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PercentageCalculatorPercent of · off · change
Operation · what percent is

What percent is X of Y

Marks out of a total, one figure as a share of another, progress against a target — all the same calculation: the part divided by the whole, times 100.

Percent of, off, change Worked answer, not just a number Nothing leaves your browser
42 out of 60
70%
PERCENT

SOURCE·Arithmetic only — no external rate·REVIEWED JUL 2026

Percentage70%
As a decimal0.7
As a fraction42/60

42 is 70% of 60 — because 42 ÷ 60 × 100 = 70.

The calculation in one line

  • Formula: (part ÷ whole) × 100
  • 42 out of 60 = 42 ÷ 60 × 100 = 70%
  • The whole is the number that follows the word “of” — get that backwards and the answer inverts.
  • Over 100% means the part is bigger than the whole. Normal for growth; a swapped input almost everywhere else.

How what percent one number is of another is worked out

  1. Identify which number is the part (A) and which is the whole (B). The whole is the number that follows the word “of”.
  2. Divide the part by the whole. This gives the proportion as a decimal — 42 ÷ 60 = 0.7.
  3. Multiply by 100 to express it as a percentage: 70%.
  4. If the answer is over 100%, the part is larger than the whole — which is correct and common for growth figures, and a sign of a swapped input everywhere else.
P = (A ÷ B) × 100

Full method, rounding and worked examples →

SOURCE·Arithmetic only — no external rate·REVIEWED JUL 2026

Fractions, decimals and percentages side by side

Marks, shares and progress bars are all the same calculation. Recognising the common fractions on sight removes the calculator from most of them.

FRACTION TO PERCENT · JUL 2026
FractionDecimalPercent
1/20.550%
1/30.333333.33%
1/40.2525%
1/50.220%
1/60.166716.67%
1/80.12512.5%
2/30.666766.67%
3/40.7575%
3/50.660%
5/60.833383.33%
5/80.62562.5%
7/100.770%
7/80.87587.5%
9/100.990%
11/120.916791.67%

SOURCE·Arithmetic only — no external rate·REVIEWED JUL 2026

The four percentage calculations, and when each one applies

Every percentage question you will ever meet is one of four shapes. Naming the shape first is what stops the classic mistakes — and it is why this site keeps the four apart instead of putting one box on the page and hoping.

N × P⁄100

P% of N. Tips, commission, deposits, interest. 15% of $200 → $30.

N × (100−P)⁄100

P% off N. Sales and discounts — compute what you pay, not what you save. 30% off $80 → $56.

A ÷ B × 100

A is what % of B. Test scores, market share, progress. 42 of 60 → 70%.

(new−old) ÷ old × 100

% change. Price rises, growth, drops. 80 → 100 is +25%; 100 → 80 is −20%.

The base is everything

Nearly every percentage error is a wrong base — dividing by the new value instead of the old one, or taking a percentage of the discounted price instead of the original. The rule that fixes all of them: the base is the number the percentage is “of”, which in change problems is always the value you started from.

It is also why percentages do not add. A 20% rise followed by another 20% rise is not 40% — it is 44%, because the second rise acts on a bigger base (1.2 × 1.2 = 1.44). Compounding is just this effect repeated.

Mental shortcuts that survive real life

  • 10% is one decimal shift. 10% of $87.50 is $8.75. Nearly everything builds from this: 5% is half of it, 20% is double, 15% is one-and-a-half.
  • x% of y equals y% of x. 8% of 25 feels hard; 25% of 8 is obviously 2. Same number.
  • For discounts, think “what fraction do I pay”. 25% off means you pay ¾. A $59.99 jacket at 25% off is about $45 before you reach for a phone.

Percentage questions, answered

What percent is 42 of 60?
70%. Divide the part by the whole and multiply by 100: 42 ÷ 60 = 0.7, and 0.7 × 100 = 70%.
Which number do I divide by?
Always the whole — the number after the word 'of'. 'What percent is 42 of 60' divides by 60. Dividing the other way gives 142.86%, which is the answer to a different question: what percent 60 is of 42.
How do I work out a percentage of a number?
Turn the percentage into a decimal by dividing it by 100, then multiply. So 15% of 200 is 0.15 × 200 = 30. The reverse works too: multiplying by 1.15 adds 15% on top, which is why that shortcut appears everywhere from tipping to GST.
How do I take a percentage off a price?
Multiply the price by (100 minus the discount) divided by 100. A 30% discount means you pay 70% of the sticker price: $80 × 0.70 = $56. Working out what you pay directly is quicker and less error-prone than working out the saving and subtracting it.
How do I work out what percent one number is of another?
Divide the part by the whole and multiply by 100. Scoring 42 out of 60 is 42 ÷ 60 × 100 = 70%. The order matters — the number after 'of' is always the one you divide by.
How is percentage change calculated?
Take the change (new minus old), divide it by the original value, and multiply by 100. Going from 80 to 100 is a 25% increase (20 ÷ 80), but going from 100 back to 80 is only a 20% decrease (20 ÷ 100). The asymmetry trips people up constantly — the base is always the number you started from.
Why is a 50% increase not cancelled by a 50% decrease?
Because the base changes. Increase 100 by 50% and you have 150; decrease 150 by 50% and you are at 75, not 100. Successive percentages multiply rather than add — a 20% rise followed by a 20% fall leaves you at 96% of where you began.
What is a percentage point?
The absolute difference between two percentages. If interest rates go from 4% to 6%, that is a rise of 2 percentage points — but a 50% increase in the rate itself. News reports mix these up routinely, and the difference is enormous.
Does the calculator store what I type?
Only in your own browser, so your last calculation is still there when you come back. Nothing you enter is sent to a server.

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