Percentage Calculator
Three modes for every percentage calculation
Percentage Change Calculator
Percentages come up all the time.
How much is that 30% discount saving you? How much did your sales grow last quarter? The math isn't hard, but it's easy to mix up the formulas when you're doing it in your head.
The calculator above handles the three most common percentage calculations. Enter your numbers, pick the mode you need, and you've got your answer.
No formulas to remember.
Below, I'll walk you through how each formula works and what your results actually mean. I've also covered the mistakes that trip up most people.
How Percentage Formulas Work
The calculator has three modes. Here's the formula behind each one, with a worked example so you can follow along.
Mode 1: Finding X% of a Number
Formula: Result = (Percentage / 100) × NumberThis is the one you use most often. Need to know 18% tip on a $75 bill? Or 30% discount on a $249 item?
Example: What is 25% of 200?
- Step 1: Convert 25% to a decimal → 25 / 100 = 0.25
- Step 2: Multiply → 0.25 × 200 = 50
So 25% of 200 is 50.
Another quick example. You scored 42 out of 50 on a test and want to know your percentage. Flip the formula around: (42 / 50) × 100 = 84%. The calculator's Mode 1 handles this direction too. Just enter 100 as the percentage and your fraction as the number, or use Mode 2 with the values directly.
Mode 2: Percentage Change (From Old to New)
Formula: Percentage Change = ((New Value - Old Value) / Old Value) × 100This tells you how much something went up or down, relative to where it started.
The Old Value means we use the absolute value (ignore the negative sign if the old value is negative).
Example: Your monthly website traffic went from 4,000 visits to 5,200 visits. What's the percentage change?
- Step 1: Find the difference: 5,200 - 4,000 = 1,200
- Step 2: Divide by the old value: 1,200 / 4,000 = 0.3
- Step 3: Multiply by 100: 0.3 × 100 = 30%
Traffic increased by 30%.
If the result is positive, it's an increase. If negative, it's a decrease. The calculator color-codes this for you. Green for increase, red for decrease.
Mode 3: Percentage Increase or Decrease
Formula (Increase)
New Value = Original + (Original × Percentage / 100)Formula (Decrease):
New Value = Original - (Original × Percentage / 100)This is the reverse of Mode 2. You know the starting value and the percentage, and you want the final number.
Example: A product costs $80, and the price is going up by 12%. What's the new price?
- Step 1: Find the increase amount → $80 × 12 / 100 = $9.60
- Step 2: Add to original → $80 + $9.60 = $89.60
For a decrease, you'd subtract instead. If that same $80 product gets a 12% discount: $80 - $9.60 = $70.40.
Some Common Mistakes to Avoid
I've seen these come up over and over.
They're easy to make, and even people who are good with numbers fall for them.
1. Thinking Opposite Percentages Cancel Out
If you increase a number by 20% and then decrease the result by 20%, you don't get back to where you started.
Here's why. Start with 100. Increase by 20% → 120. Now decrease 120 by 20% → 120 - 24 = 96. Not 100.
The decrease is applied to the larger number (120), so 20% of 120 is more than 20% of the original 100. This catches people off guard all the time, especially when thinking about investment returns. If your portfolio drops 50%, it needs to gain 100% (not 50%) to recover.
2. Confusing Percentage Change with Percentage Points
If interest rates go from 3% to 5%, that's a 2 percentage point increase. But it's a 66.7% percentage change (because 2/3 × 100 = 66.7%).
These are very different numbers, and mixing them up in a report or presentation will mislead your audience. When you hear "increased by 2%," always clarify whether that means 2 percentage points or a 2% relative change.
3. Stacking Percentage Discounts Wrong
A 30% discount followed by an additional 20% discount is NOT a 50% total discount.
Start with a $100 item. After 30% off → $70. After another 20% off → $70 × 0.80 = $56. That's a 44% total discount, not 50%. Percentages compound. They don't add.
The correct formula for stacked discounts: Total discount = 1 - (1 - d₁) × (1 - d₂). For 30% and 20%: 1 - (0.70 × 0.80) = 1 - 0.56 = 0.44, or 44%.
4. Swapping Old and New Values in Percentage Change
The order matters. Going from 80 to 100 is a 25% increase. Going from 100 to 80 is a 20% decrease. Same two numbers, different percentages, because the base value (the denominator) changes.
Always make sure the "old" value is the one you're measuring FROM, and the "new" value is the one you're measuring TO. If you swap them, your percentage will be wrong.
5. Comparing Percentages from Different Bases
Saying "Product A grew 50% and Product B grew only 10%, so Product A is doing better" can be misleading. If Product A went from 10 units to 15 units (50% growth) and Product B went from 10,000 units to 11,000 units (10% growth), Product B added 985 more units in absolute terms.
Percentages strip away the scale. Always look at the actual numbers alongside the percentages before drawing conclusions. In reports and dashboards, showing both the percentage and the absolute change gives the full picture.
Some Questions You May Have
How do I find the original number if I know the percentage and the result?
Work backward. If you know that 30% of some number equals 60, divide the result by the percentage as a decimal: 60 / 0.30 = 200. So the original number is 200. For percentage increases, if a value increased by 20% to become 240, divide by 1.20: 240 / 1.20 = 200.
What's the difference between percentage change and percentage difference?
Percentage change measures how much a single value changed over time (from old to new). The percentage difference compares two values that don't have a before/after relationship.
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