How to calculate percentage change using the right starting value

For a positive original value, calculate percentage change as ((new value − original value) ÷ original value) × 100%. The numerator is the actual change. The denominator is the value before that change, not the larger number or whichever number appears first in a sentence.

Put both values in the same unit before subtracting them. Read the direction of the comparison carefully: “from 80 to 100” starts at 80, while “from 100 to 80” starts at 100. If the wording is unclear, state which value you are treating as the original.

Keep the sign while calculating. A positive result means an increase and a negative result means a decrease. In a final sentence, write either “a change of −20%” or “a decrease of 20%”; the word decrease already supplies the direction.

Consider an invented practice question: a club recorded 80 attendees at one event and 100 at the next. The increase is 100 − 80 = 20 attendees. Relative to the original 80, that is (20 ÷ 80) × 100% = 25%. The attendance increased by 25%.

Now reverse the comparison. Going from 100 attendees to 80 gives a change of 80 − 100 = −20. The percentage change is (−20 ÷ 100) × 100% = −20%, so attendance decreased by 20%. The difference has the same size, but the starting values differ.

Check by reconstructing the new value. An increase of 25% from 80 gives 80 × 1.25 = 100. A decrease of 20% from 100 gives 100 × 0.80 = 80. If your percentage does not reproduce the new value, check the denominator and sign.

When the values are already percentages, subtracting them gives a difference in percentage points. In a fictional practice dataset, suppose the share choosing option A rises from 40% to 50%. That is an increase of 10 percentage points.

The relative percentage increase in that share is different: ((50 − 40) ÷ 40) × 100% = 25%. You can check this as 40% × 1.25 = 50%. Write which measure you mean; “increased by 10%” does not describe a rise from 40% to 50%.

If the question asks about a share, compare the shares. If it asks about the number of people, you also need the relevant group sizes. A larger percentage does not by itself establish a larger headcount when the groups differ in size.

For repeated changes, each percentage applies to the value at that stage. Starting at 100, an increase of 10% gives 110. Another increase of 10% gives 110 × 1.10 = 121. The total increase from the original 100 is 21%, rather than 20%.

An increase followed by an equal percentage decrease does not generally return you to the start. Starting at 100, increasing by 20% gives 120. Decreasing that new value by 20% gives 120 × 0.80 = 96. The second change uses 120 as its base.

Use multipliers to keep the stages visible: multiply by 1 + r/100 for an increase of r%, or 1 − r/100 for a decrease of r%. Write each stage on its own line and keep unrounded values until the final answer, unless the question specifies otherwise.

For a new question, fill in: “Original value and unit: __. New value and unit: __. Difference: new − original = __. Percentage change: difference ÷ original × 100% = __. Interpretation: __. Check: original × change multiplier = new.” This makes an incorrect base easier to spot.

If the original value is zero, this formula would divide by zero, so it cannot give a percentage change. Report the actual difference and explain the limitation. For example, a rise from 0 to 5 is an increase of 5 units, but it has no percentage increase under this formula.

This guide uses positive starting values. If a problem crosses zero or begins with a negative value, use the definition specified by the question or ask for clarification; the usual increase and decrease language can be misleading. Always finish by naming the quantity, the comparison direction and the measure you calculated.