Last updated: May 2026
Three ways to calculate percentages — results appear as you type.
Mode 1 — X% of Y: Result = (X / 100) × Y
Mode 2 — X is what % of Y: Result = (X / Y) × 100
Mode 3 — Percentage change: Result = ((New − Original) / |Original|) × 100. A positive result is an increase; negative is a decrease.
Percentage calculations come up constantly in everyday life — discounts, tax, salary increases, test scores, statistics. All three modes in this calculator use one of three core formulas:
Mode 1 example — Sale discount: A jacket is $120 and is 35% off. What's the discount?
$120 × (35 ÷ 100) = $120 × 0.35 = $42 off. Sale price = $120 − $42 = $78.00.
Mode 2 example — Test score: You got 47 out of 60 questions correct. What percentage did you score?
(47 ÷ 60) × 100 = 78.3%.
Mode 3 example — Salary raise: Your salary went from $68,000 to $74,500. What's the percentage increase?
((74,500 − 68,000) ÷ 68,000) × 100 = (6,500 ÷ 68,000) × 100 = 9.56% increase.
| Situation | Mode to Use | Example |
|---|---|---|
| Retail discount | Mode 1 (X% of Y) | 20% off $89.99 = $17.99 savings |
| Sales tax | Mode 1 (X% of Y) | 8.5% tax on $45 = $3.83 |
| Tip calculation | Mode 1 (X% of Y) | 18% on $62 = $11.16 |
| Grade / score | Mode 2 (X is what % of Y) | 38/50 = 76% |
| Market share | Mode 2 (X is what % of Y) | $2.4M of $18M market = 13.3% |
| Price change | Mode 3 (% Change) | Gas from $3.20 to $3.85 = +20.3% |
| Year-over-year growth | Mode 3 (% Change) | Revenue $1.2M → $1.55M = +29.2% |
| Weight loss / gain | Mode 3 (% Change) | 195 lbs → 178 lbs = −8.7% |
These two terms are frequently confused, especially in news and finance. If an interest rate rises from 3% to 5%, it increased by 2 percentage points — but by 66.7% in relative terms. Which one you use matters a lot: a politician saying unemployment "fell 2%" and one saying it "fell 2 percentage points" are making very different claims if the starting rate was 4%.
Use percentage points when comparing two percentages directly. Use percentage change (Mode 3) when expressing how much a value grew or shrank relative to its starting point.
How do I calculate a percentage increase quickly in my head?
For round numbers, break it into parts. 20% of $85? That's 10% ($8.50) doubled = $17. For 15%, take 10% and add half of that: $8.50 + $4.25 = $12.75. This works reliably for tips, quick discounts, and mental estimates when you don't have a calculator handy.
What's the difference between a 50% increase and a 50% decrease?
They don't cancel out. If something increases 50% and then decreases 50%, you end up with 75% of the original — a net loss of 25%. This is why percentage changes applied sequentially aren't simply additive. Always recalculate from the new base value each time.
How do I reverse a percentage — find the original price before a discount?
Divide the sale price by (1 − discount rate). If you paid $68 after a 20% discount, the original was $68 ÷ 0.80 = $85.00. This works for any "original value before percentage reduction" problem.
Why does the percentage change formula use the absolute value of the original?
To handle negative starting values correctly. If a company's profit went from −$20K to −$8K, dividing by the absolute value (20K) gives a 60% improvement — which reflects economic reality. Without the absolute value, the sign of the result would flip incorrectly when the original is negative.
How do I calculate compound percentage growth over multiple years?
Single-year percentage change doesn't account for compounding. For multi-year growth, use the CAGR formula: (End Value ÷ Start Value)^(1 ÷ Years) − 1. For example, $10,000 growing to $14,693 over 5 years is a CAGR of (14,693 ÷ 10,000)^(1/5) − 1 = 8% per year — even if the annual growth wasn't exactly 8% every year.