What is the Percentage Difference from 45 to 21?

Step by step

1. Difference: 21 − 45 = -24
2. Divide by the starting value: -24 ÷ 45 = -0.533333
3. Multiply by 100: -53.3333%

How the answer is worked out

Percentage change measures a difference against the value you started with. The value went from 45 to 21, a difference of 24. Compared with the starting value of 45, that difference is 53.3333%, so this is a 53.3333% decrease.

The new value is 46.6667% of the old one: for every 100 at the start there are now 46.6667, so 53.3333 out of every 100 have gone.

Why calculate this?

Percentage change compares a new value with an old one regardless of size: price rises, growth, discounts, score changes.

• Sales: a price cut from $45 to $21 is a 53.3333% discount.
• Weight: going from 45 to 21 kilograms is a loss of 53.3333% of the starting weight.
• Results: if a team scores 21 points this season after 45 last season, its total has dropped by 53.3333%.

A quicker way

Find 1% of the starting value: 45 ÷ 100 = 0.45. The difference of 24 is 53.3333 of those steps.

Percentage change is not the same as percentage points. If a rate moves from 45% to 21%, it changes by 24 percentage points, but by 53.3333% relative to where it started.

Check the answer

Work forwards from the start: 45 × (1 − 0.533333) = 45 × 0.466667 = 21. Getting 21 shows the answer is right.

Rounding

Rounded to a whole number the change is -53, to one decimal place -53.3 and to two decimal places -53.33. Round only at the end: rounding halfway through a calculation can change the last digit.

The formula explained

percentage change = (new value − old value) ÷ old value × 100. A positive result is an increase and a negative result is a decrease. The old value is always the base, which is why the change from A to B and from B to A are different percentages.

Another worked example: 9 to 6

1. Difference: 6 − 9 = -3
2. Divide by the starting value: -3 ÷ 9 = -0.333333
3. Multiply by 100: -33.3333%

Other ways to ask this

The same calculation is often asked in other words. All of these have the answer above:

• Percentage decrease from 45 to 21
• What percent less is 21 than 45?
• 45 to 21 as a percent change
• How much did 45 fall going to 21, in percent?
• Relative change between 45 and 21

Terms used on this page

• Old value: the starting amount, used as the base of the percentage.
• New value: the amount after the change.
• Increase: a positive change: the new value is bigger.
• Percentage point: the plain difference between two rates, not a relative change.

The answer in other forms

Related results

The other way round: Percentage difference from 21 to 45

Doing it in a spreadsheet

In Excel, Google Sheets or Numbers type =(21-45)/45*100 into any cell. Replace the numbers with cell references (for example A1 and B1) to reuse the formula for a whole column.

Common mistakes

Always divide by the starting value, not the new one. A rise from 40 to 50 is +25%, but the fall from 50 back to 40 is −20%.

Practice examples

How this answer was calculated

The result is worked out from the numbers in this page's address when the page is opened, using exact arithmetic wherever possible and rounding only for display. Nothing is copied from a printed table. If you think an answer is wrong, please tell us through the contact page and we will check it.

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