What is the Percentage Difference from 5 to 13?

Step by step

1. Difference: 13 − 5 = 8
2. Divide by the starting value: 8 ÷ 5 = 1.6
3. Multiply by 100: 160%

How the answer is worked out

Percentage change measures a difference against the value you started with. The value went from 5 to 13, a difference of 8. Compared with the starting value of 5, that difference is 160%, so this is a 160% increase.

The new value is 2.6 times the old one: for every 100 at the start there are now 260. The value has more than doubled.

Why calculate this?

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

• Prices: an item whose price rises from $5 to $13 has gone up by 160%.
• Pay: a wage that rises from $5 to $13 an hour is a 160% pay rise.
• Audiences: a channel that grows from 5 to 13 subscribers has grown by 160%.

A quicker way

Find 1% of the starting value: 5 ÷ 100 = 0.05. The difference of 8 is 160 of those steps.

Percentage change is not the same as percentage points. If a rate moves from 5% to 13%, it changes by 8 percentage points, but by 160% relative to where it started.

Check the answer

Work forwards from the start: 5 × (1 + 1.6) = 5 × 2.6 = 13. Getting 13 shows the answer is right.

Rounding

Rounded to a whole number the change is 160, to one decimal place 160.0 and to two decimal places 160.00. 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: 2 to 65

1. Difference: 65 − 2 = 63
2. Divide by the starting value: 63 ÷ 2 = 31.5
3. Multiply by 100: 3,150%

Other ways to ask this

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

• Percentage increase from 5 to 13
• What percent more is 13 than 5?
• 5 to 13 as a percent change
• How much did 5 grow going to 13, in percent?
• Relative change between 5 and 13

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 13 to 5

Doing it in a spreadsheet

In Excel, Google Sheets or Numbers type =(13-5)/5*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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