Percentage Calculator

The three percentage problems

Almost every percentage question fits into one of three patterns. Knowing which pattern you're solving makes the math instant. The calculator above has a mode for each.

1. What is X% of Y?

Multiplication. (X / 100) × Y. Common uses: applying a discount, calculating a tip, adding sales tax, figuring a sales commission, or sizing a portion. Example: 8% sales tax on a $1,200 laptop = 0.08 × 1200 = $96.

2. X is what percent of Y?

Division. (X / Y) × 100. Common uses: exam scores (got 42 of 50 right = 84%), market share, conversion rates, hit rates, or any “part of a whole” question. Example: a website with 1,200 sessions and 36 sign-ups has a 3% conversion rate.

3. Percentage change from X to Y

((Y − X) / |X|) × 100. Common uses: price increases, salary raises, weight loss, stock returns, year-over-year growth. Positive = increase, negative = decrease. Example: a stock that goes from $50 to $65 has gained 30%.

Reverse percentage problems

A common surprise: if a price was “reduced by 20%” and now costs $80, the original wasn't $96 (which would be 20% added back) — it was $100. To reverse a discount, divide by (1 − discount): $80 ÷ 0.80 = $100. To reverse a markup, divide by (1 + markup): a 25%-marked-up item selling at $50 had a base of $50 ÷ 1.25 = $40.

For sales-tax math: if a $107 receipt total includes 7% sales tax, the pre-tax price is $107 ÷ 1.07 = $100, and the tax was $7. Don't multiply $107 × 0.07 — that gives you a different (smaller) number that doesn't reconstruct the receipt.

Percentage points vs percentages: don't confuse them

One of the most-abused statistics in news headlines. They're different units:

• Percentage point — an absolute difference between two percentages. Going from 5% to 10% is a 5 percentage point increase.
• Percent (or percentage change) — a relative difference. Going from 5% to 10% is a 100% increase (you doubled).

Headlines like “Approval rating up 5%” are ambiguous and often wrong. If a politician's rating moved from 40% to 45%, that's 5 percentage points (a 12.5% relative increase). Always read “5%” in news as percentage points unless it's clearly framed as a relative change.

Compound percentages don't add up

A 10% raise followed by another 10% raise is nota 20% raise — it's a 21% raise (1.10 × 1.10 = 1.21). Conversely, a 10% loss followed by a 10% gain doesn't break even. Starting at $100, you drop to $90 (−10%), then gain 10% of $90 = $9, ending at $99. You need an 11.1% gain to recover from a 10% loss.

This is why investment returns matter so much: a 50% drawdown requires a 100% gain to break even. The asymmetry of percentage losses is why position-sizing and risk management dominate long-term returns.

Common everyday percentage problems

• Tipping 18% on $54.20 → 0.18 × 54.20 = $9.76. (See our Tip Calculator for split + round-up.)
• Sales tax at 8.25% on $50 → 0.0825 × 50 = $4.125 ≈ $4.13.
• Down payment of 20% on a $400,000 home → $80,000. (See Mortgage Calculator.)
• 10% raise on $75,000 → $7,500/year extra ≈ $625/month gross. (See Paycheck Calculator for the after-tax difference.)
• Test score 47/55 → 47 ÷ 55 × 100 = 85.45% (B+ on most US scales).

Decimals, fractions, and percent — they're the same thing

Three names for the same idea. 25% = 0.25 = 1/4. To convert: multiply or divide by 100 to flip between percent and decimal; convert decimal to fraction by writing it as “number / power of 10” and simplifying. The calculator works in decimal internally and shows results as percentages — type a decimal value if you already have it (e.g., 0.20 instead of 20).