Percentage increase comes up constantly — a rent hike, a raise at work, a stock that's up on the year. The formula is simple, but it's also one of the most commonly botched calculations in everyday math. Here's how to get it right every time.
The Formula
The key detail: you always divide by the old value — the starting point. That's the baseline the change is measured against.
Worked Example
Your rent goes from $1,850 to $2,035. The increase is 2,035 − 1,850 = $185. Divide by the original: 185 ÷ 1,850 = 0.10. Multiply by 100 and your rent went up 10%.
Three Mistakes to Avoid
1. Dividing by the new value
185 ÷ 2,035 gives 9.1% — close, but wrong. The error grows with bigger changes: a stock going from $50 to $100 is a 100% gain, not 50%.
2. Assuming increases and decreases cancel out
A 20% drop followed by a 20% gain does not get you back to even. $100 → $80 → $96. Because the second change is measured from a smaller base, you're still down 4%. This asymmetry is why large investment losses are so punishing.
3. Confusing percent with percentage points
If a mortgage rate moves from 4% to 5%, it rose one percentage point — but that's a 25% relative increase in the rate. News headlines mix these up constantly.
Reverse Percentages
Sometimes you know the after and need the before. If a jacket costs $84 after a 30% discount, don't add 30% back (that gives $109.20, which is wrong). Divide by what's left instead: 84 ÷ 0.70 = $120.
The same logic works for anything with tax included: divide by 1 plus the rate to recover the base price.
Percentage CalculatorIncrease, decrease, and reverse percentages — instantly
Quick Reference
- Increase: (new − old) ÷ old × 100
- Decrease: (old − new) ÷ old × 100
- X% of Y: Y × X ÷ 100
- Original before an increase: final ÷ (1 + rate)
- Original before a decrease: final ÷ (1 − rate)