Percentage
Calculate percentages three ways: what is X% of Y, X is what percent of Y, and percentage change.
Percentages show up in discounts, tips, interest, exam scores, taxes. A percentage is just a fraction out of 100, but framing numbers that way makes comparisons instant.
Three modes cover almost every everyday question: "What is X% of Y?", "X is what percent of Y?", and "What's the percentage change from A to B?". Pick the one that matches your question. The formula used is shown next to the result.
The three percentage questions
What is X% of Y? This is the straight calculation. Multiply X by Y and divide by 100. It's what you use for discounts, tips, commissions, and tax.
X is what percent of Y? This inverts the question — you know the part and the whole, you want the ratio. Divide part by whole, multiply by 100. Useful for exam scores, progress bars, market share.
Percentage change from A to B. This measures relative movement. Subtract old from new, divide by old, multiply by 100. A positive result is an increase, negative is a decrease. Used for growth rates, price changes, return on investment.
X% of Y = (X × Y) / 100 · X of Y = (X / Y) × 100 · Change = ((B − A) / A) × 100
- X, Y
- Input values
- A
- Starting value (original)
- B
- Ending value (new)
Practical examples
Discount at a store
Setup: A $150 jacket is on sale at 20% off.
20% of $150 = (20 × 150) / 100 = $30 discount. Final price: $120.
Takeaway: For a quick mental calc, remember: 10% is dividing by 10, so 20% is twice that. Five minutes of this trick saves time at every checkout.
Exam score to percentage
Setup: You answered 34 out of 40 questions correctly.
(34 / 40) × 100 = 85%
Takeaway: The same formula works for any "part of whole" question — from quality checks in manufacturing to survey responses.
Year-over-year growth
Setup: Revenue went from $800k last year to $1.2M this year.
((1,200,000 − 800,000) / 800,000) × 100 = 50% growth
Takeaway: Always divide by the OLD value, not the new one. Dividing by the new value is a common mistake and gives a smaller, misleading percentage.
Fast mental math tricks
- 10% = divide by 10. The foundation for most quick estimates.
- Swap the order. X% of Y always equals Y% of X. 8% of 50 is easier to compute as 50% of 8 = 4.
- Double-then-adjust. 15% tip: take 10%, then half of that, add them. (10% of $48 = $4.80, half = $2.40, total tip = $7.20.)
- Percentage points vs. percent. A rate moving from 4% to 6% is a 2 percentage point increase OR a 50% increase. Be careful which you mean — the difference is huge.
- Percentage increase then decrease ≠ zero. A 50% increase followed by a 50% decrease ends 25% below the start, not at the start. Compounding matters.
When percentages mislead
Tiny base values can produce huge percentages. Going from 2 customers to 4 is a 100% increase, but the absolute number is small. Always check the magnitude behind the ratio.
Averaging percentages is tricky. The average of a 50% discount and a 0% discount on two items is 25%, but the effective overall discount depends on the prices — weighting matters.
Don't add percentages from different bases. A 20% tax on top of a 10% service charge is not a 30% markup; you compound them (1.10 × 1.20 = 1.32, so 32%).
Frequently asked questions
What's the difference between percent and percentage point?▾
A percent is a ratio. A percentage point is the absolute difference between two percentages. If an interest rate rises from 4% to 6%, that is 2 percentage points higher, or 50% higher — both statements are true but they mean different things.
How do I calculate a percentage discount in reverse?▾
If the sale price is $80 after a 20% discount, the original price is $80 / (1 − 0.20) = $80 / 0.80 = $100. Divide by the remaining fraction, not by the discount fraction.
Why isn't a 50% increase then 50% decrease back to zero?▾
Because the decrease is applied to a larger number. $100 → +50% → $150 → −50% → $75. You end 25% below start. Compounding always wins over simple intuition.
How do I calculate weighted averages with percentages?▾
Multiply each value by its weight (expressed as decimal or percentage), sum them, and divide by the total weight. Example: grades weighted 30% exam, 40% projects, 30% final — multiply each score by its weight, sum, and the result is the weighted average.
Why does my calculator show negative percentages?▾
A negative percentage change means the ending value is lower than the starting value — a decrease. In the 'percentage change' mode, A = 200, B = 150 produces −25%, meaning B is 25% less than A.
Sources
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