How to Calculate Percentages — Formulas, Examples & Mental Math

Percent just means "per hundred." Master three formulas and a couple of tricks and you'll never be stuck at a shop counter or exam result again.

Formula 1: What is X% of Y?

Answer = Y × X ÷ 100. A restaurant bill of 4,800 with a 10% service charge adds 4,800 × 10 ÷ 100 = 480. An 18% tax on 450 is 81. This is the formula for tips, taxes, commissions and zakat alike.

Formula 2: X is what percent of Y?

Answer = X ÷ Y × 100. You scored 684 out of 850: 684 ÷ 850 × 100 = 80.5%. Your team won 13 of 20 matches: 65%. This is the formula for exam results, attendance and market share.

Formula 3: Percentage change

Change % = (new − old) ÷ old × 100. Salary went from 80,000 to 95,000: (95,000 − 80,000) ÷ 80,000 × 100 = +18.75%. Note the divisor is always the old value — that's why a 50% drop needs a 100% rise to recover: 100 → 50 is −50%, but 50 → 100 is +100%.

Mental math tricks worth knowing

• The 10% anchor: move the decimal one place (10% of 640 = 64), then build: 5% = half of that (32), 20% = double (128), 1% = a tenth (6.4). Almost any percentage can be assembled this way.
• The reversal trick: x% of y = y% of x. 8% of 50 feels hard; 50% of 8 = 4 is instant. Same number.
• Discount shortcut: 30% off means you pay 70% — one multiplication (price × 0.7) instead of two steps.
• Percentage points ≠ percent: a rate going from 10% to 15% rose 5 points but 50 percent. News headlines mix these up constantly.

Where you'll use this weekly

Exam and assignment scores, sale prices and taxes, tips, loan interest, salary raises, battery and storage indicators, statistics in the news, and profit margins if you sell anything. Percentages are the single most reused piece of school math — which is exactly why getting the three formulas straight pays off daily.

Reversing a percentage to find the original

Knowing the final figure and the rate lets you recover the starting number — the skill behind stripping tax from a receipt or finding a pre-sale price. The move is to divide, not subtract: original = final ÷ (1 + rate) after an increase, or final ÷ (1 − rate) after a decrease.

A 1,180 total including 18% tax began at 1,180 ÷ 1.18 = 1,000. Taking 18% off 1,180 instead gives 967.60, which is wrong — that 18% was charged on 1,000, not on the total. Likewise a jacket at 340 after 15% off was 340 ÷ 0.85 = 400.

Percentage points are not percentages

Mixing these up changes the meaning of a statement entirely. If an interest rate goes from 4% to 6%, that is a rise of 2 percentage points but a 50% increase in the rate. Both are accurate, and they sound wildly different — which is exactly why headlines and sales material pick whichever is more dramatic. When a figure sounds surprising, check which of the two is being quoted.

Why percentage changes don't cancel out

A 20% fall followed by a 20% rise does not return you to where you started, because each is applied to a different base. From 1,000: down 20% is 800, then up 20% of 800 is 960. You are 4% down despite the two figures matching.

The effect grows as the numbers do. A 50% loss needs a 100% gain to recover. A 75% loss needs 300%. This is the single most useful percentage fact in personal finance, and it explains why avoiding large losses matters more than chasing large gains.

Averaging percentages the right way

You cannot simply average two percentages when they come from different-sized groups. If a class of 10 scores 90% and a class of 40 scores 60%, the overall figure is not 75%. You must weight by size: (10 × 90 + 40 × 60) ÷ 50 = 66%.

The same applies to growth over multiple periods. Two years of 10% growth then 20% growth is not 15% a year — it is 1.10 × 1.20 = 1.32, so about 14.9% compounded. Small differences, but they compound into large ones over time.

Frequently asked questions