Calculate Change Percentage Formula

This calculator works out the percentage change between an original value and a new value, showing both the percentage increase and decrease with a clear step-by-step breakdown. You enter the starting (original) number and the final (new) number, and you get the percentage change, the direction of change, and the absolute difference. The formula used is the standard percentage change formula: (new – original) / original × 100.

Formula

The percentage change formula is:

Percentage change = ((New value – Original value) / Original value) × 100

Where:

• Original value – the starting amount (no unit, can be any number).
• New value – the amount after the change (same unit as original).
• Percentage change – the result, expressed as a percentage. A positive result means an increase; a negative result means a decrease.

The formula works for any quantity: prices, weights, populations, test scores, temperatures, etc., as long as both values are in the same unit. It is also called the “percent change� or “relative change� formula.

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 the difference by the original: 50 ÷ 100 = 0.5.
3. Multiply by 100 to get a percentage: 0.5 × 100 = 50%.

So the percentage change is 50%, which is an increase. The absolute difference is 50. The calculator shows the same result: 50.00%.

When to Use Percentage Change

Percentage change is used whenever you want to express how much a value has grown or shrunk relative to its starting point. Common situations include:

• Price changes: “The price went from $80 to $100 – what percent increase is that?�
• Population growth or decline over a period.
• Test scores or grades: “I improved from 60 to 75 – what percent improvement?�
• Weight or measurement changes in science experiments.
• Financial returns: “An investment grew from $1,000 to $1,200 – what return?�

The key is that you always compare the change to the original value, not to the new value. This is a common source of confusion. For example, if something goes from 100 to 150, it’s a 50% increase. But if it goes from 150 back to 100, it’s a 33.33% decrease (because the change is –50, divided by 150). The percentage change is not symmetric.

How to Read the Result

The result tells you the size of the change relative to the starting point. A positive percentage means the new value is larger than the original; a negative percentage means it is smaller. The magnitude tells you how big the change is. For example:

• +50% means the new value is 1.5 times the original.
• –25% means the new value is 0.75 times the original.
• 0% means no change.

If the original value is negative, the formula still works but the interpretation can be tricky. For instance, if original = –10 and new = –5, the change is +5, and the percentage change is (5 / –10) × 100 = –50%. That might seem counterintuitive because the value actually increased (became less negative). In such cases, it’s often clearer to talk about the absolute change or to use a different measure.

Common Mistakes and How to Avoid Them

• Dividing by the new value instead of the original. Always divide by the original (the starting point).
• Mixing up the order of subtraction. The new value comes first: new – original, not the other way around.
• Forgetting to multiply by 100. The formula gives a decimal; multiply by 100 to get a percentage.
• Using different units for original and new. Convert to the same unit first (e.g., both in dollars, both in kilograms).
• Rounding too early. If you round intermediate steps, the final percentage can be off. Keep full precision until the end.

Limits of the Formula

The percentage change formula assumes the original value is not zero. If the original is zero, the formula is undefined (division by zero). In that case, you cannot calculate a percentage change; you can only describe the absolute change.

Also, the formula is best for comparing two points in time. It does not account for the path between them. For example, a stock that goes from $100 to $110 and then to $121 has a total change of 21%, but the percentage change from start to end is 21% (since 121/100 = 1.21). If you wanted the average annual growth rate, you would need a different formula (compound annual growth rate).

Finally, percentage change 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. Always consider the context and the absolute difference as well.

Frequently Asked Questions

How do I calculate percentage increase?

Use the same formula: ((new – original) / original) × 100. If the result is positive, it’s an increase. For example, from 50 to 60: (60 – 50) / 50 × 100 = 20% increase.

How do I calculate percentage decrease?

Same formula, but the result will be negative. For example, from 80 to 60: (60 – 80) / 80 × 100 = –25%, which is a 25% decrease. Some people prefer to report the absolute value and say “25% decrease.�

What if I only know the percentage change and the original value? How do I find the new value?

Rearrange the formula: new = original × (1 + percentage/100). For a 20% increase on 50: new = 50 × (1 + 0.20) = 60. For a 20% decrease, use (1 – 0.20) = 0.80.

Is percentage change the same as percentage difference?

No. Percentage change uses the original value as the denominator. Percentage difference (also called relative difference) uses the average of the two values as the denominator: ((new – original) / ((new + original)/2)) × 100. It is used when comparing two values without a clear “before� and “after.�

What if the original value is zero?

You cannot calculate a percentage change because division by zero is undefined. In that case, report the absolute change instead, or use a different measure like “increase from 0 to 5� without a percentage.

How do I calculate percentage change in Excel or Google Sheets?

In a cell, type: =(new_cell - original_cell)/original_cell and format the cell as a percentage. For example, if original is in A1 and new is in B1, enter =(B1-A1)/A1.

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