Percentage increase turns a raw change into a relative one. A $20 rise means little on its own; as a percentage of the starting value it becomes comparable across prices, populations, and time periods. The formula is short, but the base value trips up almost everyone at least once.
The formula
Percentage increase = (new value – old value) / old value x 100. Subtract the old value from the new one, divide by the old value, multiply by 100. The old value is always the denominator, because the change is measured relative to where you started.
Worked example: a price rises from $80 to $120. Change = 120 – 80 = 40. Divide by the old value: 40 / 80 = 0.5. Multiply by 100: 50%. The price rose 50%.
Percentage decrease
The same formula gives a negative answer for a fall, which you report as a decrease. A price falls from $120 to $90. Change = 90 – 120 = -30. Divide by the old value: -30 / 120 = -0.25, a 25% decrease. Note the asymmetry: $80 to $120 is +50%, but $120 back to $80 is -33.3%, because the base changed. Both are correct; they just measure from different starting points.
A fall of more than 100% is impossible for quantities that cannot go negative, like prices. If your calculation says -120%, you divided by the wrong value or mixed up old and new.
Chained increases
Two 10% increases do not make a 20% increase. Start at $100: after 10% it is $110, after another 10% it is $121. The total increase is 21%, because the second increase applies to the higher base. Multiply the factors instead: 1.10 x 1.10 = 1.21, a 21% rise. The same applies to discounts: two 20% discounts leave 0.80 x 0.80 = 0.64, a 36% total reduction, not 40%.
To reverse an increase, divide, do not subtract. After a 50% rise from $80 to $120, returning to $80 needs a 33.3% fall, not a 50% fall.
Common traps
Dividing by the new value instead of the old one is the top error. Confusing percentage points with percent is the second: an interest rate rising from 3% to 4% rises by 1 percentage point, which is a 33.3% relative increase. And quoting a percentage without its base invites nonsense: “sales doubled” is clear, “sales rose 200%” needs the starting figure to mean anything.
Percentage points in polls and rates
When the underlying numbers are already percentages, report changes in percentage points to avoid confusion. A poll moving from 42% to 48% rises by 6 percentage points. As a relative change that is 6 / 42 x 100 = 14.3%, which sounds much bigger and means something different.
News reports that say “support rose 14%” when they mean 6 points are technically describing the relative change, but most readers hear 14 points. If you write about percentages, state both: “rose 6 points, from 42% to 48%”. That one sentence removes all ambiguity.
A final example from everyday life: a salary rising from $50,000 to $55,000 is a 10% increase, since 5,000 / 50,000 = 0.10. If prices also rose 4% in the same year, the real increase is roughly 10% minus 4%, about 6%, though the exact real calculation divides the factors: 1.10 / 1.04 = 1.0577, a 5.8% real rise. Nominal and real increases answer different questions, so state which one you mean.
Try it faster with the tool
You can follow every step above by hand, but the free Percentage Increase Calculator — Percentage Change Between Two Numbers does the arithmetic for you. Enter your numbers and it gives the answer right away, so you can check your hand calculation or skip straight to the result.
Quick tips
- Increase = (new – old) / old x 100.
- The old value is always the denominator.
- Chain increases by multiplying factors, not adding percentages.