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Percentage Alter | Increment and Decrease

For an caption and everyday examples of using percentages mostly see our page Percentages: An Introduction. For more general percentage calculations come across our page Per centum Calculators.

To calculate the percentage increase:

Offset: work out the deviation (increment) between the ii numbers yous are comparing.

Increase = New Number - Original Number

Then: separate the increment by the original number and multiply the answer past 100.

% increase = Increase ÷ Original Number × 100.

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

To calculate percentage subtract:

Starting time: work out the difference (decrease) between the 2 numbers y'all are comparing.

Decrease = Original Number - New Number

So: split up the subtract by the original number and multiply the answer past 100.

% Decrease = Decrease ÷ Original Number × 100

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

If you wish to calculate the percentage increase or decrease of several numbers and so we recommend using the first formula. Positive values point a percentage increase whereas negative values betoken percentage subtract.

Percentage Change Calculator

Use this calculator to work out the per centum modify of 2 numbers

More: Pct Calculators

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The Skills You Need Guide to Numeracy

The Skills Y'all Need Guide to Numeracy

This four-office guide takes y'all through the basics of numeracy from arithmetic to algebra, with stops in between at fractions, decimals, geometry and statistics.

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Examples - Percentage Increment and Subtract

In Jan Dylan worked a full of 35 hours, in February he worked 45.5 hours – by what percentage did Dylan's working hours increase in February?

To tackle this problem outset we calculate the departure in hours between the new and old numbers. 45.five - 35 hours = ten.5 hours. We can see that Dylan worked 10.five hours more in February than he did in Jan – this is his increase. To work out the increase every bit a per centum it is now necessary to divide the increase by the original (January) number:

10.5 ÷ 35 = 0.3 (See our division folio for instruction and examples of division.)

Finally, to go the percent nosotros multiply the answer by 100. This simply means moving the decimal place two columns to the right.

0.3 × 100 = 30

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

In March Dylan worked 35 hours over again – the same equally he did in Jan (or 100% of his January hours). What is the percentage departure between Dylan's February hours (45.v) and his March hours (35)?

Commencement summate the decrease in hours, that is: 45.v - 35 = ten.5

Then split the decrease by the original number (February hours) then:

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

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

You may have thought that because at that place was a 30% increment between Dylan's January hours (35) and February (45.v) hours, that there would also be a 30% subtract betwixt his February and March hours. Every bit you tin can see, this assumption is incorrect.

The reason is considering our original number is dissimilar in each case (35 in the get-go example and 45.five in the 2d). This highlights how important it is to make sure y'all are computing the per centum from the correct starting point.

Sometimes it is easier to prove percentage subtract every bit a negative number – to do this follow the formula to a higher place to calculate percentage increment – your respond volition be a negative number if at that place was a subtract. In Dylan'southward case the increase in hours betwixt February and March is -10.5 (negative because information technology is a decrease). Therefore -10.five ÷ 45.five = -0.23. -0.23 × 100 = -23%.

Dylan's hours could be displayed in a data table as:

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

Calculating Values Based on Percentage Modify

Sometimes it is useful to exist able to calculate actual values based on the percent increase or decrease. It is common to see examples of when this could be useful in the media.

You may see headlines like:

U.k. rainfall was 23% above average this summer.
Unemployment figures show a 2% decline.
Bankers ' bonuses slashed past 45%.

These headlines give an thought of a trend – where something is increasing or decreasing, merely often no actual data.

Without data, per centum change figures can be misleading.

Ceredigion, a county in W Wales, has a very low tearing crime rate.

Police force reports for Ceredigion in 2011 showed a 100% increase in violent crime. This is a startling number, especially for those living in or thinking most moving to Ceredigion.

However, when the underlying information is examined information technology shows that in 2010 one fierce offense was reported in Ceredigion. So an increase of 100% in 2011 meant that two violent crimes were reported.

When faced with the actual figures, perception of the corporeality of violent crime in Ceredigion changes significantly.

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

Take the case of "Great britain rainfall this summer was 23% above average" – we can tell immediately that the UK experienced almost a quarter (25%) more rainfall than average over the summertime. Nonetheless, without knowing either what the average rainfall is or how much rain fell over the catamenia in question we cannot work out how much rain actually fell.

Computing the actual rainfall for the catamenia if the average rainfall is known.

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

Get-go piece of work out i% of 250, 250 ÷ 100 = 2.5. Then multiply the reply by 23, because at that place was a 23% increase in rainfall.

2.5 × 23 = 57.5.

Total rainfall for the period in question was therefore 250 + 57.v = 307.5mm.

Calculating the average rainfall if the actual amount is known.

If the news report states the new measurement and a percentage increase, "Britain rainfall was 23% above boilerplate... 320mm of rain barbarous…".

In this example nosotros know the total rainfall was 320mm. Nosotros besides know that this is 23% higher up the average. In other words, 320mm equates to 123% (or 1.23 times) of the average rainfall. To calculate the average nosotros dissever the total (320) by one.23.

320 ÷ 1.23 = 260.1626. Rounded to ane decimal place, the average rainfall is 260.2mm.

The deviation between the average and the actual rainfall can now be calculated:
320 - 260.ii = 59.8mm.

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

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