Percent Change Calculator: Formula & How to Use

This calculator works out the percentage increase or decrease between two numbers. You enter the original (starting) value and the new (final) value, and it returns the percent change, showing whether it went up or down. The result is a plain percentage, like +15% or -8%, that you can use for prices, scores, measurements, or any before-and-after comparison.

Formula

The percent 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 value (the starting point, before the change)
• V_new = the new value (after the change)
• %Δ = the percent change, expressed as a percentage

If the result is positive, it is a percentage increase. If negative, it is a percentage decrease. The formula works for any two numbers, but it always uses the original value as the denominator — that is the key to understanding what the percentage actually means.

Worked Example

Using the calculator defaults: original value = 100, new value = 125.

1. Subtract the original from the new: 125 − 100 = 25
2. Divide by the original: 25 ÷ 100 = 0.25
3. Multiply by 100: 0.25 × 100 = 25%

The percent change is 25%, meaning the new value is 25% larger than the original. The calculator also shows the absolute difference (25) for reference.

When to Use Percent Change

Percent change is the standard way to describe how much something has increased or decreased relative to its starting point. Common uses include:

• Price changes: A product goes from $50 to $60 — that is a 20% increase.
• Grades and scores: A test score rises from 80 to 90 — that is a 12.5% improvement.
• Population or sales growth: A town grows from 10,000 to 11,000 — a 10% increase.
• Weight or measurements: A recipe calls for 200 g of flour but you use 250 g — that is a 25% increase.

It is especially useful when comparing changes of different magnitudes. A $10 increase on a $50 item is 20%, but the same $10 increase on a $1,000 item is only 1%. Percent change puts those into perspective.

How to Read the Result

The result tells you the size of the change relative to the original value, not the absolute difference. For example:

• +100% means the new value is double the original (e.g., 50 → 100).
• −50% means the new value is half the original (e.g., 80 → 40).
• +300% means the new value is four times the original (e.g., 10 → 40).

A common confusion: a 100% increase is not the same as a 100% decrease. A 100% decrease would bring the value to zero (e.g., 50 → 0), but you cannot have a decrease greater than 100% because that would imply a negative value — the formula will give a result below −100% only if the new value is negative, which may not make sense in your context.

Common Mistakes and Pitfalls

• Using the new value as the denominator: Some people mistakenly divide by the new value. That gives a different number and is not percent change. Always divide by the original value.
• Confusing percentage points with percent change: If an interest rate goes from 4% to 5%, that is a 1 percentage point increase, but a 25% increase relative to the original rate. Percent change is relative, not absolute.
• Rounding too early: If you round intermediate steps, you can get a slightly different final answer. Keep full precision until the end, then round to the desired decimal places.
• Zero original value: If the original value is zero, the formula divides by zero and is undefined. You cannot calculate a meaningful percent change from zero; instead, describe the change in absolute terms.
• Negative original values: If the original value is negative (e.g., −10 to −5), the formula still works mathematically, but the interpretation can be tricky. A change from −10 to −5 gives +50%, even though the value increased (became less negative). Always consider whether percent change makes sense for your data.

Limits of the Formula

The percent change formula assumes a simple, linear relationship between the two values. It does not account for compound growth over multiple periods — for that you would use the compound annual growth rate (CAGR). It also does not tell you the actual magnitude of the change, only the relative one. For example, a 50% increase on $2 is only $1, while a 10% increase on $1,000 is $100 — the percentage alone does not convey the real impact.

When the original value is very small, even a tiny absolute change can produce a huge percentage. A jump from 1 to 2 is a 100% increase, but if you are measuring something like a defect rate, that might be negligible in absolute terms. Always look at the absolute difference alongside the percentage.

Frequently Asked Questions

What is the difference between percent change and percentage difference?

Percent change uses the original value as the denominator and describes a change over time or between two states. Percentage difference (also called relative difference) uses the average of the two values as the denominator and is used to compare two values without a clear “before� and “after�. For example, going from 100 to 120 is a 20% change, but the percentage difference between 100 and 120 is 18.18% (20 ÷ 110 × 100).

How do I calculate percent change when the original value is zero?

You cannot — the formula would divide by zero. In that case, the concept of percent change is undefined. Instead, report the absolute change (e.g., “increased by 5 units�) or use a different metric like fold change (new value ÷ original value, but that also fails when original is zero).

Can percent change be more than 100%?

Yes, if the new value is more than double the original. For example, 50 → 150 is a 200% increase. There is no upper limit for increases; only decreases are capped at 100% (which brings the value to zero).

What is the percent change from 80 to 100?

Using the formula: ((100 − 80) ÷ 80) × 100 = (20 ÷ 80) × 100 = 25%. So it is a 25% increase.

Is percent change the same as percent error?

No. Percent error compares a measured value to a known true value, and the denominator is the true value (or sometimes the absolute value of the true value). Percent change compares two values over time, and the denominator is always the original value. They use similar math but answer different questions.

How do I reverse a percent change?

To undo a percentage increase of X%, divide the new value by (1 + X/100). For example, if something increased by 25% to 125, the original is 125 ÷ 1.25 = 100. To undo a decrease of Y%, divide by (1 − Y/100). This works because the original value was multiplied by that factor.

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in a | Original value | - | 100 | 0
in b | New value | - | 125 | 0
out pct | Percent change | % | ((b - a) / a) * 100 | 2
out diff | Absolute difference | - | b - a | 2