How to Calculate Percentage Increase & Decrease — Step by Step

Whether you are negotiating a salary raise, tracking stock performance, or comparing product prices over time, knowing how to calculate percentage increase and decrease is one of the most practical math skills you can have. This guide walks you through the formula, provides worked examples, highlights common mistakes, and explains the crucial difference between percentage change and percentage point.

The Percentage Change Formula

The universal formula for percentage change works in both directions — increases and decreases:

Percentage Change = ((New Value − Old Value) / Old Value) × 100

A positive result means an increase. A negative result means a decrease. The absolute value tells you the magnitude of the change, while the sign tells you the direction.

Worked Example 1 — Salary Raise

Suppose your annual salary increases from $52,000 to $56,160. Plug the numbers into the formula:

1. Subtract the old value from the new value: $56,160 − $52,000 = $4,160.
2. Divide by the old value: $4,160 ÷ $52,000 = 0.08.
3. Multiply by 100: 0.08 × 100 = 8%.

Your salary increased by 8 percent. When evaluating a raise, compare this number to your local inflation rate. If inflation is running at 3 percent, your real purchasing-power gain is closer to 5 percent.

Worked Example 2 — Price Change

A pair of headphones that cost $120 last year now costs $96 after a sale. What is the percentage change?

1. $96 − $120 = −$24.
2. −$24 ÷ $120 = −0.20.
3. −0.20 × 100 = −20%.

The price decreased by 20 percent. Knowing this helps you objectively evaluate whether a deal is genuinely good or just clever marketing.

Worked Example 3 — Stock Gains and Losses

You buy a stock at $45 per share and it rises to $54. Later it drops from $54 back down to $45. Are the percentage gain and loss the same? No — and this is where many people get tripped up.

Gain: ($54 − $45) ÷ $45 × 100 = +20%.

Loss: ($45 − $54) ÷ $54 × 100 = −16.67%.

Even though the stock returned to the same dollar price, the percentage loss is smaller than the percentage gain because the base value changed. This asymmetry matters for portfolio analysis and is one of the most misunderstood aspects of percentage math.

Common Mistakes to Avoid

Using the wrong base value. The most frequent error is dividing by the new value instead of the old value. The denominator in the formula must always be the original (starting) value. Swapping it produces an incorrect result.

Confusing percentage change with absolute change. A $10 increase on a $50 item is a 20 percent change, while a $10 increase on a $500 item is only a 2 percent change. The same dollar amount can represent vastly different percentage changes depending on the starting figure.

Assuming symmetry. As the stock example above illustrates, a 20 percent increase followed by a 20 percent decrease does not return you to the starting value. After a 20 percent gain on $100, you have $120. A 20 percent loss on $120 leaves you at $96, not $100. Always recalculate from the new base.

Forgetting the sign. A negative result is not an error. It simply indicates a decrease. Make sure you preserve the sign so the direction of the change is clear.

Percentage Change vs. Percentage Point

These two terms sound similar but mean different things, and mixing them up is surprisingly common in news headlines and everyday conversation.

Percentage change is the relative difference between two values expressed as a percentage of the original. If an interest rate moves from 4 percent to 5 percent, the percentage change is (5 − 4) ÷ 4 × 100 = 25 percent.

Percentage point is the simple arithmetic difference between two percentages. In the same example, the interest rate moved by 1 percentage point (from 4 percent to 5 percent).

A headline reading “Unemployment rose by 2 percent” is ambiguous. Does it mean a 2 percent relative increase (e.g., from 5.0 percent to 5.1 percent) or a 2 percentage-point increase (e.g., from 5 percent to 7 percent)? When precision matters, always specify which one you mean.

When to Use Each Measure

Use percentage change when comparing values of different magnitudes or when you want to understand relative growth. Year-over-year revenue growth, investment returns, and inflation rates are all best expressed as percentage changes.

Use percentage points when comparing two rates or proportions that are already expressed as percentages. Changes in market share, approval ratings, and interest rates are clearer when stated in percentage points because the reader immediately sees the absolute shift.

Try It Yourself

Ready to calculate your own percentage increases and decreases without the mental math? Our free Percentage Calculator handles the formula instantly. Select the Percentage Change mode, enter your old and new values, and get the result along with a plain-English explanation of the math — no sign-up required.

Want every percentage formula in one place? Check out our Percentage Formulas Cheat Sheet.