how to calculate a percentage increase of a percentage

What does “percentage increase of a percentage” mean?

This phrase can sound confusing at first, but it’s straightforward once you separate the layers:

• You start with an original percentage (for example, 20%).
• You then increase that percentage by another percentage (for example, increase 20% by 10%).

In that case, you are not adding 10 percentage points. You are adding 10% of 20%, which is 2%. So the new percentage becomes 22%.

The core formula

To calculate a percentage increase of a percentage, use:

Equivalent step-by-step form:

1. Convert the increase rate to decimal: Increase Rate ÷ 100
2. Add 1 to get the multiplier
3. Multiply the original percentage by that multiplier

Step-by-step example

Example: Increase 20% by 10%

1. Original percentage = 20
2. Increase rate = 10% = 0.10
3. Multiplier = 1 + 0.10 = 1.10
4. New percentage = 20 × 1.10 = 22%

So the new rate is 22%, and the increase is 2 percentage points.

More examples

Example 1: Increase 15% by 40%

15 × (1 + 40/100) = 15 × 1.4 = 21%

New percentage: 21%

Example 2: Increase 8% by 25%

8 × 1.25 = 10%

New percentage: 10%

Example 3: Increase 50% by 5%

50 × 1.05 = 52.5%

New percentage: 52.5%

Percentage increase vs. percentage points (important)

This is where many mistakes happen:

• Percentage increase: relative change. “Increase 20% by 10%” means 20% grows by 10% of itself, giving 22%.
• Percentage points: absolute change. “Increase from 20% to 30%” is a 10-point increase.

These are not interchangeable. In finance, business, and data reporting, mixing them up can produce serious interpretation errors.

Using a base amount (turn percentages into real values)

Sometimes you need to know the practical impact of a changed percentage. For example:

• Original rate = 12%
• Increase rate = 25%
• Base amount = 800

First, update the percentage:

12 × 1.25 = 15%

Then apply to base amount:

• Original value = 800 × 12% = 96
• New value = 800 × 15% = 120
• Increase in value = 24

This is why the calculator above includes an optional base amount field.

What if there are multiple increases?

If a percentage is increased multiple times, apply each increase one after another (compound effect):

Start with 20%, increase by 10%, then by 15%:

1. After first increase: 20 × 1.10 = 22%
2. After second increase: 22 × 1.15 = 25.3%

Final result is 25.3%, not 25%.

Common mistakes to avoid

• Adding the two percentages directly (e.g., 20% + 10% = 30%) when the task asks for a percentage increase of a percentage.
• Confusing percentage change with percentage points.
• Forgetting to convert increase rate to decimal before multiplying.
• Rounding too early in multi-step calculations.

Quick checklist

• Identify the original percentage.
• Identify the increase rate.
• Use 1 + increase/100 as multiplier.
• Multiply original percentage by multiplier.
• If needed, apply resulting percentage to a base amount.

Final takeaway

To calculate a percentage increase of a percentage, think in terms of scaling. You’re taking the original percentage and multiplying it by a growth factor. Once you remember this pattern, you can solve these problems quickly and avoid confusing percentage increases with percentage-point changes.