calculate percentage change

What is percentage change?

Percentage change tells you how much a value has increased or decreased relative to its starting point. It is one of the most useful math tools for personal finance, investing, business reporting, grades, and everyday decisions.

Instead of only saying a number went up by 20, percentage change tells you whether that 20 is big or small compared with where you started. A $20 increase from $40 is huge; from $1,000 it is tiny. Percentages give context.

How to calculate percentage change

Core formula

Use this formula whenever you want to compare a new value to an original value:

• Percentage Change = ((New Value − Original Value) ÷ Original Value) × 100

Step-by-step method

• Subtract the original value from the new value.
• Divide the result by the original value.
• Multiply by 100 to convert to a percentage.
• If the final number is positive, it is an increase.
• If the final number is negative, it is a decrease.

Percentage increase vs percentage decrease

The same formula handles both directions:

• Positive result: percentage increase (growth).
• Negative result: percentage decrease (decline).
• Zero result: no change.

For example, moving from 50 to 65 gives +30%. Moving from 65 back to 50 gives about -23.08%, not -30%. This is because percentages depend on the base value each time.

Worked examples

Example 1: Price increase

A product price changes from $80 to $100.

• Change = 100 − 80 = 20
• 20 ÷ 80 = 0.25
• 0.25 × 100 = 25%

The price increased by 25%.

Example 2: Website traffic decrease

Monthly traffic falls from 12,000 visits to 9,600 visits.

• Change = 9,600 − 12,000 = -2,400
• -2,400 ÷ 12,000 = -0.2
• -0.2 × 100 = -20%

Traffic decreased by 20%.

Example 3: Salary growth

Your salary goes from $52,000 to $57,200.

• Change = 57,200 − 52,000 = 5,200
• 5,200 ÷ 52,000 = 0.1
• 0.1 × 100 = 10%

Your salary increased by 10%.

Common mistakes people make

• Using the new value as the denominator instead of the original value.
• Forgetting to multiply by 100 after division.
• Ignoring the sign (positive or negative).
• Assuming an increase and reverse decrease are equal percentages.
• Trying to compute percentage change from zero (undefined).

What if the original value is zero?

If the original value is 0 and the new value is not 0, percentage change is mathematically undefined because division by zero is impossible. In this case, report absolute change (the raw difference) or describe the movement qualitatively.

If both old and new are 0, there is no change.

Percentage change vs percentage points

These are not the same:

• Percentage points measure direct subtraction of rates (e.g., 12% to 15% = +3 percentage points).
• Percentage change measures relative change (from 12% to 15% is a 25% increase because 3 ÷ 12 = 0.25).

Use the right one for clearer communication, especially in business and economic reports.

Where percentage change is useful

• Tracking investment returns over time.
• Comparing monthly expenses and savings progress.
• Analyzing revenue, profit, and conversion rate changes.
• Measuring health metrics such as weight changes.
• Reviewing student performance and test-score trends.

Quick tips for accurate calculations

• Always verify which value is the original baseline.
• Keep extra decimal places during intermediate steps.
• Round only at the end for reporting.
• Use a calculator for consistency when comparing many values.

Final thoughts

If you can calculate percentage change quickly, you gain a practical advantage in finance, productivity, and decision-making. The calculator above helps you do it in seconds: enter old value, enter new value, and read the result as a clear increase or decrease.