What is the Percentage Difference from 31 to 51?

Step by step

1. Difference: 51 − 31 = 20
2. Divide by the starting value: 20 ÷ 31 = 0.645161
3. Multiply by 100: 64.5161%

How the answer is worked out

Percentage change measures a difference against the value you started with. The value went from 31 to 51, a difference of 20. Compared with the starting value of 31, that difference is 64.5161%, so this is a 64.5161% increase.

The new value is 1.6452 times the old one: for every 100 at the start there are now 164.5161.

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 $31 to $51 has gone up by 64.5161%.
• Pay: a wage that rises from $31 to $51 an hour is a 64.5161% pay rise.
• Audiences: a channel that grows from 31 to 51 subscribers has grown by 64.5161%.

A quicker way

Find 1% of the starting value: 31 ÷ 100 = 0.31. The difference of 20 is 64.5161 of those steps.

Percentage change is not the same as percentage points. If a rate moves from 31% to 51%, it changes by 20 percentage points, but by 64.5161% relative to where it started.

Check the answer

Work forwards from the start: 31 × (1 + 0.645161) = 31 × 1.645161 = 51. Getting 51 shows the answer is right.

Rounding

Rounded to a whole number the change is 65, to one decimal place 64.5 and to two decimal places 64.52. 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: 7 to 81

1. Difference: 81 − 7 = 74
2. Divide by the starting value: 74 ÷ 7 = 10.571429
3. Multiply by 100: 1,057.1429%

Other ways to ask this

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

• Percentage increase from 31 to 51
• What percent more is 51 than 31?
• 31 to 51 as a percent change
• How much did 31 grow going to 51, in percent?
• Relative change between 31 and 51

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 51 to 31

Doing it in a spreadsheet

In Excel, Google Sheets or Numbers type =(51-31)/31*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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