To calculate percentage increase, subtract the original value from the new value, divide by the original value, then multiply by 100: ((new − original) ÷ original) × 100. For example, a value that rises from 80 to 100 increases by 25%, because the increase of 20 is one-quarter of the starting value.
1. Find the increase, divide by the original, and multiply by 100
Let O be the original value and N the new value. The formula is:
Percentage increase = ((N − O) ÷ O) × 100
- Subtract the original value from the new value: N − O.
- Divide that difference by the original value: (N − O) ÷ O.
- Multiply by 100 to express the result as a percentage.
For a change from 80 to 100, the increase is 100 − 80 = 20. Then 20 ÷ 80 = 0.25, and 0.25 × 100 = 25% increase. The denominator is 80 because percentage increase measures the change against the starting amount. Monash University uses this same final-minus-initial calculation for percentage change: Core Concepts of Financial Mathematics.
2. Compare the new value with 100% of the original
Think of the original value as 100%. Divide the new value by the original to find what percentage of that baseline the new value represents, then subtract 100 percentage points.
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- For 80 to 100, calculate 100 ÷ 80 = 1.25, or 125%.
- Subtract the original 100%: 125% − 100% = 25% increase.
This method makes the distinction between the final amount and the increase explicit: 100 is 125% of 80, so the increase is 25%, not 125%.
3. Use a growth multiplier
Divide the new value by the original to get a multiplier. Subtract 1, then multiply by 100:
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Percentage increase = ((N ÷ O) − 1) × 100
For 80 to 100: ((100 ÷ 80) − 1) × 100 = 25%. This is the same calculation rearranged, and it is convenient when working with successive changes because each rate corresponds to a multiplier.
Which method should you use?
| Method | Best for | Calculation for 80 to 100 |
|---|---|---|
| Increase ÷ original | Showing each step and identifying the baseline | (100 − 80) ÷ 80 × 100 = 25% |
| Compare with 100% | Understanding how large the new value is relative to the original | 100 ÷ 80 = 125%; 125% − 100% = 25% |
| Growth multiplier | Checking a result or chaining changes | (100 ÷ 80 − 1) × 100 = 25% |
All three methods are equivalent. Monash University’s financial mathematics material also explains finding a new value as a proportion of the original when applying a percentage change: Core Concepts of Financial Mathematics.
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Common mistakes and edge cases
Using the new value as the denominator
For a rise from 80 to 100, dividing the increase of 20 by 100 gives 20%. That answers a different question: the increase as a share of the ending value. Percentage increase uses the starting value, so the correct calculation is 20 ÷ 80 × 100 = 25%.
Interpreting a decrease as an increase
Keep the subtraction order as new value minus original value. If the result is negative, the value decreased. For example, Monash’s example of a car value changing from $10,000 to $8,000 gives (8,000 − 10,000) ÷ 10,000 × 100 = −20%, meaning a 20% decrease.
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Starting from zero
If the original value is zero, the formula divides by zero and the percentage change is undefined. Report the absolute change instead, or use a measure suited to the particular context; do not describe an ordinary percentage increase from zero.
Applying successive percentage changes
When each change is based on the value after the preceding change, apply the next rate to that updated value. The rates compound through multiplication of their factors; adding the rates is only valid when they use the same base.
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Calculating a new value from a percentage rate
Percentage increase can also mean finding the amount after applying a rate, which is different from measuring the percentage change between two known values. Convert the rate to a decimal and multiply the original by 1 plus that decimal. For a 20% increase, multiply by 1.20. For a decrease, multiply by 1 minus the rate; Monash’s example of a $120 bag discounted by 20% gives $120 × 0.80 = $96. The same source presents calculating the percentage amount and adjusting the original as an equivalent approach.
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