Percentages appear in almost every part of daily life. Whether you are working out a restaurant tip, calculating a sale discount, checking your exam score, or tracking a salary increase, the same handful of formulas cover every situation. This guide walks through each one with clear examples you can follow step by step.
Skip the manual math. Our free percentage calculator handles all five formula types instantly. Enter your numbers and get the result in one click.
Open Percentage Calculator →Formula 1: Finding X% of a Number
This is the most common percentage calculation. You have a number and you want to find a specific percentage of it. The formula is straightforward:
Result = (Percentage / 100) x Number
Or: Result = Percentage x 0.01 x Number
You want to leave a 15% tip on a $240 restaurant bill.
15% of 240 = (15 / 100) x 240 = 0.15 x 240 = $36.00
More examples:
- 20% tax on $85 = 0.20 x $85 = $17.00
- 8.5% sales tax on $200 = 0.085 x $200 = $17.00
- 30% discount off $120 = 0.30 x $120 = $36 savings
Quick shortcut: To find 10% of any number, move the decimal point one place left. $480 becomes $48. For 5%, halve the 10% amount: $24. For 15%, add the 10% and 5% results together: $48 + $24 = $72.
Formula 2: What Percentage Is X of Y?
Sometimes you know both numbers but need to express the relationship as a percentage. This appears constantly in test scores, completion rates, and survey results.
Percentage = (X / Y) x 100
You answered 45 questions correctly out of 60 total.
(45 / 60) x 100 = 0.75 x 100 = 75%
More examples:
- Project is 32 out of 40 days complete: (32/40) x 100 = 80%
- 18 out of 25 team members attended: (18/25) x 100 = 72%
- Spent $350 of a $500 budget: (350/500) x 100 = 70% used
Use the percentage calculator with the "X is what % of Y?" tab to get instant results for this calculation.
Formula 3: Percentage Increase
A percentage increase tells you how much something has grown relative to its starting value. This is useful for salary changes, price comparisons, and tracking growth.
% Increase = ((New Value - Old Value) / Old Value) x 100
Monthly salary increased from $4,000 to $4,500.
((4500 - 4000) / 4000) x 100 = (500 / 4000) x 100 = 0.125 x 100 = 12.5% increase
More examples:
- Website visits grew from 1,200 to 1,560: ((1560 - 1200) / 1200) x 100 = 30% increase
- Product price went from $45 to $54: ((54 - 45) / 45) x 100 = 20% increase
- Investment grew from $10,000 to $12,400: ((12400 - 10000) / 10000) x 100 = 24% return
Formula 4: Percentage Decrease
A percentage decrease works the same way as a percentage increase, but the new value is smaller than the old one. It answers questions like "by how much did the price drop?" or "how much weight was lost relative to starting weight?"
% Decrease = ((Old Value - New Value) / Old Value) x 100
A jacket was $80 and is now $60.
((80 - 60) / 80) x 100 = (20 / 80) x 100 = 0.25 x 100 = 25% decrease
Note: Both percentage increase and decrease use the original (old) value as the denominator, not the new value. This is one of the most common calculation errors.
The percentage change calculator handles both increases and decreases automatically, displaying the result in green for increases and red for decreases.
Formula 5: Finding the Original Value Before a Percentage
What if you know the final price after a discount but need to find what the original price was? This is a reverse percentage calculation.
Original = Sale Price / (1 - Discount as decimal)
Original = Sale Price / (1 - Discount% / 100)
A shirt costs $68 after a 15% discount. What was the original price?
Original = $68 / (1 - 0.15) = $68 / 0.85 = $80.00
For a percentage increase (finding the original before a markup):
Original = Final Value / (1 + Increase as decimal)
Example: A price tag shows $115 after a 15% markup. Original = $115 / 1.15 = $100.
Common Mistakes to Avoid
Mistake 1: Using the wrong base value. When calculating percentage change, always divide by the original (starting) value, not the new value. Getting this backwards gives completely wrong results.
- Using percentage as a whole number: 15% means 0.15, not 15. Always divide by 100 before multiplying, or write it as a decimal first.
- Confusing "15% more than" with "15% of": If a price is 15% more than $100, the answer is $115, not $15. You add the percentage to the original.
- Double discounts: A 20% discount followed by a 10% discount is not the same as a 30% discount. The second discount applies to the already-reduced price. The actual total discount is 28%.
- Percentage points vs percentages: An interest rate going from 3% to 4% is an increase of 1 percentage point, but a 33.3% increase in the rate itself. These mean very different things.
Use a Calculator for Instant Results
Once you understand the formulas, the calculations are simple. But for everyday use, there is no reason to work them out by hand every time.
Our free percentage calculator covers all five formula types above. Switch between tabs for "X% of Y," "X is what % of Y," and "% change." Results appear as you type, no button press needed. Works on mobile.
Calculate Percentages Free →If you are often calculating discounts or sale prices, the discount calculator gives you the sale price, discount amount, and total savings all in one view.