Percentage Calculations: Common Formulas and Pitfalls
Percentage calculations appear simple but hide common errors, especially around percentage change, percentage points, and compound percentages. This guide clarifies the math behind everyday percentage problems.
Key Takeaways
- Result = Number x (Percentage / 100) = 200 x 0.15 = 30
- If an interest rate goes from 5% to 7%, that's:
- Discounts**: A 20% off then 10% off coupon gives 28% off, not 30%.
Percentage Calculator
Calculate percentages, increases, decreases, and ratios
Basic Percentage Formulas
Finding a Percentage of a Number
What is 15% of 200? Result = Number x (Percentage / 100) = 200 x 0.15 = 30
Finding What Percentage One Number Is of Another
30 is what percentage of 200? Percentage = (Part / Whole) x 100 = (30 / 200) x 100 = 15%
Percentage Change
From 200 to 250: Change = ((New - Old) / Old) x 100 = ((250 - 200) / 200) x 100 = +25%
Common Pitfalls
Percentage Points vs Percent Change
If an interest rate goes from 5% to 7%, that's:
- A 2 percentage point increase
- A 40% percent increase (from 5 to 7)
These are very different and often confused in news reports.
Asymmetric Percentage Changes
A 50% decrease followed by a 50% increase does NOT return to the original:
- Start: 100 → 50% decrease → 50 → 50% increase → 75
This is because the percentage base changes after the first operation.
Compounding Percentages
Multiple sequential percentage changes cannot simply be added:
- 10% increase then 20% increase is NOT a 30% increase.
- Correct: 1.10 x 1.20 = 1.32, or a 32% total increase.
Practical Applications
- Discounts: A 20% off then 10% off coupon gives 28% off, not 30%.
- Tax: Sales tax on a discounted item applies to the discounted price.
- Margins: A 30% markup is not the same as a 30% margin.
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