How do I calculate a percentage change from a starting amount?
Quick answer
Subtract the starting amount from the new amount, divide that difference by the starting amount, then multiply by 100 and write the result as a percent. Formula: ((new amount − starting amount) ÷ starting amount) × 100. The starting amount is the reference because the calculation asks how large the change is compared with where you began. [S1]
The question, the details, the next step.
I know how much something changed, but how do I turn that into a percentage of where it started?
Compare the change with the starting amount—not with the new amount. The calculation is:
((new amount − starting amount) ÷ starting amount) × 100
First subtract to find the change. Then divide by the starting amount to find what fraction of that amount the change represents. Multiplying by 100 converts the fraction to a percentage. The original amount is the reference for this one-time percentage-change calculation. [S1]
Keep the subtraction order straight: new minus starting. A positive result indicates an increase; a negative result indicates a decrease.
Could you show that with a nonfinancial example and label each number?
Suppose a plant is 20 centimeters tall at the start of a week and 25 centimeters tall at the end. These are example measurements, not a claim about a particular plant.
- Starting amount: 20 cm.
- New amount: 25 cm.
- Change: 25 − 20 = 5 cm.
- Divide by the starting amount: 5 ÷ 20 = 0.25.
- Convert to a percent: 0.25 × 100 = 25%.
So, under these example assumptions, the plant’s height increased by 25% compared with its starting height. The 20 cm is the reference because the question is how large the 5 cm increase is relative to the height at the beginning. Using 25 cm instead would compare the change with the ending height, which answers a different question.
What if the amount went down, or the difference comes out as a decimal?
Use the same formula; a decrease will produce a negative result. For example, assume a stack of paper goes from 40 sheets to 30 sheets. The change is 30 − 40 = −10 sheets. Divide by the starting amount: −10 ÷ 40 = −0.25. Multiply by 100 to get −25%, so the amount decreased by 25%.
A decimal before conversion is normal: 0.25 × 100 = 25, so the percentage is 25%; 0.08 × 100 = 8, so it is 8%. Keep the units consistent for the starting and new amounts. In words, you can say “decreased by 25%” to make the direction clear.
How can I check my work and explain it clearly to someone else?
Check that you divided by the starting amount and that the sign matches the direction of change. You can also check by applying the percentage as a decimal to the starting amount, then adding that change for an increase or subtracting its size for a decrease.
Copyable explanation: “[Starting amount] changed to [new amount]. The change was [new amount − starting amount]. Dividing that change by [starting amount] gives [decimal]; multiplying by 100 gives [percentage]%. Therefore, it [increased/decreased] by [percentage]% compared with the starting amount.”
This method compares two amounts in the same units. It calculates the percentage change from the values you provide; it does not establish whether a particular measurement was collected accurately. [S1]
A practical checklist
Write down the starting amount and the new amount, with units.
Subtract: new amount minus starting amount.
Divide the difference by the starting amount.
Multiply by 100 and write the result as a percentage.
Check that the sign and wording match an increase or decrease.
A few more useful answers
Why do I divide by the starting amount?
Because percentage change asks what fraction of the starting amount the difference represents. Dividing by the new amount uses a different reference. [S1]
Should I include a minus sign for a decrease?
The calculation gives a negative percentage for a decrease. In plain language, you can state the size and say it “decreased by” that percentage.
Can I calculate percentage change if the starting amount is zero?
Not with this formula: division by zero is undefined. State the two amounts and explain that this percentage-change calculation does not apply when the starting amount is zero.
Sources
References used for this guide.
- [S1] OpenStax Intermediate Algebra: Use a Problem-Solving Strategy openstax.org · Checked