Percentages show up everywhere: sales, tips, raises, test scores, interest rates. Nearly every percentage question is one of four types. Figure out which one you have, and the math is one step.

Percent means "per hundred"

25% means 25 out of every 100, or 0.25 as a decimal. To turn a percent into a decimal, divide by 100 (move the decimal point two places left). 7% is 0.07, 150% is 1.5.

The four questions

1. What is X% of a number?

Answer = (X ÷ 100) × number

15% of $80: 0.15 × 80 = $12.

2. X is what percent of Y?

Percent = (X ÷ Y) × 100

You answered 42 out of 50 questions correctly: 42 ÷ 50 × 100 = 84%.

3. What is the percent change?

Percent change = (new − old) ÷ old × 100

Rent went from $1,250 to $1,350: (1,350 − 1,250) ÷ 1,250 × 100 = 8% increase.

A stock fell from $40 to $34: (34 − 40) ÷ 40 × 100 = −15%, a 15% decrease.

4. Increase or decrease a number by X%

Increase: number × (1 + X ÷ 100)
Decrease: number × (1 − X ÷ 100)

A $50,000 salary with a 4% raise: 50,000 × 1.04 = $52,000.

A $90 item at 30% off: 90 × 0.70 = $63.

Solve any of these four instantly.

Open the Percentage Calculator

Working backward: finding the original number

If you know the result after a percent change, divide instead of multiply.

A shirt is $42 after 30% off. What was the original price? $42 ÷ 0.70 = $60.

Your paycheck is $2,080 after a 4% raise. What was it before? $2,080 ÷ 1.04 = $2,000.

A common mistake is to add the percent back: $42 + 30% = $54.60. That's wrong because the 30% was taken from the larger original price.

Mental math shortcuts

  • 10%: move the decimal one place left. 10% of $64 is $6.40.
  • 5%: half of 10%. 5% of $64 is $3.20.
  • 20%: double 10%. 20% of $64 is $12.80.
  • 15%: 10% plus half of that. $6.40 + $3.20 = $9.60.
  • 1%: move the decimal two places. 1% of $2,350 is $23.50.
  • Swap trick: X% of Y equals Y% of X. 8% of 50 is the same as 50% of 8, which is 4.

Percent vs. percentage points

When a rate changes, there are two ways to describe it. If an interest rate goes from 4% to 5%:

  • It rose by 1 percentage point (5 − 4).
  • It rose by 25 percent ((5 − 4) ÷ 4 × 100).

Both are correct, but they mean different things. News stories and loan offers often use whichever sounds more dramatic, so check which one you're reading.

Percent increases and decreases aren't symmetric

If something drops 50% and then rises 50%, you don't end up where you started. $100 down 50% is $50. $50 up 50% is $75. To get back to $100 from $50, you need a 100% increase. Keep this in mind with investments, prices, and hours cut and restored.