Percentage Calculator: How to Calculate Percentage Increase and Decrease
Master the mathematical formulas for finding the percentage of a number, percentage increase, and percentage difference. Free math percentage calculator included.
Percentages are absolutely everywhere in our daily lives—from calculating a store discount during a Black Friday sale, to analyzing your retirement stock market growth, or simply understanding election population statistics.
While percentages are a fundamental pillar of daily math, figuring out percentage increases, decreases, or the percentage difference between two totally different numbers can quickly become confusing.
Our comprehensive guide breaks down the exact math formulas so you can calculate percentages manually with ease, or you can simply use our digital tool to skip the headache.
1️⃣ How to Find the Percentage of a Number
The most incredibly common percentage problem you will face is figuring out a specific slice of a whole number. For example, if a winter jacket costs $80 and you have a 15% off coupon, how much money is 15% actually worth?
The Formula:
Percentage Amount = (Percentage / 100) × Base Number
Real World Example Calculation:
- Convert the 15% into a decimal format:
15 / 100 = 0.15 - Multiply that decimal by the base price:
0.15 × $80 - Result: You just saved $12.00.
2️⃣ How to Calculate Percentage Increase or Decrease
If your tech stock portfolio aggressively grows from $1,000 to $1,200, what is the exact percentage increase? You calculate this by finding the absolute mathematical difference between the two numbers, and dividing it by the original starting number.
The Formula:
Percentage Change = [(New Value - Old Value) / |Old Value|] × 100
| Scenario | Old Value | New Value | Percentage Change |
|---|---|---|---|
| Stock Growth (Increase) | $1,000 | $1,200 | +20% |
| Retail Markdown (Decrease) | $200 | $150 | -25% |
| Website Traffic (Decrease) | 5,000 users | 4,000 users | -20% |
💡 Pro Tip: Always divide by the original number. A widespread math mistake when a price drops from $200 to $150 is dividing the $50 difference by the new $150 price. You must divide by the original $200!
3️⃣ What is X as a Percentage of Y?
If you scored 45 questions correct out of a 60-question final exam, what is your percentage grade? This is simple division disguised as a percentage problem.
The Formula:
Percentage = (Part / Whole) × 100
Real World Example Calculation:
- Divide the partial amount by the whole amount:
45 / 60 = 0.75 - Multiply the resulting decimal by 100 to get a whole number:
0.75 × 100 - Result: Your final grade is a solid 75%!
🚀 Want to skip the complicated math? Use our completely free Percentage Calculator to solve all three of these complex scenarios effortlessly. Just enter your numbers into the fields and get the exact answer instantly—no scrap paper or mental gymnastics required!
Try our Percentage Calculator
Master the mathematical formulas for finding the percentage of a number, percentage increase, and percentage difference. Free math percentage calculator included.