Percentage Change: Formula, Examples & Calculator
By CalcMulti Editorial Team··6 min read
Percentage change measures how much a value has grown or shrunk relative to its starting point. It is the backbone of financial analysis, scientific measurement, and everyday comparisons — from stock returns to grade improvements to population growth.
This guide explains the percentage change formula, walks through worked examples, distinguishes increase from decrease, and covers the most common errors (including the asymmetry trap that catches most people off-guard).
Formula
% Change = ((New − Old) ÷ Old) × 100
The Percentage Change Formula
Formula: % Change = ((New Value − Old Value) ÷ Old Value) × 100
The result is positive when the new value is higher (increase) and negative when lower (decrease).
Step-by-step: (1) Subtract old from new. (2) Divide by the old value. (3) Multiply by 100.
Example 1 — salary raise: Salary goes from $4,000 to $4,600/month.
% Change = ((4600 − 4000) ÷ 4000) × 100 = (600 ÷ 4000) × 100 = +15%
Example 2 — price drop: Gas price falls from $3.80 to $3.23 per gallon.
% Change = ((3.23 − 3.80) ÷ 3.80) × 100 = (−0.57 ÷ 3.80) × 100 = −15%
Percentage Change vs Percentage Difference
These are often confused but answer different questions:
Percentage change compares a new value to an old value, and direction matters. Old and New are not interchangeable. Used when there is a clear "before" and "after".
Percentage difference compares two values without implying one is the reference. Formula: |A − B| ÷ ((A + B) ÷ 2) × 100. Used when neither value is a baseline — e.g., comparing two independent measurements.
In finance and science, almost always use percentage change (with a clear reference period).
| Metric | Formula | When to use |
|---|---|---|
| % Change | (New − Old) / Old × 100 | Before/after comparisons, growth rates |
| % Difference | |A−B| / ((A+B)/2) × 100 | Comparing two equal-status values |
| % of a total | Part / Total × 100 | Share of a whole (budget allocation, etc.) |
The Asymmetry Trap: Why +X% then −X% ≠ 0
One of the most important (and counterintuitive) percentage facts: a percentage increase followed by the same percentage decrease does NOT cancel out.
Example: A portfolio worth $10,000 gains 30% one year, then loses 30% the next.
Year 1: $10,000 × 1.30 = $13,000
Year 2: $13,000 × 0.70 = $9,100
Net result: −$900 (−9%). Not zero.
Why? Each percentage applies to a different base. The 30% gain is on $10,000 (+$3,000). The 30% loss is on $13,000 (−$3,900). Bigger base → bigger absolute loss.
This is why investment losses are harder to recover from than they appear: a 50% loss requires a 100% gain just to break even.
| Loss suffered | Gain needed to recover | Example |
|---|---|---|
| 10% | 11.1% | $100 → $90 → needs $10 more = $100 |
| 20% | 25% | $100 → $80 → needs $20 more = $100 |
| 33% | 50% | $100 → $67 → needs $33 more = $100 |
| 50% | 100% | $100 → $50 → needs $50 more = $100 |
| 75% | 300% | $100 → $25 → needs $75 more = $100 |
Practical Examples by Context
Stock market: Apple at $150 closes at $162 → ((162−150)÷150)×100 = +8.0%
Inflation: CPI was 282.3 last year, 295.6 this year → ((295.6−282.3)÷282.3)×100 = +4.7%
Test score improvement: First test 65/100, second test 78/100 → ((78−65)÷65)×100 = +20%
Weight loss: Started at 210 lbs, now 189 lbs → ((189−210)÷210)×100 = −10%
Website traffic: 12,000 visits last month, 15,000 this month → ((15000−12000)÷12000)×100 = +25%
Need a Calculator?
The Percentage Increase Calculator computes increase and decrease percentages instantly, including sequential changes.
The Percentage Calculator handles all three percentage problems: find the part, find the rate, and find the base.
For stock-specific calculations including CAGR and total return, use the Stock Return Calculator.
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Frequently Asked Questions
Educational use only. Content is based on publicly documented mathematical formulas and reviewed for accuracy by the CalcMulti Editorial Team. Last updated: March 2026.