Formula
\text{Percentage Decrease} = \frac{\text{Original Value} - \text{New Value}}{\text{Original Value}} \times 100\%Used to calculate: The percentage by which a value has decreased relative to its original value.
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What Is the Percentage Decrease Formula?
The percentage decrease formula measures how much a value has fallen compared with its original value. It expresses the decrease as a percentage of the original value.
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Formula and Variables
\text{Percentage Decrease} = \frac{O - N}{O} \times 100\%| Symbol | Meaning | Unit |
| O | Original or initial value | Depends on the problem |
| N | New or final value | Depends on the problem |
| Percentage Decrease | Decrease relative to the original value | Percent (%) |
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How to Use the Formula
Identify the original value and the new value. Subtract the new value from the original value to find the decrease. Divide the decrease by the original value, then multiply by 100 to express the result as a percentage.
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When Is This Formula Used?
The percentage decrease formula is used when a quantity becomes smaller and the size of the decrease needs to be expressed relative to its original value.
Common uses:
– Measuring decreases in prices or costs
– Calculating declines in financial or statistical data
– Comparing decreases in measurements or quantities
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Important Notes
– A percentage decrease measures the decrease relative to the original value.
– The original value cannot be zero because division by zero is undefined.
– The original and new values should use the same units before applying the formula.
– A common point of confusion is dividing the decrease by the new value instead of the original value.
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Alternate Forms
Alternate form:
N = O\left(1 - \frac{p}{100}\right)Alternate form:
O = \frac{N}{1 - \frac{p}{100}}—
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