How to Calculate Percentages

Percentages are everywhere — discounts, interest, tips, tax, statistics, exam results, pay rises — and yet almost everyone hesitates on at least one type. The good news is that all percentage problems reduce to a handful of patterns. Once you can tell which pattern you are looking at, the arithmetic is easy. This guide covers every common type, with the shortcuts that make most of them doable in your head.

The one idea underneath everything

Per centliterally means “per hundred.” So 25% is just another way of writing 25 out of 100, which is the fraction 25/100, which is the decimal 0.25.

That gives you the master move: to use a percentage, divide it by 100 and multiply. Almost every formula below is a variation on that single step.

Type 1: A percentage of a number

The most common question. What is 20% of 150?

Formula: (percentage ÷ 100) × number

20 ÷ 100 = 0.20, and 0.20 × 150 = 30.

Mental shortcut: find 10% first by moving the decimal point one place left. 10% of 150 is 15, so 20% is double that — 30. This trick alone handles a huge share of everyday percentage maths.

• 5% = half of 10%
• 15% = 10% + 5%
• 25% = a quarter — divide by 4
• 50% = half

Type 2: What percentage is X of Y?

What percentage is 30 of 150?

Formula: (part ÷ whole) × 100

30 ÷ 150 = 0.2, and 0.2 × 100 = 20%.

The thing to get right here is which number is the “whole.” It is the total, the original, the thing you are comparing against. Getting this backwards is the most common percentage error there is.

Type 3: Percentage increase and decrease

A price rose from 80 to 100. What percentage increase is that?

Formula: (change ÷ original) × 100

The change is 100 − 80 = 20. So 20 ÷ 80 = 0.25 → a 25% increase.

The critical word is original. You always divide by where you started, not where you ended up. Divide by 100 instead of 80 and you would get 20% — wrong.

Decrease works identically: a fall from 100 to 80 is a change of 20 over an original of 100 = a 20% decrease.

Note that these are not symmetrical, which surprises people. Going 80 → 100 is a 25% increase, but 100 → 80 is a 20% decrease. Same numbers, different percentages, because the starting point changed.

Type 4: Reverse percentages (the tricky one)

After a 20% discount, an item costs $80. What was the original price?

The trap: people take 20% of 80 (= 16) and add it back to get $96. That is wrong. The discount was 20% of the original price, not of the sale price.

Think of it this way: after a 20% discount you are paying 80% of the original. So:

Formula: original = final ÷ (1 − discount ÷ 100)

80 ÷ 0.80 = $100. Check it: 20% of 100 is 20, and 100 − 20 = 80. ✓

The same logic works for tax added on: if a price including 15% tax is $115, the pre-tax price is 115 ÷ 1.15 = $100 — not 115 minus 15%.

Type 5: Percentages don't simply add up

This catches almost everyone. A 20% discount followed by a further 10% is not 30% off.

Start with $100. After 20% off: $80. Then 10% off that: $72. The total saving is $28 — an effective 28%, not 30%.

The reason is that the second percentage applies to a smaller base. The same effect appears everywhere: a 10% pay cut followed by a 10% pay rise does not restore your original salary. 100 → 90 → 99. You are still 1% down.

Percentage vs. percentage points

A genuinely important distinction, and one that news reports get wrong constantly.

If an interest rate rises from 4% to 6%, that is an increase of 2 percentage points. But as a percentage change, it is a 50% increase (2 ÷ 4 = 0.5).

Both statements are true and they describe the same event, but they sound wildly different — which is exactly why people reach for whichever one supports their argument. When you see a dramatic percentage claim about a rate, check which one is meant.

Common mistakes to avoid

• Dividing by the wrong number. For an increase or decrease, always divide by the original.
• Adding stacked percentages. Apply them one after another instead.
• Reversing a percentage by adding it back. Divide, do not add.
• Assuming a rise then a fall of the same percentage cancels out. It never does.
• Confusing percentages with percentage points.

Frequently asked questions

How do I find 15% quickly? Take 10% (move the decimal one place left), halve it to get 5%, and add them together.

Is 20% of 50 the same as 50% of 20? Yes — both are 10. Percentages are commutative, which sometimes makes an awkward calculation trivially easy.

How do I convert a fraction to a percentage? Divide the top by the bottom, then multiply by 100. So 3/8 = 0.375 = 37.5%.

Can a percentage be over 100? Certainly. If something triples, that is a 200% increase — the new value is 300% of the old one.

Calculate percentages now

Use our Percentage Calculator for any of these calculations in one place. For shopping specifically, the Discount Calculator handles sale prices and stacked discounts, and the Tip Calculator splits a bill. Read more on calculating discounts.