Percent Change Formula & How to Calculate It

This calculator works out the percent change between two numbers: you enter an original (old) value and a new value, and it returns the percentage increase or decrease. The result tells you how much the new value has grown or shrunk relative to the original, expressed as a percentage. Use it for prices, populations, test scores, or any before-and-after comparison where the direction of change matters.

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 = percent change (can be positive, negative, or zero)

The result is a percentage. A positive number means an increase; a negative number means a decrease. The denominator is always the original value, not the new one — that is the most common mistake people make.

Worked Example

Using the default values from the calculator: 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 to get a percentage: 0.5 × 100 = 50%

So the percent change is 50%, meaning the new value is 50% larger than the original. The calculator shows the same result: 50.00%.

When to Use Percent Change vs. Percentage Points

Percent change is used when you want to express how much a quantity has grown or shrunk relative to its starting point. For example, if a store’s sales went from 200 items to 260 items, that is a 30% increase. If a city’s population dropped from 10,000 to 9,000, that is a 10% decrease.

Do not confuse percent change with percentage points. If an interest rate rises from 4% to 5%, that is a 1 percentage point increase, but the percent change is 25% (because 1 ÷ 4 = 0.25). The two numbers answer different questions: percentage points measure the raw difference, while percent change measures the difference relative to the starting value.

How to Read the Result

The sign of the result tells you the direction:

• Positive (e.g., +25%) → the new value is higher than the original.
• Negative (e.g., −25%) → the new value is lower than the original.
• Zero → the two values are equal.

The magnitude tells you the size of the change relative to the original. A 100% change means the value doubled; a 200% change means it tripled. A 50% decrease means the value is half of the original.

Common Mistakes and Pitfalls

• Using the new value as the denominator. The formula always divides by the original value. If you divide by the new value, you get a different (and usually wrong) number.
• Mixing up the order. (New − Old) is not the same as (Old − New). Swapping them flips the sign, turning an increase into a decrease.
• Forgetting to multiply by 100. The raw ratio (e.g., 0.5) is not a percentage; you must multiply by 100 to express it as one.
• Rounding too early. If you round intermediate steps, the final percentage can be off. Keep full precision until the end, then round to the desired number of decimal places.
• Ignoring the sign. A −20% change is not the same as a 20% change; the first is a decrease, the second is an increase.

Limits and When the Formula Fails

The formula works whenever the original value is not zero. If the original value is zero, division by zero is undefined — you cannot calculate a percent change. For example, going from 0 to 10 has no meaningful percent change; some people say it is “infinity percent,� but that is not a valid mathematical result.

Also, the formula is symmetric in the sense that a 50% increase followed by a 50% decrease does not return to the original value. Starting at 100, a 50% increase gives 150, then a 50% decrease gives 75. This is because the second percentage is applied to the new, larger base. For reversing a change, use the formula for percent change in reverse: to undo a 50% increase, you need a 33.3% decrease (because 50 ÷ 150 = 0.333).

Frequently Asked Questions

What is the percent change from 25 to 30?

Using the formula: ((30 − 25) ÷ 25) × 100 = (5 ÷ 25) × 100 = 20%. So it is a 20% increase.

How do I calculate percent decrease?

Same formula. If the new value is less than the original, the result will be negative. For example, from 80 to 60: ((60 − 80) ÷ 80) × 100 = (−20 ÷ 80) × 100 = −25%. That is a 25% decrease.

What if the original value is zero?

You cannot calculate percent change because division by zero is undefined. In that case, report the absolute difference or simply state that the value went from 0 to the new number, without a percentage.

Is percent change the same as percentage difference?

No. Percent change uses the original value as the denominator and is directional (positive for increase, negative for decrease). Percentage difference uses the average of the two values as the denominator and is always positive. For example, from 10 to 20: percent change is +100%, but percentage difference is (10 ÷ 15) × 100 = 66.67%.

How do I find the original value if I know the new value and the percent change?

Rearrange the formula: Original = New ÷ (1 + (percent change ÷ 100)). For a 20% increase to reach 120: Original = 120 ÷ 1.20 = 100. For a 20% decrease to reach 80: Original = 80 ÷ 0.80 = 100.

Why do we multiply by 100?

Because a percentage is a fraction out of 100. The raw ratio (new − old) ÷ old gives a decimal like 0.25. Multiplying by 100 converts it to 25%, which is more intuitive for comparison.

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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
out diff | Absolute difference | - | new - old | 2