Percent Change Formula: How to Calculate

This calculator works out the percentage change between an original value and a new value. You enter the starting number and the final number, and you get the percentage increase or decrease, along with the absolute difference. The first result shown is the percent change, which is positive for an increase and negative for a decrease.

Formula

The percentage change formula is:

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

In symbols: %Δ = (V_new − V_old) / V_old × 100

• V_old – the original (starting) value, in any unit
• V_new – the new (final) value, in the same unit
• %Δ – the percent change, a dimensionless number

The formula works for any quantity that can be measured on a ratio scale – prices, populations, temperatures (in Kelvin), weights, scores, etc. The result tells you how much the new value has grown or shrunk relative to the original, expressed as a percentage.

Worked Example

Using the default values from the calculator above (original = 50, new = 75):

1. Subtract the original from the new: 75 − 50 = 25
2. Divide by the original: 25 ÷ 50 = 0.5
3. Multiply by 100: 0.5 × 100 = 50%

The percent change is 50%, meaning the new value is 50% larger than the original. The absolute difference is 25 (75 − 50).

If the new value were 40 instead, the calculation would be: (40 − 50) ÷ 50 × 100 = −20%, a 20% decrease.

When to Use Percent Change

Percent change is used whenever you want to express a change relative to the starting point, not as an absolute difference. It is the standard way to report:

• Price increases or discounts (e.g., a $10 price rise on a $100 item is 10%)
• Population growth or decline over a period
• Sales or revenue growth quarter-over-quarter
• Test score improvements
• Weight loss or gain
• Inflation rates (CPI changes)

The key advantage is that percent change allows comparison between different-sized bases. A $1 increase on a $2 item (50%) is very different from a $1 increase on a $200 item (0.5%), and percent change makes that clear.

How to Read the Result

A positive result means an increase; a negative result means a decrease. The magnitude tells you the size of the change relative to the original. For example:

• 100% change means the new value is double the original (increase) or zero (decrease)
• 50% change means the new value is 1.5 times the original (increase) or half (decrease)
• 0% means no change

Be careful with the phrase “percentage points� vs. “percent.� If a rate goes from 10% to 15%, that is a 5 percentage point increase, but a 50% increase relative to the original rate. These are different concepts and are often confused in news reports.

Common Mistakes and Pitfalls

• Dividing by the new value instead of the original – always divide by the original (the starting point). Dividing by the new value gives a different number and is not the percent change.
• Unit mix-ups – both values must be in the same unit. You cannot compute percent change from 5 kg to 10 pounds without converting.
• Negative original values – if the original is negative, the formula still works mathematically but the interpretation is tricky. For example, going from −10 to −5: (−5 − (−10)) / (−10) × 100 = −50%, which is a 50% “decrease� even though the value increased. In such cases, percent change is often not meaningful; consider using absolute change.
• Rounding too early – keep full precision during intermediate steps and round only the final result. Rounding early can produce errors of several percentage points.
• Confusing percent change with percentage of – “50% of 100� is 50, but “50% change from 100� is 150. The word “change� is critical.

Limits of the Formula

The formula assumes a simple ratio relationship. It does not account for:

• Compounding – if you want the average annual growth rate over multiple periods, you need the compound annual growth rate (CAGR), not a simple percent change.
• Non-linear relationships – percent change is linear in the difference, so it is not suitable for exponential growth or decay models.
• Zero or negative bases – if the original value is zero, the formula is undefined (division by zero). If it is negative, the result can be misleading as noted above.
• Small bases – with very small original values, even tiny absolute changes produce huge percentage changes. For example, going from 1 to 2 is a 100% increase, but that may not be practically significant.

For these situations, use other metrics like absolute change, CAGR, or log returns.

Percent Change vs. Percentage Difference

These two are often confused. Percent change compares a new value to an original value, using the original as the denominator. Percentage difference compares two values symmetrically, using the average of the two as the denominator:

Percentage Difference = |V1 − V2| / ((V1 + V2)/2) × 100

For example, from 50 to 75: percent change is 50%, but percentage difference is |50−75| / ((50+75)/2) × 100 = 25 / 62.5 × 100 = 40%. Use percent change when there is a clear chronological order (before/after), and percentage difference when comparing two values without a reference point.

Frequently Asked Questions

How do I calculate percent change in Excel?

In Excel, if the original value is in cell A1 and the new value in B1, enter =(B1-A1)/A1 in another cell and format it as a percentage. This gives the percent change directly.

What is the difference between percent change and percentage points?

Percent change is the relative change (new − old) / old × 100. Percentage points are the absolute difference in percentage values. For example, a rate moving from 10% to 15% is a 5 percentage point increase but a 50% increase (relative to the original 10%).

Can percent change be negative?

Yes. A negative percent change indicates a decrease. For instance, going from 80 to 60 is (60−80)/80 × 100 = −25%, meaning the value decreased by 25%.

What if the original value is zero?

The formula is undefined because you cannot divide by zero. In such cases, percent change is not meaningful. You can report the absolute change instead, or use a different metric like “increase from zero� which is technically infinite.

How do I calculate percent change from negative to positive?

The formula still works, but the result is often counterintuitive. For example, from −10 to 10: (10 − (−10)) / (−10) × 100 = −200%. This is not a meaningful “percent change� because the base is negative. It’s better to use absolute change or a different measure.

Is percent change the same as percent error?

No. Percent error compares a measured value to a true value, using the absolute value of the error divided by the true value, times 100. Percent change compares two values over time. The formulas are similar but the interpretation and use differ.

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in orig | Original value | - | 50 | 0
in new | New value | - | 75 | 0
out pct | Percent change | % | (new - orig) / orig * 100 | 2
out diff | Absolute difference | - | new - orig | 2