A percentage is a number or ratio expressed as a fraction of 100. The word "percent" comes from the Latin per centum, meaning "by the hundred." Percentages are used everywhere — from calculating discounts and tax to understanding statistics and grades.
This distinction matters enormously in finance and news reporting. If a bank's interest rate rises from 2% to 4%, that is a 2 percentage point increase — but it is a 100% relative increase in the rate itself. Politicians and headlines often use these terms interchangeably, which can be deeply misleading. When you see "rates rose by 2%", ask whether that means 2 percentage points or a 2% relative change — the difference can be enormous.
Percentages don't add up simply when applied repeatedly. If a stock gains 10% one year and loses 10% the next, you do NOT break even. Starting with $1,000: after +10% you have $1,100. After −10% of $1,100 you have $990 — a net loss of $10. This is why compound growth requires more than additive thinking. Use the formula: Final = Initial × (1 + r₁) × (1 + r₂) × ... for each successive period.
If something costs $169.50 after a 15% discount, what was the original price? Don't subtract 15% from $169.50 — that gives the wrong answer. Instead: Original = Sale Price ÷ (1 − 0.15) = $169.50 ÷ 0.85 = $199.41. The same logic applies to tax: if $226 includes 13% HST, the pre-tax amount = $226 ÷ 1.13 = $200.00. This reverse calculation is one of the most commonly misapplied percentage operations.
You encounter percentages constantly: GST (5%) federally on most goods; HST (13%) in Ontario, New Brunswick, Newfoundland; PST + GST in BC, Saskatchewan, Manitoba; mortgage interest rates (typically 4–7% in 2025); RRSP contribution room (18% of prior year income); salary raises (typically 2–5% annually); and credit card interest rates (19.99% is the standard in Canada). Understanding percentage math helps you evaluate every one of these situations clearly.
This free percentage calculator online makes it easy to solve every type of percentage problem in seconds. Find what percent one number is of another, calculate a percentage of any value, or work out percentage increase and decrease — all with one simple percentage calculator online tool.
Common uses include calculating discounts while shopping, figuring out tip percentages, tracking grade changes, and analyzing data trends. The percentage calculator handles all three classic % question types: "What is X% of Y?", "X is what percent of Y?", and "What is the percentage change from X to Y?"
Percentage = (Part ÷ Whole) × 100. For example, scoring 42 out of 50 on a test: (42 ÷ 50) × 100 = 84%. To find a percentage of a number: multiply the number by the decimal form of the percentage. For example, 30% of 200 = 0.30 × 200 = 60.
Percentage change = ((New Value − Old Value) ÷ Old Value) × 100. If a price goes from $80 to $92: ((92 − 80) ÷ 80) × 100 = 15% increase. Note that increases and decreases are not symmetric: a 15% increase followed by a 15% decrease does NOT return to the starting value.
Percentage points measure the arithmetic difference between two percentages. If an interest rate rises from 2% to 4%, that is a 2 percentage point increase but a 100% relative increase. News articles and financial reports often confuse these terms — always clarify which is meant when the stakes are high.
Divide the discounted price by (1 − discount rate). If an item costs $70 after a 30% discount: original = $70 ÷ 0.70 = $100. A common mistake is subtracting 30% from $70, which gives $49 — wrong. The formula works because $70 represents 70% of the original price.
Multiply the pre-tax price by (1 + tax rate). Ontario HST is 13%: $200 × 1.13 = $226 total. To find only the tax amount: $200 × 0.13 = $26. To reverse a tax-included price back to pre-tax: divide by (1 + rate): $226 ÷ 1.13 = $200.
20% of 150 = 0.20 × 150 = 30. Mental math shortcut: 10% of 150 is 15 (move decimal left one place), and 20% is double that = 30. Use this halving/doubling technique to estimate percentages quickly in your head.
In compound growth, percentages apply to the growing total, not the original amount. Three years of 5% growth is NOT 15% — it is (1.05³) − 1 = 15.76%. After a 10% gain then a 10% loss: $1,000 → $1,100 → $990. You end up below where you started, because the loss applies to a larger base.
For 10%: move the decimal left one place ($85 → $8.50). For 20%: double the 10% amount ($8.50 × 2 = $17). For 15%: take 10% + half of 10% ($8.50 + $4.25 = $12.75). For 18%: take 20% minus 10% of that ($17 − $1.70 = $15.30). These shortcuts work instantly in your head.