Everyday money
Percentage vs. percentage points: Definition, Formula and Example
Percentage points measure the arithmetic difference between percentage rates; percentage change measures the difference relative to a starting value.
Scope: General financial concept; examples are hypothetical.
Other names and related labels: Relative percentage change; Percentage-point change; Basis points.
How it works
A move from 5% to 6% is one percentage point but a 20% relative increase in the rate. A basis point is one hundredth of a percentage point. Always name the base when describing a percentage increase, discount, tip or margin.
Relative change = (new value − old value) / old value × 100%; percentage-point change = new percentage − old percentage
Relative change is undefined when the old value is zero. Negative starting values require additional interpretation; a percentage-point difference does not require division.
An interest rate moves from 5% to 6%
Compare the quoted rate figures, not the resulting loan payment.
- Percentage-point increase: 6 − 5 = one point.
- Relative increase: (6 − 5)/5 = 20%.
- One percentage point equals 100 basis points.
The rate rises by one percentage point, or 100 basis points; its relative increase is 20%.
Both percentages use the same rate definition and period; no claim that a payment rises by 20%.
The worked example uses the assumptions above. Related tools may model a different scope; check their descriptions before comparing results.
A discount and an equal percentage increase do not cancel
Reducing $100 by 20% gives $80; increasing $80 by 20% gives $96. The second change uses a smaller base. Recovering the original $100 requires a 25% increase from $80.
Explore with a calculator
- Percentage Calculator
Compare percentages, relative changes and percentage-point differences.
- Discount Calculator
Apply discounts and inspect the base price.
- Tip and Bill Split Calculator
Calculate an entered tip and bill allocation without implying a local tipping rule.
Sources and checks
Definition and example arithmetic checked . Sources explain the concepts; numerical examples use the assumptions stated above.
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