Whether it’s a salary raise, investment growth, or rising prices — percentage increase tells you how much something grew relative to where it started. One formula, three steps, zero confusion. (New to percentages? Start with our Complete Guide to Percentages.)
The Formula in 3 Steps
- Subtract: New value minus old value (this is the raw increase).
- Divide: divide that by the OLD value (always the starting point).
- Multiply by 100: convert the decimal to a percentage.
Example — salary raise: $50,000 → $55,000. Step 1: 55,000 − 50,000 = 5,000. Step 2: 5,000 ÷ 50,000 = 0.10. Step 3: 0.10 × 100 = 10%.
Worked Examples
Investment growth
$2,000 grows to $2,600: (2,600 − 2,000) ÷ 2,000 = 600 ÷ 2,000 = 30% gain.
Rent hike
$1,200/month → $1,350: (1,350 − 1,200) ÷ 1,200 = 150 ÷ 1,200 = 12.5% increase.
Test scores
68% → 85%: (85 − 68) ÷ 68 = 17 ÷ 68 = 25% improvement. Note: that’s 17 percentage points, but a 25% relative increase — see our pillar guide for why the distinction matters.
The #1 Mistake: Wrong Denominator
People divide by the NEW value instead of the old. $50k → $55k: dividing 5,000 by 55,000 gives 9.09% — wrong. The growth happened from $50k, so $50k is the base. Always ask: “increase from what?” — that’s your denominator.
Increase vs Decrease: The Asymmetry
Up 10% then down 10% doesn’t return to start: $100 → $110 → $99. The decrease applies to the bigger base. This asymmetry is why investors fear drawdowns: a 50% loss needs a 100% gain just to break even. (Investopedia has more on percentage change in investing.)
| If you lose… | You need this gain to recover |
|---|---|
| 10% | 11.1% |
| 20% | 25% |
| 30% | 42.9% |
| 50% | 100% |
Quick Mental Math Shortcut
To apply an increase (not just measure one), multiply by (1 + rate): add 15% → ×1.15. $80 + 15% = 80 × 1.15 = $92. One step, no formula.
Conclusion
A percentage increase is only ever one question: how big is the change compared with where you started? Get the denominator right — always the original value — and the rest is arithmetic: subtract, divide, multiply by 100. The traps are consistent: reversing an increase with the same percentage decrease, confusing percentage points with percent, and trusting a headline number without asking “percent of what?” Work the examples above until the three steps feel automatic, use the mental shortcut when an estimate is enough, and reach for the percentage increase calculator when the answer actually matters. Small formula, huge consequences — now it is yours. The same percentage math powers everyday tools like our tip calculator, which works out restaurant tips, totals and bill splits in seconds.
Frequently Asked Questions
What is the percentage increase formula?
((New Value − Old Value) ÷ Old Value) × 100. The old (original) value is always the denominator.
How do I calculate increase in Excel?
With old in A1 and new in B1: =(B1-A1)/A1, then format as Percentage. That’s it.
Can percentage increase be over 100%?
Yes — it just means more than doubling. $50 → $150 is a 200% increase (tripled).
What’s the difference between increase and percentage points?
Going from 10% to 15% is +5 percentage points but a 50% relative increase. Points = simple subtraction; percent = relative to the base.
How do I find the original value after an increase?
Divide by (1 + rate): $55k after a 10% raise → 55,000 ÷ 1.10 = $50k. (Full reverse-percentage guide in our pillar article.)
Related
- The Complete Guide to Percentages — the full pillar
- Percentage Calculator — instant answers
- Compound Interest Calculator — growth over time