Percent Change Equation: Formula & How to Calculate

This calculator works out the percent change between an old value and a new value, giving you the percentage increase or decrease in one step. You enter the original number and the new number, and you get back the percent change, the absolute difference, and the direction (increase or decrease). The formula is: Percent Change = ((New Value − Old Value) ÷ Old Value) × 100.

Formula

The percent change equation is written as:

Percent Change = ((New Value − Old Value) / Old Value) × 100%

Where:

• Old Value – the original or starting amount (no units needed; it can be dollars, items, people, etc.)
• New Value – the amount after the change (same units as the old value)
• Percent Change – the result, expressed as a percentage. A positive result means an increase; a negative result means a decrease.

If you prefer to work with a decimal, the formula is: (New − Old) / Old, then multiply by 100 to get the percentage.

Worked Example

Using the default values from the calculator: Old Value = 50, New Value = 75.

1. Subtract the old value from the new value: 75 − 50 = 25
2. Divide by the old value: 25 ÷ 50 = 0.5
3. Multiply by 100 to get a percentage: 0.5 × 100 = 50%

The percent change is 50%, which means the value increased by 50% from 50 to 75. The absolute difference is 25.

When to Use Percent Change

Percent change is used whenever you want to compare an old value to a new value and express the difference relative to the starting point. Common situations include:

• Price increases or decreases (e.g., a product goes from $20 to $25)
• Population growth or decline over a period
• Test score improvements (e.g., from 60 to 75)
• Stock or investment performance (though often called “return�)
• Comparing data from one year to the next

The key is that you always divide by the old value, not the new one. This makes percent change different from “percentage difference� (which divides by the average of the two values) and from “percentage of� (which is a ratio).

How to Read the Result

A positive percent change means the new value is larger than the old value. A negative percent change means the new value is smaller. For example:

• Old = 100, New = 120 → +20% (increase)
• Old = 100, New = 80 → −20% (decrease)
• Old = 100, New = 100 → 0% (no change)

Be careful when the old value is zero or negative. The formula requires a non-zero old value; dividing by zero is undefined. If the old value is negative, the result can be counterintuitive (e.g., from −10 to −5 gives +50% even though the absolute value went up). In those cases, consider using absolute change or a different metric.

Common Mistakes and Limitations

• Dividing by the new value instead of the old. This gives a different (and usually wrong) number. Always divide by the starting value.
• Confusing percent change with percentage points. A rise from 10% to 15% is a 5 percentage point increase, but a 50% increase (because (15−10)/10 = 0.5).
• Rounding too early. Keep extra decimal places during intermediate steps, then round the final answer. For example, (1/3) × 100 = 33.33…%, not 33%.
• Using the formula when the old value is zero. The result is undefined; you cannot calculate a meaningful percent change.
• Ignoring the sign. A negative result is not an error; it indicates a decrease.

The formula is symmetric in time but not in values: going from 50 to 75 is a 50% increase, but going from 75 back to 50 is a 33.33% decrease. This asymmetry is normal and expected.

Percent Change vs. Percentage Difference

People often mix up these two. Percent change uses the old value as the denominator, while percentage difference uses the average of the two values as the denominator:

Percentage Difference = (|New − Old| / ((New + Old)/2)) × 100%

For 50 and 75, the percentage difference is |75−50| / ((75+50)/2) = 25 / 62.5 = 0.4 = 40%. This is useful when you want a symmetric comparison (e.g., comparing two products’ prices) without designating one as the “old� value. For tracking changes over time, percent change is the correct choice.

Alternatives to Percent Change

Depending on your goal, you might use:

• Absolute change: New − Old (e.g., 25 units). Useful when the starting value is close to zero.
• Percentage of: (Part / Whole) × 100. For example, 75 out of 150 is 50%.
• Percentage point difference: Used when comparing two percentages (e.g., interest rates).
• Log change: ln(New/Old). Sometimes used in finance and economics because it is symmetric and handles compounding better.

Percent change is best when you want to express growth or decline relative to a starting point, and when the old value is positive and not too close to zero.

Frequently Asked Questions

How do I calculate percent change in Excel?

In Excel, if your old value is in cell A1 and new value in B1, type =(B1-A1)/A1 and format the cell as a percentage. The result will show as a decimal (e.g., 0.5 becomes 50% when formatted).

What is the difference between percent change and percent error?

Percent error compares a measured value to a known true value, using the absolute difference divided by the true value. Percent change compares two values over time, without designating one as “true.� The formulas are similar, but the context and interpretation differ.

Can percent change be more than 100%?

Yes. If the new value is more than double the old value, the percent change exceeds 100%. For example, from 10 to 30 is a 200% increase. There is no upper limit.

What if the old value is zero?

You cannot calculate percent change because division by zero is undefined. In that case, report the absolute change (new value) or use a different measure, such as “new value is 5 units� instead of a percentage.

How do I find the original value after a percent increase?

If you know the new value and the percent increase, divide the new value by (1 + percent/100). For example, if something is $120 after a 20% increase, the original is 120 / 1.20 = $100.

Is percent change the same as percentage increase or decrease?

Yes. “Percent increase� and “percent decrease� are specific cases of percent change. The formula is identical; the sign tells you the direction.

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in old | Old Value | - | 50 | 0
in new | New Value | - | 75 | 0
out pct | Percent Change | % | ((new - old) / old) * 100 | 2
out diff | Absolute Difference | - | abs(new - old) | 2