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Common Percentages Reference Table

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How to Calculate Percentages

A percentage is a number expressed as a fraction of 100. The word comes from the Latin per centum, meaning "by the hundred." Percentages are used everywhere: grades, discounts, tax rates, interest rates, poll results, nutrition labels, and statistics.

Real-world uses

Where "percent" and the % symbol come from

The word percent comes from the Latin per centum, meaning "by the hundred". The idea is ancient: the Romans levied taxes as fractions of 100, such as the centesima rerum venalium, a 1% duty on goods sold at auction. As commerce grew in medieval and Renaissance Italy, merchants worked routinely in hundredths and wrote per cento, which clerks abbreviated. Over the 15th to 17th centuries that abbreviation drifted from "per 100" through looped, shorthand forms into the modern % sign — essentially the two zeros of "100" carried over with a separating slash. Per-mille (‰, parts per thousand) and the basis point (one hundredth of a percent) extend the same idea to finer fractions.

A handy trick: x% of y equals y% of x

Because a percentage is just a multiplication, it is commutative: x% of y always equals y% of x. This is more than a curiosity — it is a genuine mental-maths shortcut. Suppose you need 4% of 75. Computed directly that is awkward, but 75% of 4 is obviously 3, and the two are identical. Likewise 18% of 50 is hard to picture, while 50% of 18 is plainly 9. Whenever one of the two numbers is a "friendly" value — a round number, or something you can halve or quarter in your head — flip the calculation around and the answer often falls straight out.

Increases and decreases don't reverse

One of the most common and costly percentage mistakes is assuming that an increase and a decrease of the same percentage cancel out. They do not. Start with 100, raise it by 50% to get 150, then cut that by 50% and you land on 75, not 100 — because the second percentage is taken from the larger number. The same asymmetry governs investments: a holding that falls 50% must then gain 100% just to break even, and a 20% loss needs a 25% gain to recover. Whenever you chain a rise and a fall, compute each step on the value that actually exists at that moment, not on the original.

Stacked percentages multiply — they don't add

Successive percentage changes compound rather than sum. Two consecutive 20% increases are not a 40% increase: 1.20 × 1.20 = 1.44, a 44% total rise. Stacked discounts work the same way — "30% off, then an extra 20% off" is not 50% off but 0.70 × 0.80 = 0.56, i.e. 44% off, because the second discount applies to the already-reduced price. To combine percentage changes, convert each to a multiplier (a 15% rise is ×1.15, a 15% fall is ×0.85), multiply the multipliers together, and translate the result back to a single percentage.

Markup vs margin: the most confused pair in business

Markup and profit margin are both percentages about the same sale, but they use different denominators, and mixing them up causes real pricing errors. Markup is profit as a percentage of cost; margin is profit as a percentage of the selling price. Sell a $100-cost item for $150 and you have a 50% markup (50 ÷ 100) but only a 33.3% margin (50 ÷ 150). Because the selling price is always larger than the cost, the margin percentage is always smaller than the markup percentage for the same sale. When someone quotes "a 50% margin", make sure they do not actually mean a 50% markup — the difference can quietly halve your expected profit.

Relative vs absolute change: how statistics mislead

The same change can be made to sound large or small depending on whether it is expressed in relative or absolute terms — a favourite tool of misleading headlines. If a medication lowers a risk from 2% to 1%, that is a 50% relative reduction (the risk halved) but only a 1 percentage-point absolute reduction (one fewer case per hundred people). Both numbers are true; they describe the same fact very differently. When you read a dramatic percentage, ask "percent of what, and how big was the base?" A huge relative change on a tiny base is often far less significant than it sounds — which is exactly the difference between a "percent change" and a "percentage point" change that trips so many people up.

Basis points: percentages of percentages

In finance, changes in interest rates and yields are often quoted in basis points (bps). One basis point is one hundredth of a percent — 0.01% — so 100 basis points equal one percentage point. The term exists precisely to avoid the percent-versus-percentage-point ambiguity: saying a central bank "raised rates by 25 basis points" is unmistakable, whereas "raised rates by 0.25%" could be misread. If you ever need to translate, divide basis points by 100 to get percentage points (50 bps = 0.5 percentage points).

Adding and removing tax (VAT, GST, sales tax)

Sales taxes are a percentage problem people meet every day. To add a tax, multiply by one plus the rate: an item priced ₹1,000 before 18% GST costs 1,000 × 1.18 = ₹1,180. To remove a tax and find the pre-tax amount from a tax-inclusive total, you must divide, not subtract — the reverse-percentage rule. From a ₹1,180 inclusive price the net is 1,180 ÷ 1.18 = ₹1,000, and the tax portion is the difference, ₹180. The frequent error is to take 18% of the gross (₹1,180 × 0.18 = ₹212.40), which overstates the tax, because the 18% was charged on the net amount, not the gross.

The Rule of 72: estimating growth in your head

A final shortcut links percentages to growth over time. The Rule of 72 estimates how long a quantity growing at a fixed percentage takes to double: simply divide 72 by the percentage rate. Money earning 6% a year doubles in roughly 72 ÷ 6 = 12 years; at 8% it takes about 9 years. The same rule works in reverse for anything that inflates — prices rising 3% a year double in about 24 years. It is an approximation (the exact figure comes from logarithms), but it is remarkably accurate for the single-digit rates most savings, loans and inflation figures fall into, and it turns abstract percentages into an intuitive sense of time.

Fractions, decimals and percentages are the same thing

A percentage is just one of three ways to write the same value. To turn a percentage into a decimal, divide by 100 (or move the decimal point two places left): 25% becomes 0.25. To go the other way, multiply by 100: 0.4 becomes 40%. A fraction converts to a percentage by dividing the top by the bottom and multiplying by 100, so three-quarters is 3 ÷ 4 × 100 = 75%. Holding all three forms in mind makes mental arithmetic easier — it is obvious that 50% is a half, 25% a quarter, 10% a tenth and 1% a hundredth — and it is why "find X% of Y" is really just "multiply Y by the decimal form of X".

You can't simply average percentages

Averaging two percentages by adding them and dividing by two is a classic error, because percentages taken from different-sized bases are not directly comparable. If you score 50% on a 10-question quiz and 90% on a 100-question exam, your overall percentage is not (50 + 90) ÷ 2 = 70%; it is the total correct over the total possible: (5 + 90) ÷ 110 ≈ 86%. To combine percentages correctly you need a weighted average, in which each percentage is weighted by the size of the group it came from. The same logic applies to interest rates, response rates and conversion rates — always weight by the base before you average.

Percentage error and percentage difference

Two related measures come up in science and measurement. Percentage error compares a measured or estimated value with a known true value: take the absolute difference, divide by the true value and multiply by 100 — a thermometer reading 102° when the real temperature is 100° has a 2% error. Percentage difference, by contrast, compares two values when neither is "correct": you divide the absolute difference by the average of the two, because there is no true baseline to divide by. Choosing the right one matters — use percentage error when there is a reference value to be right or wrong against, and percentage difference when you are simply comparing two equally-valid measurements.

Average growth: CAGR beats a simple average

When something grows by a different percentage each year, averaging those percentages overstates the real result, because growth compounds. The honest figure is the compound annual growth rate (CAGR) — the single steady rate that would take you from the starting value to the ending value over the same number of years. An investment that gains 50% one year and loses 50% the next has a simple average of 0%, yet ₹100 became ₹150 then ₹75 — a real loss, and a CAGR well below zero. Whenever you summarise growth over multiple periods, the compound rate, not the arithmetic average, is the number that tells the truth.

Quick mental-math anchors

A few reference points make most everyday percentages easy without a calculator. 10% is the master key: move the decimal point one place left (10% of 84 is 8.4), and from it you can build the rest — 5% is half of 10%, 20% is double it, 15% is 10% plus 5%, and 1% is the decimal moved two places. To find a tip on a $60 bill: 10% is $6, so 20% is $12 and 15% is $9. Combined with the commutative trick (x% of y equals y% of x) and these anchors, a surprising share of real-world percentage questions can be answered in your head in seconds.