How to Calculate Percentages: The Three That Cover Almost Everything

Almost every percentage question in real life is one of three calculations. Learn all three and you will rarely be stuck again.

Plantrino Guides · Updated 2026 · About a 9-minute read

Percentages turn up everywhere — discounts, tips, exam scores, interest rates, price rises. Yet many people freeze when a percentage question appears, not because it is hard, but because it was never broken into clear pieces. Here is the simple truth: nearly every everyday percentage problem is one of just three calculations. This guide covers all three, then works through the places where people reliably get tripped up: stacked discounts, reversing a percentage, and the difference between per cent and percentage points.

First, What "Per Cent" Means

The word percent comes from "per hundred." A percentage is simply a fraction with 100 on the bottom. So 25% means 25 out of 100, which is the same as the fraction 25/100, or the decimal 0.25. Converting between the two is the foundation of everything below: to turn a percentage into a decimal, divide by 100; to go the other way, multiply by 100.

That single conversion is doing more work than it looks. Once a percentage is a decimal, it behaves like any ordinary number — you can multiply with it, divide by it, and chain it together. Most percentage confusion comes from trying to reason in percentage form instead of converting first.

Calculation 1: Finding a Percentage of a Number

This is the "what is 20% of 80?" type of question — the one you need for discounts, tips, and taxes.

To find 20% of 80: convert 20% to 0.20, then multiply — 0.20 × 80 = 16. A jacket priced at 80 with 20% off is reduced by 16, so it costs 64.

A faster version of the same move: instead of calculating the discount and subtracting it, multiply by what is left. Taking 20% off means keeping 80%, so 0.80 × 80 = 64 in one step. That single-multiplier habit becomes essential later when discounts stack.

Calculation 2: Finding What Percentage One Number Is of Another

This answers "32 is what percent of 50?" — useful for test scores, progress toward a goal, or what share of a budget an expense represents.

If you scored 32 out of 50 on a test: 32 ÷ 50 = 0.64, then × 100 = 64%. The trick is identifying which number is the "part" and which is the "whole" — the whole is always the total you are comparing against.

This is the calculation behind most household budgeting questions. If rent is $580 a week and take-home pay is $1,450 a week, then 580 ÷ 1,450 = 0.40, so rent is eating 40% of income. The arithmetic is trivial; the value is that a share is comparable across time and across people in a way that a raw dollar figure is not.

Calculation 3: Percentage Increase or Decrease

This is the "the price went from 50 to 60 — what percentage rise is that?" question. It is everywhere in news and money: pay rises, price changes, growth figures.

For a price moving from 50 to 60: the change is 60 − 50 = 10. Then 10 ÷ 50 = 0.20, and × 100 = a 20% increase. If the number had fallen, the result would be negative, indicating a decrease. The crucial rule: always divide by the old value, because you are measuring change relative to the starting point.

Putting Real Numbers on It

Here is a single afternoon that uses all three calculations. The figures below are purely for illustration.

Nadia earns $1,500 a week before tax and is offered a rise to $1,590. Which calculation is that? It is a change, so she divides by the old value: (1,590 − 1,500) ÷ 1,500 = 0.06, or a 6% rise. Note what she did not do — she did not divide by the new figure, which would have given 5.66% and understated the rise.

She then checks how much of that pay her rent takes. Rent is $600 a week, so 600 ÷ 1,500 = 0.40, or 40% today. After the rise, 600 ÷ 1,590 = 0.377, or about 37.7%. Same rent, smaller share — that is calculation 2 doing the work.

On the way home she sees a $220 pair of boots marked 35% off. Using the single-multiplier shortcut: she keeps 65%, so 0.65 × 220 = $143. The saving is $220 − $143 = $77. That is calculation 1.

Three questions, three formulas, no guessing. The skill is not the arithmetic — a phone does that. The skill is recognising which of the three questions you are actually being asked.

Why Percentages Do Not Stack

This is the single most common percentage mistake, and retailers rely on it. A sign reads "35% off, plus a further 10% off at the register." That is not 45% off.

Take the $220 boots again. The 35% discount brings them to $143. The extra 10% is taken off that reduced figure, not the original: 0.90 × 143 = $128.70. A straight 45% off would have been 0.55 × 220 = $121. The stacked version costs $7.70 more, even though the signs add up to the same number.

The same logic runs in reverse for increases. Two consecutive 10% price rises are not a 20% rise. A $100 item becomes $110, then $121 — a 21% total rise. The extra 1% is the second rise applying to the first rise as well. Over many periods this compounding is exactly what makes long-run growth and inflation figures behave the way they do.

The Asymmetry of Ups and Downs

A percentage fall and the percentage rise needed to undo it are never the same size, and the gap widens as the numbers get bigger. If an investment worth $100 drops 50%, it is worth $50. To get back to $100 it must now gain $50 on a base of $50 — a 100% rise, not 50%.

Smaller moves show the same pattern in miniature. A 20% fall from $100 leaves $80, and recovering to $100 requires a 25% gain ($20 ÷ $80). This is not a trick of the maths so much as a reminder that the base changed. Whenever you see a fall and a rise quoted together, check what each one was measured against.

A Handy Shortcut

For calculation 1, remember that "X% of Y" always equals "Y% of X." That sounds like a curiosity, but it is genuinely useful. Working out 4% of 75 in your head is awkward; flipping it to 75% of 4 — which is just three-quarters of 4, or 3 — is effortless. The answer is the same either way.

Two more mental shortcuts worth having. To find 10% of anything, move the decimal point one place left; 1% moves it two places. Build the rest from those blocks: 15% is 10% plus half of 10%, and 35% is three lots of 10% plus half of 10%. For a rough sense check on a bill, that is quicker than reaching for a phone and accurate enough to catch an error.

Reversing a Percentage

One more situation worth knowing: undoing a percentage. If an item costs 90 after a 10% discount, you cannot simply add 10% back, because the 10% was taken off the original, larger price. Instead, divide by the remaining fraction: 90 ÷ 0.90 = 100. The original price was 100. The same logic applies to removing a tax that was added to a total.

Australians meet this most often with GST, which is added at 10%. Because the tax was calculated on the pre-tax price, you cannot take 10% off a GST-inclusive total to strip it out — that gives the wrong answer. On a $110 inclusive price, taking 10% off gives $99, but the correct pre-tax figure is 110 ÷ 1.10 = $100. The familiar Australian shortcut of dividing an inclusive price by 11 to find the GST component is exactly this reversal, tidied up: $110 ÷ 11 = $10 of GST. Our GST guide works through that in more detail.

Common Mistakes

Dividing by the new value instead of the old. Percentage change is always measured against where you started. Using the new figure as the base quietly shrinks every rise and exaggerates every fall.

Adding stacked discounts together. "30% off plus 20% off" is a 44% total discount, not 50%, because the second cut applies to an already reduced price.

Removing a percentage by subtracting it. Taking 10% off a GST-inclusive total does not remove the GST. Divide by the multiplier instead.

Confusing per cent with percentage points. A fee moving from 1% to 2% is one percentage point, but it has doubled. Whichever framing sounds more dramatic is usually the one being quoted at you.

Assuming a fall and a rise cancel out. Down 30% then up 30% does not return you to the start; it leaves you at 91% of the original.

Reporting more precision than the inputs deserve. If your starting figures are rounded estimates, quoting a result to two decimal places suggests a certainty that is not there.

Frequently Asked Questions

Percentages stop being intimidating once you see that they collapse into three core questions: a percentage of a number, what share one number is of another, and how much something changed. Learn the three formulas, use a single multiplier when discounts or rises stack, watch for the percentage-point trap, and you will handle almost any percentage life throws at you.