How do I find what percent one number is of another?

Divide the part by the whole and multiply by 100: (part ÷ whole) × 100. Example: 30 ÷ 200 × 100 = 15%.

What is the difference between percent and percentage points?

Percentage points are the arithmetic gap between two percents (50% − 40% = 10 points). Percent change is relative: 10 ÷ 40 = 25% increase. Use our Percentage Increase/Decrease calculator for the latter.

How do I add a percentage to a number?

Multiply by 1 + rate: Y × (1 + X/100). Example: 200 + 15% = 200 × 1.15 = 230.

How do I reverse a percentage increase?

Divide by the factor, don't subtract. If a price after 20% VAT is £120, the pre-VAT price is 120 ÷ 1.20 = £100.

Can percentages exceed 100%?

Yes. 150% of 80 = 120. Above 100% simply means more than the whole — common for growth ('sales up 250%') and proportions.

Math · Free tool

Percentage Calculator

What is X% of Y? What % is X of Y? Answered with steps.

Percentages run modern life — shop discounts, exam scores, tax, interest, battery levels, election swings. Yet the same word covers three different questions: what is 20% of 250? what percent is 45 of 180? and what is 180 plus 15%? Mixing them up is the single biggest source of percentage errors. This calculator separates the three modes, shows the exact arithmetic, and teaches the mental model so you rarely need a calculator again.

A percent is simply a fraction out of 100. 37% means 37 per hundred, or 0.37 as a decimal. Every percentage problem is therefore a multiply-or-divide by 100 in disguise. Once you see that, problems like restaurant bills, salary hikes and test scores collapse to one-line sums. Below you will find the three formulas, a worked example for each, classroom-tested shortcuts, and the traps — percentage points vs percent, compounding percentages, and the infamous '50% off then 50% on' illusion.

Use the tool above: pick a mode, enter two numbers, and press Calculate. Each answer includes the step-by-step working teachers expect and auditors accept.

Updated 2026-09-01 · 6-min read · Formula + steps included

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The three percentage formulas

(1) X% of Y = (X ÷ 100) × Y • (2) X as % of Y = (X ÷ Y) × 100 • (3) Y + X% = Y × (1 + X/100)

All three come from the definition percent = per hundred. To find a share, convert the percent to a decimal and multiply. To find what share one number is of another, divide and scale by 100. To add a percent, multiply by one-plus-the-decimal — the growth factor used in finance and retail.

X: The percentage figure (e.g. 20 for 20%)
Y: The base or whole amount
Result: The part, share, or grown value depending on mode

Worked examples — all three modes

Three 10-second problems covering 95% of real percentage questions:

20% of 250: 20 ÷ 100 = 0.20; 0.20 × 250 = 50.
45 is what % of 180? 45 ÷ 180 = 0.25; 0.25 × 100 = 25%.
180 increased by 15%: factor = 1 + 0.15 = 1.15; 180 × 1.15 = 207.
Check by reversal: 50 ÷ 250 = 0.20 = 20% ✓; 207 ÷ 180 = 1.15 = +15% ✓.

Result: Answers: 50, 25%, and 207. Each reverses cleanly — the hallmark of correct percentage maths.

How to use this percentage calculator

Match your question to the right mode first — that is 90% of the skill.

Step 1: Choose the mode

'X% of Y' for shares and discounts, 'X is what % of Y' for grades and proportions, 'increase' for hikes and growth.

Step 2: Enter the two numbers

Decimals are fine (e.g. 12.5% of 4,800). Commas are ignored. Negative percentages mean decreases.

Step 3: Calculate and read steps

The result card shows the answer plus the one-line working you can copy into homework, invoices or emails.

Step 4: Reset for the next sum

Reset clears inputs and errors without reloading, so you can chain calculations quickly.

Where percentages matter most

Five everyday domains where fluent percentages save money or marks:

Shopping & discounts

A £84 jacket at 30% off: 0.30 × 84 = £25.20 off, pay £58.80. Stack a further 10% code on £58.80, not £84 — sequential discounts multiply (0.70 × 0.90 = 0.63), so you pay 63% of original.

Exams & grading

42/60 = 70%. To find marks needed for 80% on a 75-mark paper: 0.80 × 75 = 60 marks. Teachers award method marks for showing (score ÷ total) × 100.

Pay & tax

A 4.5% rise on £32,000: 32,000 × 1.045 = £33,440. Income-tax bands are marginal — only earnings above the threshold face the higher percent.

Health & nutrition

Labels show % daily value per serving, not per pack. Two servings at 15% each = 30% of your daily salt — multiply by servings eaten.

Data & presentations

Saying 'grew from 40% to 50%' is a 10 percentage-point rise but a 25% relative increase. State which you mean to avoid misleading your audience.

Pro tips

Mental-math shortcuts the calculator quietly uses:

10% is move-the-decimal: 10% of 473 = 47.3. Build 5% (half), 20% (double 10%), 1% (move two places).
To add VAT at 20%, multiply by 1.2; to remove it, divide by 1.2 — not subtract 20%.
Reverse-check every answer: if 20% of Y is P, then P ÷ Y must equal 0.20.
For repeated % changes, multiply factors: +10% then −10% = 1.10 × 0.90 = 0.99 (−1% overall).
Round only at the end; keep 2 extra decimals mid-calculation to avoid penny errors.