Percentage Increase and Decrease: Formula and Common Mistakes

Percentage change compares a new value with an old value. It is useful for tracking a price, usage total or measurement over time. The old value is the baseline: choosing a different baseline changes the answer.

Use the old value as the denominator

Percentage change = (new value − old value) / old value × 100%

1. Subtract the old value from the new value.
2. Divide that difference by the old value.
3. Multiply by 100 and attach the percent sign.

For a price changing from 80 to 100, the difference is 20. Dividing by 80 gives 0.25, so the increase is 25%. Enter old value 80 and new value 100 in the Percentage Change Calculator to check it.

For positive starting values, a positive result means an increase and a negative result means a decrease. No change gives 0%.

Reversing the change changes the baseline

Going from 100 down to 80 is (80 − 100) / 100 × 100 = −20%. It is not −25%, because the starting value is now 100 rather than 80.

The middle row removes 20% of 120, which is 24. Equal percentage increases and decreases therefore do not generally cancel. Multiplying the factors makes this clear: 1.20 × 0.80 = 0.96.

Percentage points are not percentage change

If a rate moves from 5% to 6%, it rises by 1 percentage point. Relative to the original 5%, the increase is (6 − 5) / 5 × 100 = 20%. State which measure you mean; saying only “up 1%” is ambiguous.

The calculator accepts numeric old and new values. Entering 5 and 6 gives the relative 20% change; it does not label the one-percentage-point difference for you.

Zero and negative baselines require care

An old value of zero cannot be used as the denominator. A change from zero to 10 is an increase of 10 units, but its ordinary percentage change is undefined. The calculator rejects zero rather than showing Infinity. Describe the absolute change or select a different, justified measure.

Negative baselines are mathematically allowed by this tool, but the sign can be counterintuitive. From −100 to −50 it returns −50% using the stated signed-denominator formula, even though the number becomes less negative. Do not automatically label that result a deterioration or a 50% decrease in a business report. Explain the original numbers and use a convention appropriate to the subject.

Choose the tool that matches your question

• “What is 15% of 200?” Use the Percentage Calculator.
• “What is the price after a 15% reduction?” Use the Discount Calculator.
• “How much did 200 change to reach 230?” Use percentage change: +15%.

Keep original, unrounded values when available and round the final percentage for display. Do not compare totals from unequal periods without considering the difference in duration. For adding a percentage to a restaurant bill, see the tip and total-bill guide.

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