Name the original value
Percentage change compares the difference with the original value: change divided by original, multiplied by 100. The denominator is the value you started from, not automatically the smaller number. Mark the starting period or group before copying figures from a table.
- Change = new minus original
- Divide by original
- Multiply by 100
Separate percentage points from percentage change
If a rate rises from 20% to 25%, the increase is 5 percentage points. Relative to the original 20%, it is a 25% increase. Both numbers can be correct, so the wording decides which one is required. Look for “percentage points” explicitly.
- Point change: subtract the percentages
- Percentage change: divide the difference by the original percentage
Worked example: keep the base visible
Appointments rise from 480 to 540. The change is 60 and the original is 480, so 60 ÷ 480 × 100 = 12.5%. Dividing by 540 would measure the increase as a share of the new value and answer a different question.
- Original 480
- Change 60
- 60 ÷ 480 = 0.125
- Answer 12.5%
Handle decrease signs and wording
For a decrease, calculate original minus new when the answer expects a positive decrease percentage. If a question asks for signed change, new minus original will be negative. Decide the required form before calculating so a correct magnitude is not paired with the wrong direction.
- Increase and decrease need a direction
- Read the answer units
- Do not drop a minus sign accidentally
Use multipliers for reverse percentages
After a 20% increase, the new value equals original × 1.20. To recover the original, divide the new value by 1.20 rather than subtracting 20% of the new number. Increases and decreases are based on different starting values, so equal percentages do not simply cancel.
- Increase multiplier: 1 + rate
- Decrease multiplier: 1 - rate
- Reverse by dividing by the multiplier
Estimate before selecting
Round the change and base enough to predict the scale. A rise of about 60 on a base near 500 is a little above 10%, so 1.25% or 125% should be rejected immediately. Estimation catches keypad errors and often eliminates options before exact calculation.
- Predict order of magnitude
- Check denominator
- Confirm whether the answer is a percent or points
Frequently asked questions
What is the formula for percentage change?
Change divided by the original value, multiplied by 100.
What is a percentage-point change?
It is the arithmetic difference between two percentages.
How do I reverse a percentage increase?
Divide the final value by one plus the percentage rate written as a decimal.
Which value is the denominator?
Use the original or baseline value identified by the question.
Editorial information
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