Percent Rate of Change Formula & How to Use It

This calculator works out the percent rate of change between two values: you enter the original (old) value and the new value, and it returns the percentage increase or decrease. The formula is simple: subtract the old value from the new, divide by the old value, then multiply by 100. A positive result means an increase, a negative result means a decrease.

Formula

Percent rate of change = ((new value − original value) ÷ original value) × 100

Where:

• original value – the starting amount, before the change (no unit, or any unit as long as both values use the same one)
• new value – the amount after the change (same unit as original)
• result – expressed as a percentage (%).

The formula works for any quantity that can be measured on a ratio scale: prices, populations, speeds, weights, temperatures (only if using Kelvin), test scores, and so on. The two values must be in the same unit, and the original value must not be zero.

Worked Example

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

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

The percent rate of change is 50%, meaning the new value is 50% larger than the original. The calculator rounds to two decimal places, so if the result were 33.333… it would show 33.33%.

When to Use Percent Change vs. Percentage Points

Percent change tells you how much a value has grown or shrunk relative to its starting point. It is not the same as a change in percentage points. For example, if an interest rate goes from 4% to 5%, the percent change is (5−4)/4 × 100 = 25%, but the rate increased by only 1 percentage point. Both are correct; they answer different questions. Use percent change when you want to describe the relative growth or decline of a single quantity. Use percentage points when you are comparing two percentages directly.

How to Choose the Right Base Value

The choice of the original value matters a lot. The formula always divides by the original (before) value, not the new value. This is the standard convention for percent change. If you reverse the order, you get a different number. For example, going from 50 to 75 is a 50% increase, but going from 75 back to 50 is a 33.33% decrease. Always identify which value came first chronologically or logically, and use that as the denominator.

Common Mistakes and How to Avoid Them

• Using the wrong denominator – always divide by the original value, not the new one.
• Mixing units – both values must be in the same unit (e.g., both dollars, both kilograms). If one is in cents and the other in dollars, convert first.
• Forgetting to multiply by 100 – the raw quotient is a decimal, not a percentage. Multiply by 100 to get the percent.
• Zero original value – division by zero is undefined. If the original value is 0, percent change is not meaningful; describe the change in absolute terms instead.
• Rounding too early – round only at the final step to keep accuracy.

Limits of the Formula

The formula assumes a simple, one-step change between two points. It does not account for the path of change (e.g., multiple steps, compounding). For compound growth over several periods, you need the compound annual growth rate (CAGR) formula: ((final/initial)^(1/n) − 1) × 100, where n is the number of periods. Also, percent change is sensitive to small bases: a change from 1 to 2 is a 100% increase, while a change from 100 to 101 is only 1%, even though the absolute change is the same. Always consider the absolute change alongside the percent change for context.

Frequently Asked Questions

What is the difference between percent change and percent difference?

Percent change uses the original value as the denominator and describes change over time. Percent difference (also called relative difference) uses the average of the two values as the denominator and is used when comparing two values without a clear “before� and “after.� For example, the percent difference between 50 and 75 is (25 / 62.5) × 100 = 40%, while the percent change from 50 to 75 is 50%.

Can percent change be negative?

Yes. A negative result means a decrease. For example, if the original value is 80 and the new value is 60, the percent change is ((60−80)/80) × 100 = −25%, meaning a 25% decrease.

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

Use the formula: =(new - old) / old and then format the cell as a percentage. For example, if old is in A1 and new is in B1, enter =(B1-A1)/A1 in C1 and apply percentage formatting. The result will display as a percentage, such as 50%.

What if the original value is zero?

Division by zero is undefined, so the percent change formula cannot be used. In that case, report the absolute change (the new value itself) or describe the situation qualitatively, such as “increased from zero to 10.�

Does percent change work for negative numbers?

It can, but the interpretation is tricky. For example, going from −10 to −5: ((−5 − (−10)) / −10) × 100 = (5 / −10) × 100 = −50%. The negative sign indicates a decrease, but the actual value moved upward (became less negative). For clarity, it is often better to describe the change in words or use absolute values when dealing with negative bases.

How is percent change different from percentage increase/decrease?

They are the same thing. “Percent increase� and “percent decrease� are just specific cases of percent change. If the result is positive, it is a percent increase; if negative, it is a percent decrease.

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