Percentage Calculator — three calculations people actually need
X% of Y, X as a percentage of Y, and percentage change from X to Y.
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Three distinct questions get called "percentage", and picking the wrong one is how a report ends up with a figure nobody can reproduce.
Select the mode above. The result shows which calculation was applied so it can be checked.
Why increases and decreases do not cancel
Revenue rises from 50,000 to 100,000, then falls back to 50,000. The percentage change is not symmetrical:
50,000 → 100,000 +100.00%
100,000 → 50,000 −50.00%Same absolute movement, different percentages, because each is measured against its own starting value. The rise is measured against 50,000; the fall against 100,000.
The practical consequence: a 20% loss requires a 25% gain to recover. A 50% loss requires 100%. A 90% loss requires 900%. This asymmetry is why drawdowns matter more than volatility in anything cumulative.
A related trap in reporting: a conversion rate moving from 2% to 3% is a one percentage point increase and a 50% relative increase. Both are true. Quoting the relative figure without saying so is how a modest improvement gets described as dramatic.
The three calculations
X% of Y — (X ÷ 100) × Y. Discounts, commissions, tips.
X is what % of Y — (X ÷ Y) × 100. Shares, completion rates, conversion.
% change from X to Y — ((Y − X) ÷ |X|) × 100. Growth and decline over time.
Percentage points versus percent
If a rate moves from 5% to 7%, that is a two percentage point rise and a 40% relative rise. Both describe the same movement. Confusing them is common in reporting and almost always flatters the result.
Percentages of percentages
A 10% increase followed by a 10% increase is a 21% total increase, not 20%, because the second applies to the already-increased figure. Multiply the factors — 1.1 × 1.1 = 1.21 — rather than adding the percentages.
Frequently asked questions
What is the difference between percent and percentage points?
If a rate moves from 5% to 7%, that is a rise of two percentage points and a relative rise of 40%. Both are accurate descriptions of the same change. Quoting the relative figure without saying so is a common way of making a modest movement sound dramatic.
Why is a 50% loss not recovered by a 50% gain?
Because each percentage is measured against a different base. A 50% fall from 100 leaves 50; a 50% gain on 50 returns only 75. Recovering the original value requires a 100% gain. The deeper the fall, the more asymmetric the recovery.
Do two 10% increases equal a 20% increase?
No, they equal 21%, because the second increase applies to the already-increased figure. Multiply the factors rather than adding the percentages: 1.1 times 1.1 is 1.21.
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