Percentage Calculations You'll Actually Use

Percentage problems look different on the surface but they're all the same two formulas combined in different ways. Once you see the structure, the specific problem doesn't matter much.

The two building blocks

Every percentage problem is one of these:

1. Find the percentage amount: What is X% of Y? → Y × (X/100)
2. Find what percent: X is what percent of Y? → (X ÷ Y) × 100

Everything else — discounts, tips, tax, markups, percentage change — is built from these.

Calculating a tip

What is 20% of $65?

$65 × 0.20 = $13

Shortcut: 10% of anything = move the decimal left one place. $65 → $6.50. Double it for 20% → $13.

Calculating a discount

A $120 jacket is 30% off. What's the final price?

Discount amount: $120 × 0.30 = $36. Final price: $120 − $36 = $84.

Or faster: if it's 30% off, you pay 70%. $120 × 0.70 = $84. Same answer in one step.

Calculating sales tax

$85 item, 8.5% sales tax. What's the total?

$85 × 1.085 = $92.23

Multiply by (1 + tax rate) to get the total in one step. You're adding the tax to 100% of the price.

Percentage change

This one is slightly different in structure.

Formula: ((New − Old) ÷ Old) × 100

Your salary went from $52,000 to $58,000. What percent increase is that?

((58,000 − 52,000) ÷ 52,000) × 100 = (6,000 ÷ 52,000) × 100 = 11.5%

Negative percentage change = decrease. If the price dropped from $80 to $68: ((68 − 80) ÷ 80) × 100 = −15%.

Working backwards from a discounted price

You paid $72 after a 20% discount. What was the original price?

If $72 is 80% of the original price: $72 ÷ 0.80 = $90.

This is the version that trips people up. You can't just add 20% back — $72 × 1.20 = $86.40, which is wrong. You have to divide by what percentage you actually paid.

Quick mental math tricks

Finding 1%: Move the decimal two places left. 1% of $348 = $3.48.

Finding 5%: Find 10%, divide by 2.

Finding 15%: Find 10%, add half of that. 10% of $60 = $6. Half = $3. 15% = $9.

Finding 25%: Divide by 4.

These shortcuts only work cleanly on round numbers. On real-world prices, a calculator is faster than mental gymnastics. But knowing the structure means you can check any answer quickly.

The version most people get wrong

Percent of percent.

If something increases by 50% and then decreases by 50%, you don't end up where you started. You end up lower.

$100 → +50% → $150 → −50% → $75.

The second 50% is applied to the new, higher number. A 50% decrease is larger in absolute terms than the 50% increase was. Same percentage, different base.