Percentage Change Formula & How to Calculate It

This calculator works out the percentage change between an old (original) value and a new value, and returns both the percentage increase or decrease and the size of the change itself. You enter the original number and the new number, and the calculator gives you the percentage change, plus the absolute difference. The formula is: Percentage Change = (New Value − Original Value) ÷ Original Value × 100.

Formula

The percentage change formula is written as:

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

• Original Value – the starting or old amount (no unit, or any unit you choose).
• New Value – the ending or updated amount (same unit as the original).
• Percentage Change – the relative difference expressed as a percent (%).

A positive result means an increase; a negative result means a decrease. The absolute difference (New − Old) tells you the raw size of the change in the same units as your inputs.

Worked Example

Using the default values from the calculator: Original = 100, New = 150.

1. Subtract the original from the new: 150 − 100 = 50.
2. Divide by the original: 50 ÷ 100 = 0.5.
3. Multiply by 100 to get a percentage: 0.5 × 100 = 50%.

The percentage change is 50%, and the absolute difference is 50 units. The calculator shows the same result: 50.00%.

When to Use Percentage Change

Percentage change is used whenever you want to compare a new value to an old one in relative terms, rather than just looking at the raw difference. Common uses include:

• Tracking growth or decline in sales, revenue, or profit.
• Measuring population change, inflation, or stock price movement.
• Comparing test scores, grades, or performance metrics over time.
• Evaluating changes in quantities like distance, weight, or temperature (when the scale has a true zero).

The key advantage is that it gives a scale-free comparison: a change from 10 to 15 and a change from 100 to 150 are both a 50% increase, even though the raw changes are 5 and 50.

How to Read the Result

A positive percentage change means the new value is larger than the original. For example, if your electricity bill went from $80 to $96, the percentage change is (96−80)/80 × 100 = 20%, so your bill increased by 20%. A negative percentage change means the new value is smaller. If a stock drops from $50 to $40, the change is (40−50)/50 × 100 = −20%, a 20% decrease.

Note that a decrease can never exceed 100% (you cannot lose more than the whole original amount), but an increase has no upper limit. A change from 0 to any positive number is undefined in percentage terms because division by zero is not possible – the calculator will show an error or “undefined� in that case.

Common Mistakes and Pitfalls

• Reversing the order: Always subtract the original from the new, not the other way around. Swapping gives the opposite sign and a different magnitude.
• Using the new value as the denominator: The formula always divides by the original value. Dividing by the new value gives a different number, often called the “percentage of the new value� rather than the percentage change.
• Confusing percentage change with percentage points: If a rate goes from 4% to 6%, the percentage change is 50% (because (6−4)/4 × 100 = 50%), but the increase in percentage points is only 2. These are different concepts.
• Ignoring units: The original and new values must be in the same unit (e.g., both in dollars, both in kilograms). Mixing units gives a meaningless result.
• Rounding too early: Round only the final answer, not intermediate steps, to avoid small errors.

Percentage Change vs. Percentage Difference

Percentage change compares a new value to an old value using the old value as the base. Percentage difference, on the other hand, compares two values symmetrically by dividing the absolute difference by the average of the two values, then multiplying by 100. For example, comparing 100 and 150:

• Percentage change (from 100 to 150) = (150−100)/100 × 100 = 50%.
• Percentage difference = |150−100| / ((100+150)/2) × 100 = 50/125 × 100 = 40%.

Use percentage change when there is a clear chronological order (old → new). Use percentage difference when you are comparing two values without a time order, such as two prices from different stores.

Limitations of the Formula

The formula assumes the original value is not zero. If the original is zero, the division is undefined, and no percentage change can be calculated. Also, the formula gives a relative measure, so it can be misleading when the original value is very small: a change from 1 to 2 is a 100% increase, but the absolute change is only 1 unit. Always consider the absolute difference alongside the percentage.

The formula works for any unit (dollars, kilograms, liters, etc.) as long as both values use the same unit. It does not account for compounding over multiple periods – for that, you would use a compound growth formula.

Frequently Asked Questions

What is the formula for percentage change?

The formula is: (New Value − Original Value) ÷ Original Value × 100. This gives the percentage increase or decrease relative to the original value.

How do I calculate a 10% increase?

To increase a number by 10%, multiply it by 1.10. For example, 50 increased by 10% is 50 × 1.10 = 55. To decrease by 10%, multiply by 0.90.

What is the difference between percentage change and percentage difference?

Percentage change uses the original value as the base, while percentage difference uses the average of the two values as the base. Percentage change is used when there is an old and a new value; percentage difference is used for symmetric comparisons.

Can percentage change be more than 100%?

Yes, for increases. For example, a change from 10 to 25 is a 150% increase. For decreases, the maximum is 100% (going to zero), because you cannot lose more than the original amount.

What if the original value is zero?

Then the percentage change is undefined because you cannot divide by zero. In that case, you might use the absolute difference or describe the change in words.

How do I calculate percentage change in Excel?

Use the formula =(new_value - old_value)/old_value and format the cell as a percentage. For example, if old is in A1 and new in B1, enter =(B1-A1)/A1 in C1.

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in old | Original value | - | 100 | 0
in new | New value | - | 150 | 0
out pct | Percentage change | % | (new - old) / old * 100 | 2
out diff | Absolute difference | - | new - old | 2