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What is the Percentage Difference from 83 to 81?

From 83 to 81 is a 2.4096% decrease

Step by step

  1. Difference: 81 − 83 = -2
  2. Divide by the starting value: -2 ÷ 83 = -0.024096
  3. Multiply by 100: -2.4096%

How the answer is worked out

Percentage change measures a difference against the value you started with. The value went from 83 to 81, a difference of 2. Compared with the starting value of 83, that difference is 2.4096%, so this is a 2.4096% decrease.

The new value is 97.5904% of the old one: for every 100 at the start there are now 97.5904, so 2.4096 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 $83 to $81 is a 2.4096% discount.
  • Weight: going from 83 to 81 kilograms is a loss of 2.4096% of the starting weight.
  • Results: if a team scores 81 points this season after 83 last season, its total has dropped by 2.4096%.

A quicker way

Find 1% of the starting value: 83 ÷ 100 = 0.83. The difference of 2 is 2.4096 of those steps.

Percentage change is not the same as percentage points. If a rate moves from 83% to 81%, it changes by 2 percentage points, but by 2.4096% relative to where it started.

Check the answer

Work forwards from the start: 83 × (1 − 0.024096) = 83 × 0.975904 = 81. Getting 81 shows the answer is right.

Rounding

Rounded to a whole number the change is -2, to one decimal place -2.4 and to two decimal places -2.41. 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: 16 to 18

  1. Difference: 18 − 16 = 2
  2. Divide by the starting value: 2 ÷ 16 = 0.125
  3. Multiply by 100: 12.5%

Why the change back is different

A 2.4096% fall followed by a 2.4096% rise does not bring you back to 83: it gives 82.9518. The second percentage is taken of 81, not of 83, so to undo this change you need 2.4691% instead.

Other ways to ask this

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

  • Percentage decrease from 83 to 81
  • What percent less is 81 than 83?
  • 83 to 81 as a percent change
  • How much did 83 fall going to 81, in percent?
  • Relative change between 83 and 81

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

Change-2.4096%
Difference-2
New ÷ old0.975904
Directiondecrease

Related results

83 to 79

From 83 to 79 is a 4.8193% decrease

83 to 80

From 83 to 80 is a 3.6145% decrease

83 to 82

From 83 to 82 is a 1.2048% decrease

83 to 91

From 83 to 91 is a 9.6386% increase

The other way round: Percentage difference from 81 to 83

Doing it in a spreadsheet

In Excel, Google Sheets or Numbers type =(81-83)/83*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

16 to 18
Show answer

From 16 to 18 is a 12.5% increase

16 to 10
Show answer

From 16 to 10 is a 37.5% decrease

48 to 69
Show answer

From 48 to 69 is a 43.75% increase

83 to 15
Show answer

From 83 to 15 is a 81.9277% decrease

30 to 60
Show answer

From 30 to 60 is a 100% increase

32 to 15
Show answer

From 32 to 15 is a 53.125% decrease

53 to 29
Show answer

From 53 to 29 is a 45.283% decrease

6 to 47
Show answer

From 6 to 47 is a 683.3333% increase

91 to 69
Show answer

From 91 to 69 is a 24.1758% decrease

95 to 26
Show answer

From 95 to 26 is a 72.6316% decrease

Calculate another

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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Questions

What is the Percentage Difference from 83 to 81?

Going from 83 to 81 is a 2.4096% decrease. Formula and steps.

Is going from 83 to 81 an increase or a decrease?

A decrease: the value fell by 2, which is 2.4096% of the starting value.

What is the percentage change from 81 back to 83?

2.4691%. It is a different number because the starting value is now 81, not 83.

What is the percentage difference between 83 and 81?

When neither value is the starting point, use the average as the base: 2 ÷ 82 × 100 = 2.439%. That is the symmetric percentage difference.

How do I calculate percentage change in Excel or Google Sheets?

Put the old value in A1 and the new value in B1, then type =(B1-A1)/A1 and format the cell as a percentage. For these numbers it shows -2.4096%.