How to calculate percentages and percentage change

Three different questions

15% of 200 is 30: multiply 200 by 15 and divide by 100. If 30 is part of 200, it represents 15%: divide 30 by 200 and multiply by 100.

The change from 80 to 100 is 25%: subtract 80 from 100, divide by the initial value 80 and multiply by 100. The denominator explains why returning from 100 to 80 is a 20% decrease, not 25%.

Zeros and negative numbers

A proportion with a zero denominator is undefined. Ordinary percentage change from an initial value of zero is also undefined.

With negative initial values, the signed formula may seem unintuitive. Interpret it in context rather than automatically describing it as financial growth.

1. Choose the operation answering your question.
2. Enter quantities and percentages with their signs.
3. Calculate and check the denominator and units.
4. Copy the result without confusing percentages with percentage points.

Percentages and percentage points

Going from 10% to 15% adds 5 percentage points but represents a relative increase of 50%. These figures describe different things.

Decimal results may be rounded for display. Do not imply more precision than your source data supports; this calculator does not replace financial or tax decisions.

Criteria for reviewing and delivering the result

Separate initial quantity, calculated portion and final amount in an exercise. This prevents copying a reduction as though it were the remainder. Record each percentage’s base when comparing changes. The same absolute difference gives different rates on different bases. When comparing rates that are already percentages, also express percentage points to distinguish movement of the rate from relative change. These descriptions answer related but different questions.

Successive changes use the appropriate base at each stage. A decrease followed by the same rate of increase does not guarantee recovery of the initial amount. Check with small quantities and retain intermediate values before rounding. For discrete units, such as allocated objects, define how fractions are handled and document that rule. The tools provide arithmetic but do not decide which values belong to one collection or whether movement is favourable. Keep the problem and units with the results for understandable review. A clear explanation of the base is often more useful than a percentage displayed with many decimal places. Verify the value copied into the next step so portion and final total are not inadvertently interchanged.