To know how to calculate percentage increase or general percentage change, divide the difference between the new and old values by the original value, then multiply by 100. For discounts, multiply the original price by the discount percentage divided by 100, then subtract that amount from the original price to find the final sale price.
Percentages show up everywhere — a shirt that's "30% off," a salary that went up by 8%, a phone bill that jumped from last month. And yet, most of us still pause and think "wait, how do I actually work this out?" before reaching for a calculator.
Here's the good news: once you understand the logic behind percentages (not just the formula), you'll never second-guess yourself again. Let's break it down.
What Does "Percentage" Actually Mean?
A percentage is just a fraction of 100. When something is "20%," it means 20 out of every 100. That's it. Once that clicks, every percentage problem becomes a question of: "20 out of 100 of what?"
How Do You Find a Percentage of a Number?
This is the one you'll use the most — working out a tip, a discount, a tax amount.
Formula: (Percentage ÷ 100) × Number
Example: What's 15% of 2,400?
(15 ÷ 100) × 2,400 = 0.15 × 2,400 = 360
So 15% of 2,400 is 360. That's the whole trick — turn the percentage into a decimal, then multiply.
How Do You Calculate Percentage Increase and Decrease?
This is where people usually get tripped up, because there are two numbers involved — an "old" one and a "new" one.
Formula: ((New Value − Old Value) ÷ Old Value) × 100
Example: Last month you spent $200 on groceries. This month it's $230. What's the percentage increase?
((230 − 200) ÷ 200) × 100 = (30 ÷ 200) × 100 = 15%
Your grocery spending went up by 15%. If the new number is smaller than the old one, you'll get a negative result — that's your percentage decrease.
How Do You Calculate a Store Discount?
Discounts combine both ideas above. You're not just finding a percentage — you're subtracting it from the original price. If you have complex or stacked discounts to resolve on the fly, our specialized Discount Calculator does the heavy lifting for you instantly.
Formula: Original Price − (Original Price × Discount% ÷ 100)
Example: A jacket costs $80, and it's 25% off.
Discount amount = 80 × (25 ÷ 100) = 20
Final price = 80 − 20 = $60
You save $20, and pay $60. Simple once you see it laid out.
How Do You Calculate a Reverse Percentage?
Sometimes you know the final number and the percentage, but need the original. Say you paid $60 for something after a 25% discount — what was the original price?
Formula: Final Value ÷ (1 − Discount% ÷ 100)
60 ÷ (1 − 0.25) = 60 ÷ 0.75 = $80
This one trips up even people who are otherwise good with numbers, because it's tempting to just add 25% back to $60 — but that gives you $75, not $80. The discount was taken off the original price, not the sale price, so you have to reverse it correctly.
How Can You Calculate Percentages Without Doing Mental Math?
Honestly, you don't need to memorize any of this to use it day to day. That's exactly why we built a free Percentage Calculator that handles all four of these — percentage of a number, increase/decrease, discounts, and reverse percentages — instantly, without you touching a formula. Just plug in your numbers and get your answer in one tap.
Frequently Asked Questions
Is percentage increase the same as percentage points?
No. If interest rates go from 5% to 7%, that's a 2 percentage point increase, but a 40% percentage increase relative to the original 5%. They're easy to mix up, so pay attention to which one a question is actually asking for.
How to find the original price before a discount?
If you want to know how to find the original price before a discount, divide the final sale price by (1 minus the discount percentage divided by 100). For example, if a jacket costs $60 after a 25% discount, dividing 60 by 0.75 gives you the original price of $80.
How to calculate percentage increase if it is over 100%?
To calculate percentage increase over 100%, use the same standard formula: subtract the original value from the new value, divide by the original value, and multiply by 100. If an item's price goes from $10 to $35, that represents a 250% increase.
What's the fastest way to estimate a percentage in my head?
Find 10% first (just move the decimal point one place left), then scale up or down from there. 10% of 240 is 24 — so 20% is 48, and 5% is 12.