Percent Change Calculation Formula

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 formula is straightforward: subtract the old value from the new value, divide by the old value, then multiply by 100. A positive result is a percentage increase, a negative result is a percentage decrease.

Formula

In words: Percent change = (New value − Old value) ÷ Old value × 100

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

• V_old – the original or baseline value (no unit, any consistent unit works)
• Vnew – the value after the change (same unit as V_old)
• %Δ – the percent change, expressed as a percentage (can be positive, negative, or zero)

The formula is the same whether the change is an increase or a decrease. If the new value is larger, the numerator is positive and you get a positive percent change (increase). If the new value is smaller, the numerator is negative and you get a negative percent change (decrease). If the two values are equal, the result is 0%.

Worked Example

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

1. Subtract the old value from the new value: 75 − 50 = 25
2. Divide that difference by the old value: 25 ÷ 50 = 0.5
3. Multiply by 100 to get a percentage: 0.5 × 100 = 50%

The result is a 50% increase. The calculator rounds to two decimal places, so it displays 50.00%. If you instead entered new = 25, the calculation would be (25 − 50) / 50 × 100 = −50%, a 50% decrease.

When to Use Percent Change

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

• Price changes: a product goes from $20 to $25 – that’s a 25% increase.
• Population growth: a town grows from 10,000 to 12,000 – that’s a 20% increase.
• Test scores: a student improves from 60% to 75% – that’s a 25% increase (relative to the original score).
• Financial returns: an investment grows from $1,000 to $1,200 – that’s a 20% return.
• Scientific measurements: a reaction yield rises from 0.5 g to 0.7 g – that’s a 40% increase.

The key is that the old value is the reference point. Percent change always compares the new value to the old value, not the other way around.

How to Read the Result

A positive result means the new value is larger than the old value. A negative result means it is smaller. A zero result means no change. The magnitude tells you how large the change is relative to the starting point.

For example, a 50% increase means the new value is 1.5 times the old value. A 100% increase means the new value is double the old value. A 100% decrease would mean the new value is zero, which is the lowest possible value for a decrease (you cannot go below zero for most physical quantities).

Percent change is not the same as percentage points. If a tax rate goes from 10% to 15%, that is a 5 percentage point increase, but a 50% increase in the tax rate (because 5/10 = 0.5). Always clarify which one you mean in reports or conversations.

Common Mistakes and How to Avoid Them

• Dividing by the new value instead of the old value. The formula always divides by the old value. Dividing by the new value gives a different number and is a common error.
• Mixing up increase and decrease signs. A decrease will always give a negative result. If you get a positive result when you expected a decrease, check your subtraction order.
• Using inconsistent units. Both values must be in the same unit. You cannot compare 5 meters to 500 centimeters directly; convert one first (500 cm = 5 m, so the change is 0%).
• Rounding too early. If you round intermediate steps, you may get a slightly different final answer. Keep full precision until the end, then round to the desired number of decimal places.
• Forgetting to multiply by 100. The raw fraction (new−old)/old is a decimal like 0.5, not a percentage. Multiply by 100 to express it as 50%.

Also note that percent change is undefined when the old value is zero, because you cannot divide by zero. In that case, percent change is not a meaningful measure; you might instead report the absolute difference or use a different metric.

Limits of the Formula

The percent change formula is simple and widely used, but it has limitations:

• Zero or negative old values. If the old value is zero, the formula is undefined. If the old value is negative (e.g., temperature changes from −10°C to 5°C), the percent change can be misleading because the sign of the denominator affects the interpretation. For example, going from −10 to 5 gives (5 − (−10)) / (−10) × 100 = −150%, which looks like a decrease even though the temperature rose.
• Not symmetric. An increase from 50 to 75 is a 50% increase, but a decrease from 75 to 50 is a 33.33% decrease. The percentage depends on which value is the reference.
• Large changes can exceed 100%. A value can increase by more than 100% (e.g., from 10 to 30 is a 200% increase). This is fine mathematically, but some people find it counterintuitive.
• Small bases amplify changes. A change from 1 to 2 is a 100% increase, while a change from 100 to 101 is only a 1% increase. The absolute difference is the same (1), but the percent change differs greatly.

For these reasons, always consider the context. Percent change is most meaningful when the old value is positive and reasonably large relative to the change.

Percent Change vs. Percentage Difference

People often confuse percent change with percentage difference. The two are related but not the same:

• Percent change uses the old value as the denominator: (new − old) / old × 100.
• Percentage difference uses the average of the two values as the denominator: |new − old| / ((old + new)/2) × 100. It is always positive and is used when comparing two values without a clear “before� and “after.�

For example, comparing 50 and 75: percent change is +50% (from 50 to 75), but the percentage difference is |75−50| / ((50+75)/2) × 100 = 25 / 62.5 × 100 = 40%. The percentage difference is often used in scientific comparisons where neither value is the baseline.

Frequently Asked Questions

How do I calculate percent change in Excel?

In Excel, if the old value is in cell A1 and the new value is in B1, enter the formula =(B1-A1)/A1 in another cell, then format that cell as a percentage. Excel will multiply by 100 automatically when you apply the percentage format. Alternatively, use =(B1/A1)-1, which gives the same result.

What is the difference between percent change and percent error?

Percent change compares a new value to an old value, while percent error compares a measured or estimated value to a known true value. Percent error is calculated as |measured − true| / |true| × 100, and it is always positive. Percent change can be positive or negative and uses the old value as the reference, not a “true� value.

Can percent change be more than 100%?

Yes. If the new value is more than double the old value, the percent change exceeds 100%. For example, going from 10 to 30 is a 200% increase. There is no upper limit for percent increase; percent decrease is capped at 100% (which would mean the new value is zero).

Why do I get a negative percent change when the value increased?

You likely subtracted in the wrong order. The formula is (new − old) / old × 100. If you subtract old from new, you get a positive numerator for an increase. If you accidentally do (old − new) / old × 100, you will get a negative result for an increase. Double-check your subtraction order.

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

Rearrange the formula: old = new / (1 + percent change/100). For example, if the new value is 120 and the percent increase is 20%, then old = 120 / (1 + 0.20) = 120 / 1.20 = 100. For a decrease of 20%, use old = new / (1 − 0.20).

What if the old value is zero?

Percent change is undefined when the old value is zero because you cannot divide by zero. In that case, you cannot use the formula. Instead, report the absolute change (new − old) or describe the change qualitatively (e.g., “increased from zero to 5�).

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in old | Old 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