How To Find The Percentage Increase Or Decrease

Percentage Change | Increase and Subtract

For an explanation and everyday examples of using percentages generally meet our page Percentages: An Introduction. For more than full general percentage calculations see our page Percentage Calculators.

To calculate the percentage increment:

First: work out the difference (increase) between the two numbers yous are comparing.

Increase = New Number - Original Number

And then: dissever the increase past the original number and multiply the answer past 100.

% increase = Increase ÷ Original Number × 100.

If your respond is a negative number, then this is a percent decrease.

To summate percentage decrease:

Get-go: work out the difference (decrease) betwixt the two numbers you are comparing.

Decrease = Original Number - New Number

Then: divide the decrease past the original number and multiply the reply by 100.

% Decrease = Decrease ÷ Original Number × 100

If your answer is a negative number, then this is a percentage increase.

If you wish to summate the percentage increase or decrease of several numbers then nosotros recommend using the kickoff formula. Positive values betoken a percent increase whereas negative values indicate percentage decrease.

Percentage Change Calculator

Utilize this reckoner to work out the pct change of two numbers

More: Percentage Calculators

Examples - Percentage Increase and Decrease

In January Dylan worked a total of 35 hours, in Feb he worked 45.5 hours – by what percentage did Dylan'due south working hours increase in February?

To tackle this problem first we calculate the deviation in hours betwixt the new and old numbers. 45.5 - 35 hours = 10.five hours. Nosotros can meet that Dylan worked ten.5 hours more in Feb than he did in January – this is his increase. To work out the increase as a percentage it is now necessary to split the increase past the original (Jan) number:

x.five ÷ 35 = 0.3 (Encounter our division folio for instruction and examples of division.)

Finally, to go the percentage we multiply the reply past 100. This but ways moving the decimal identify two columns to the right.

0.3 × 100 = 30

Dylan therefore worked 30% more hours in February than he did in January.

In March Dylan worked 35 hours again – the same every bit he did in January (or 100% of his January hours). What is the percentage difference betwixt Dylan's February hours (45.5) and his March hours (35)?

Get-go summate the subtract in hours, that is: 45.five - 35 = x.5

Then split the decrease past the original number (February hours) so:

ten.five ÷ 45.v = 0.23 (to two decimal places).

Finally multiply 0.23 past 100 to requite 23%.Dylan's hours were 23% lower in March than in February.

Yous may accept thought that because at that place was a 30% increase between Dylan'due south January hours (35) and Feb (45.5) hours, that there would besides be a xxx% decrease between his February and March hours. As yous can run into, this assumption is wrong.

The reason is because our original number is different in each case (35 in the first example and 45.5 in the second). This highlights how of import it is to brand sure you lot are calculating the per centum from the correct starting betoken.

Sometimes it is easier to show pct decrease equally a negative number – to exercise this follow the formula in a higher place to calculate percent increment – your respond will be a negative number if there was a decrease. In Dylan'due south case the increase in hours between February and March is -10.5 (negative because it is a decrease). Therefore -x.5 ÷ 45.5 = -0.23. -0.23 × 100 = -23%.

Dylan'southward hours could be displayed in a data table equally:

Month	Hours Worked	Percentage Change
January	35
February	45.v	30%
March	35	-23%

Calculating Values Based on Per centum Change

Sometimes it is useful to be able to calculate actual values based on the percentage increase or decrease. Information technology is mutual to see examples of when this could be useful in the media.

You may see headlines like:

United kingdom of great britain and northern ireland rainfall was 23% above average this summer.
Unemployment figures testify a 2% decline.
Bankers ' bonuses slashed past 45%.

These headlines requite an thought of a tendency – where something is increasing or decreasing, simply often no actual data.

Without data, percentage change figures can exist misleading.

Ceredigion, a county in W Wales, has a very low trigger-happy crime charge per unit.

Law reports for Ceredigion in 2011 showed a 100% increase in violent crime. This is a startling number, particularly for those living in or thinking about moving to Ceredigion.

However, when the underlying data is examined information technology shows that in 2010 ane vehement crime was reported in Ceredigion. So an increment of 100% in 2011 meant that ii violent crimes were reported.

When faced with the actual figures, perception of the amount of vehement crime in Ceredigion changes significantly.

In social club to work out how much something has increased or decreased in real terms we need some actual data.

Take the instance of "Britain rainfall this summer was 23% above average" – nosotros can tell immediately that the Uk experienced nigh a quarter (25%) more rainfall than average over the summer. However, without knowing either what the average rainfall is or how much rain roughshod over the period in question we cannot work out how much pelting actually fell.

Calculating the actual rainfall for the period if the average rainfall is known.

If we know the average rainfall is 250mm, we can piece of work out the rainfall for the period past computing 250 + 23%.

Showtime work out 1% of 250, 250 ÷ 100 = two.5. And then multiply the respond by 23, because in that location was a 23% increase in rainfall.

ii.5 × 23 = 57.5.

Full rainfall for the menstruum in question was therefore 250 + 57.five = 307.5mm.

Calculating the average rainfall if the actual amount is known.

If the news written report states the new measurement and a percentage increase, "Great britain rainfall was 23% higher up average... 320mm of pelting fell…".

In this example we know the total rainfall was 320mm. We besides know that this is 23% above the average. In other words, 320mm equates to 123% (or one.23 times) of the boilerplate rainfall. To calculate the average nosotros divide the total (320) by i.23.

320 ÷ one.23 = 260.1626. Rounded to ane decimal place, the average rainfall is 260.2mm.

The difference betwixt the average and the actual rainfall can now exist calculated:
320 - 260.ii = 59.8mm.

We tin conclude that 59.8mm is 23% of the average rainfall amount (260.2mm), and that in real terms, 59.8mm more pelting cruel than boilerplate.

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