ask most often, with the formula for each.
| Question | Formula | Example | Answer |
|---|---|---|---|
| What is X% of Y? | Y × (X ÷ 100) | 15% of 80 | 12 |
| X is what percent of Y? | (X ÷ Y) × 100 | 18 out of 72 | 25% |
| Percent increase | (New − Old) ÷ Old × 100 | 50 → 65 | 30% increase |
| Percent decrease | (Old − New) ÷ Old × 100 | 80 → 60 | 25% decrease |
X% of Y
To find 15% of 80, change 15% to 0.15 and multiply: 80 × 0.15 = 12. This is the formula behind tips, sales tax and “how much is 20% of my budget?”
X is what percent of Y
If you got 18 questions right out of 72, divide the part by the whole: 18 ÷ 72 = 0.25. Multiply by 100 and you get 25%. The key is that the “whole” always goes on the bottom.
Percent increase and decrease
Percent change always compares the difference to the starting value. If a price goes from 50 to 65, the difference is 15, and 15 ÷ 50 = 0.30, so that’s a 30% increase. If it goes from 80 to 60, the difference is 20, and 20 ÷ 80 = 0.25, so that’s a 25% decrease.
Sale prices and discount rates
Shopping math is just the formulas above in a different outfit.
Finding the sale price. A jacket costs $120 and is 25% off. The discount is 120 × 0.25 = $30, so you pay $90. A faster way: if you get 25% off, you pay 75% of the price, so 120 × 0.75 = $90.
Finding the discount rate. A lamp was $80 and is now $60. You saved $20, and 20 ÷ 80 = 0.25, so the discount is 25%.
Finding the original price. This is where people slip. If something costs $64 after 20% off, the original price is not 64 × 1.2 (which gives $76.80). Since $64 is 80% of the original, divide instead: 64 ÷ 0.80 = $80.
Stacked discounts: why 20% + 10% is not 30%
Stores sometimes advertise “an extra 10% off sale prices.” It sounds like 20% plus 10% equals 30% off, but each discount is applied to a different number.
Take a $100 item:
- 20% off $100 leaves $80.
- An extra 10% off $80 is $8, leaving $72.
You paid $72, so the total discount is 28%, not 30%. The general rule is to multiply what’s left after each discount: 0.80 × 0.90 = 0.72, which means you pay 72% and save 28%. The order doesn’t matter here; 10% then 20% also lands on $72.
| Discounts | Simple sum (wrong) | Real total discount |
|---|---|---|
| 20% + 10% | 30% | 28% |
| 30% + 20% | 50% | 44% |
| 50% + 50% | 100% | 75% |
That last row shows why “50% + 50% off” never makes something free.
Percent vs. percentage points
When a rate is already a percentage, “percent” and “percentage points” mean different things.
Say a savings rate rises from 4% to 5%. That’s an increase of 1 percentage point (5 − 4). But as a percent change, it’s a 25% increase, because 1 ÷ 4 = 0.25. Both statements are true; they just answer different questions. News stories about interest rates, election polls and unemployment often mix these up, so it’s worth checking which one is meant.
How to calculate it with Deftivo
If you’d rather not do the arithmetic by hand, Deftivo has two free calculators that run right in your browser.
For general percentage questions:
- Open the percentage calculator.
- Find the panel for your question: “Percent of a number,” “What percent is it?” or “Percentage change.”
- Enter your two numbers in the blanks.
- Read the result. The formula used appears underneath, so you can compare it with the ones above.
For shopping and sale prices:
- Open the discount calculator.
- Pick the panel you need: “Sale price,” “Discount percentage,” “Original price” or “Two discounts (stacked).”
- Enter the numbers you know, such as the original price and the discount.
- Read the result. For a sale price, it shows what you pay and what you save; for stacked discounts, it also shows the real total discount.
Both tools work in the browser, so there’s nothing to install or sign up for.
Tips and common mistakes
- Using the wrong base. Percent change is always measured from the starting value. Going from 60 to 80 is a 33.3% increase, but going from 80 to 60 is a 25% decrease.
- Expecting changes to cancel out. A 50% rise followed by a 50% drop does not bring you back to where you started. 100 becomes 150, then 75.
- Adding stacked discounts. Multiply the remaining shares (like 0.8 × 0.9) instead of adding the percentages.
- Reversing a percentage the wrong way. To find the original price before a discount or the amount before tax, divide by the remaining share rather than multiplying back up.
- Rounding too early. Keep extra decimal places until the final step, especially when chaining several calculations.
- Mixing up points and percent. When comparing two rates, say clearly whether you mean the gap in points or the relative change.
FAQ
How do I quickly work out a percentage in my head?
Start with 10%, which is just moving the decimal point one place left: 10% of 85 is 8.5. From there, 5% is half of that and 20% is double it. Combining these pieces gets you close to most everyday percentages.
Why is my percent increase different from my percent decrease for the same two numbers?
Because the starting value changes. Going up from 50 to 75 is a 50% increase measured against 50, while going down from 75 to 50 is a 33.3% decrease measured against 75. The gap is the same, but the base is different.
Can a percent increase be more than 100%?
Yes. If something doubles, that’s a 100% increase, and if it triples, that’s a 200% increase. A decrease, however, can’t go beyond 100%, because that would mean falling below zero.
How do I work out the total discount when two discounts are combined?
Turn each discount into the share you still pay (20% off becomes 0.80, 10% off becomes 0.90) and multiply them together. Subtract the result from 1 to get the total discount: 1 − 0.72 = 0.28, or 28%. The discount calculator can help you check each step.