Percentage Change Formula: How to Calculate It

The percentage change formula measures how much a value has increased or decreased relative to its original value, expressed as a percent. You calculate it by dividing the difference between the new and old values by the absolute value of the old value, then multiplying by 100. Enter any starting value and new value below to get the percentage change, along with the direction of the change.

Formula

The percentage change formula is written as:

Percentage Change = ((New Value − Original Value) / |Original Value|) × 100

Where:

• New Value – the value after the change (unit: same as the original)
• Original Value – the value before the change (unit: same as the new value)
• |Original Value| – the absolute value of the original (always positive)
• Percentage Change – the result, expressed as a percent (%)

Using the absolute value in the denominator ensures that a change from a negative number to a positive number gives a meaningful positive percentage, and a change from positive to negative gives a negative percentage. Without the absolute value, the sign of the result would flip incorrectly when the original value is negative.

Worked Example

Using the default values from the calculator above: original value = 50, new value = 75.

1. Subtract the original from the new: 75 − 50 = 25
2. Divide by the absolute value of the original: 25 / |50| = 25 / 50 = 0.5
3. Multiply by 100 to get the percentage: 0.5 × 100 = 50%

The result is a 50% increase. The calculator shows the same: 50.00%.

When to Use Percentage Change

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

• Tracking price changes of goods or services over time
• Measuring population growth or decline
• Comparing sales figures from one period to another
• Evaluating changes in test scores, temperatures, or measurements
• Analyzing stock or index movements (though financial contexts often use specific variants)

The key idea is that percentage change normalizes the difference by the original size, so you can compare changes across different scales. A 10-point increase from 100 to 110 is a 10% change, while a 10-point increase from 1000 to 1010 is only a 1% change.

How to Read the Result

A positive percentage change means the new value is larger than the original (an increase). A negative percentage change means the new value is smaller (a decrease). For example:

• Original = 80, New = 100 → (100−80)/80 × 100 = +25% (increase)
• Original = 100, New = 80 → (80−100)/100 × 100 = −20% (decrease)
• Original = 50, New = 50 → (50−50)/50 × 100 = 0% (no change)

Note that a 50% increase followed by a 50% decrease does not return you to the original value. For example, 100 increased by 50% gives 150, then decreased by 50% gives 75. This asymmetry is a common source of confusion; percentage changes are not additive in the way that simple numbers are.

Common Mistakes and Pitfalls

Several errors frequently occur when calculating percentage change:

• Using the new value as the denominator – the formula always uses the original value as the base. Using the new value gives a different (and often misleading) result.
• Ignoring the absolute value for negative originals – if the original value is negative, forgetting the absolute value will produce a result with the wrong sign. For example, a change from −10 to −5 should be a +50% change (improvement), but without absolute value you get (−5 − (−10)) / −10 = 5 / −10 = −50%, which is incorrect.
• Confusing percentage change with percentage points – a change from 10% to 15% is a 5 percentage point increase, but a 50% relative increase. The formula gives the relative change (50%), not the absolute difference in percentage points.
• Rounding too early – rounding intermediate steps can lead to inaccurate final results. Keep full precision until the final step, then round to the desired number of decimal places.

Limitations and Alternatives

Percentage change works best when the original value is positive and not too close to zero. When the original value is zero, the formula is undefined because division by zero is not possible. In such cases, you cannot calculate a meaningful percentage change; you might instead report the absolute difference or simply state that the value went from zero to some positive number.

For very small original values, percentage change can be extremely large and may exaggerate the practical significance. For example, a change from 1 to 3 is a 200% increase, but the absolute difference is only 2 units. In these situations, consider reporting both the absolute difference and the percentage change.

Alternatives to percentage change include:

• Absolute difference – simply the new value minus the original value (e.g., 25 units).
• Relative difference with a different base – sometimes the average of the two values is used as the denominator (e.g., for symmetric comparisons). This is called the “relative percent difference� and is used in some scientific contexts.
• Logarithmic change – for time series with exponential growth, the natural log of the ratio (ln(new/original)) is sometimes used because it is symmetric and additive over time.

Choose the method that best fits your data and the question you are trying to answer. For most everyday comparisons, the standard percentage change formula is appropriate.

Frequently Asked Questions

What is the formula for percentage change?

The formula is: ((New Value − Original Value) / |Original Value|) × 100. For example, if a price goes from $50 to $75, the percentage change is ((75−50)/50) × 100 = 50%.

How do I calculate a percentage decrease?

Use the same formula. If the new value is lower than the original, the result will be negative. For example, from 80 to 60: ((60−80)/80) × 100 = −25%, which is a 25% decrease.

What if the original value is zero?

You cannot calculate a percentage change when the original value is zero because division by zero is undefined. In that case, report the absolute difference or simply state that the value increased from zero to the new number.

Is percentage change the same as percentage difference?

No. Percentage change uses the original value as the base, while percentage difference typically uses the average of the two values as the base. For example, from 10 to 20: percentage change is 100%, but percentage difference is (20−10)/((10+20)/2) × 100 = 66.67%.

Why do we use absolute value in the denominator?

Using the absolute value ensures that the sign of the result correctly reflects the direction of change, even when the original value is negative. Without it, a change from −10 to −5 would incorrectly show a negative percentage instead of a positive improvement.

Can percentage change be more than 100%?

Yes. If the new value is more than double the original, the percentage change exceeds 100%. For example, from 50 to 150 is a 200% increase. There is no upper limit for percentage increases; decreases are capped at −100% (when the new value is zero).

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in old | Starting value | - | 50 | 0
in new | New value | - | 75 | 0
out pct_change | Percentage change | % | ((new - old) / abs(old)) * 100 | 2
out difference | Absolute difference | - | abs(new - old) | 2