Percentage change is one of the most useful formulas in everyday math — and also one of the most commonly misused. Here’s the correct formula, worked examples, and how to do it in spreadsheets.
The Basic Formula
Percentage change = ((New Value − Old Value) ÷ Old Value) × 100
- Positive result = percentage increase
- Negative result = percentage decrease
Percentage Increase Example
Your salary goes from $60,000 to $72,000. What’s the percentage increase?
((72,000 − 60,000) ÷ 60,000) × 100
= (12,000 ÷ 60,000) × 100
= 0.20 × 100
= 20%Percentage Decrease Example
A stock drops from $200 to $150. What’s the percentage decrease?
((150 − 200) ÷ 200) × 100
= (−50 ÷ 200) × 100
= −0.25 × 100
= −25%Reverse: Finding the New Value From a Percentage Change
If you know the old value and the percentage change, you can find the new value:
New Value = Old Value × (1 + Percentage Change ÷ 100)
Your investment of $1,000 grows by 15%:
$1,000 × (1 + 15 ÷ 100)
= $1,000 × 1.15
= $1,150Reverse: Finding the Old Value From a Percentage Change
If you know the new value and the percentage change, what was the original?
Old Value = New Value ÷ (1 + Percentage Change ÷ 100)
Something is now priced at $92 after a 15% increase. What was the original?
$92 ÷ 1.15 = $80.00How to Do It in Excel / Google Sheets
If your old value is in A2 and new value is in B2:
=(B2 - A2) / A2 * 100Format the cell as a percentage, and you can skip the × 100:
=(B2 - A2) / A2Common Mistakes to Avoid
Using the Wrong Base Value
A product discounts from $100 to $80, then back to $100. Is that a 20% increase or 25% increase?
From $80 to $100:
($100 − $80) ÷ $80 × 100 = 25%The correct base is always the original value before the change.
Confusing Percentage Points with Percent
A bank interest rate goes from 3% to 4%. That’s a 1 percentage point increase, but a 33.3% relative increase:
(4% − 3%) ÷ 3% = 33.3%Negative Denominators
Dividing by a negative old value gives misleading results. Always use a positive base.
Percentage Change vs Absolute Change
| Scenario | Values | Absolute Change | Percentage Change |
|---|---|---|---|
| Salary | $60k → $72k | +$12,000 | +20% |
| Stock | $200 → $150 | −$50 | −25% |
| Interest rate | 3% → 4% | +1 pp | +33.3% |
Summary
Percentage change formula: ((New − Old) ÷ Old) × 100. Positive is increase, negative is decrease. Always use the original value as the base. When comparing interest rates, note the difference between percentage points (absolute) and percent change (relative).
Calculate all percentage scenarios instantly with the Percentage Calculator.