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Percentage Calculator

The three percentage questions everyone actually asks — solved instantly, with the math shown.

Solve any percentage problem

Answer
How it was computed

The three percentage problems

Almost every real-world percentage question is one of three types, and each has a one-line formula.

1. What is X% of Y? Used for tips, discounts, taxes, and commissions.

Answer = (X ÷ 100) × Y

Example: a 15% tip on an $80 dinner is (15 ÷ 100) × 80 = $12. A 30%-off sale on a $250 jacket saves (30 ÷ 100) × 250 = $75, so you pay $175.

2. X is what percent of Y? Used for grades, progress toward goals, and comparing parts to wholes.

Answer = (X ÷ Y) × 100

Example: you got 42 questions right out of 48. That's (42 ÷ 48) × 100 = 87.5%.

3. Percent change from X to Y. Used for price changes, raises, portfolio moves, and statistics.

Change = (Y − X) ÷ |X| × 100

Example: rent goes from $1,600 to $1,750. The increase is (1750 − 1600) ÷ 1600 × 100 = +9.4%. The result is positive for increases and negative for decreases — and the denominator is always the starting value, which is the step people most often get backwards.

The mistake everyone makes: percent change isn't symmetric

A 50% drop followed by a 50% gain does not get you back to even. Start at $100, lose 50% — you have $50. Gain 50% of $50 — you have $75. Going down 50% requires going up 100% to recover, because the base changed. The same trap appears in headlines: "X is 200% more than Y" means X is three times Y, not two times. When the numbers matter, run them.

Percentage points vs. percent

If an interest rate moves from 4% to 5%, it rose one percentage point but 25 percent (1 ÷ 4 × 100). News reports mix these up constantly. Percentage points are the raw difference; percent change compares the difference to the starting value. Both are correct numbers — they answer different questions.

Frequently asked questions

How do I calculate a percentage discount?

Multiply the price by the discount percent divided by 100, then subtract. A 25% discount on $90: 90 × 0.25 = $22.50 off, so you pay $67.50. Shortcut: pay (100 − 25) = 75% of the price — 90 × 0.75 = $67.50.

How do I add sales tax to a price?

Multiply the price by (1 + tax rate). An $80 item with 8.375% tax: 80 × 1.08375 = $86.70.

How do I reverse a percentage — find the original price before a discount?

Divide by (1 − discount). If you paid $67.50 after 25% off, the original was 67.50 ÷ 0.75 = $90. Don't add 25% back to $67.50 — that gives the wrong answer ($84.38) because the base changed.

Why is my percent change negative?

A negative result means the value decreased. Going from 80 to 60 is (60 − 80) ÷ 80 × 100 = −25%.

Can a percentage be more than 100%?

Yes. 150% of 40 is 60, and growing from 20 to 70 is a +250% change. Over 100% simply means more than the whole original amount.

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