Percentage Growth Calculator

A percentage is a fraction with the denominator as 100. When we express some fraction as a percentage, we express how many parts of the 100, the fraction denotes. In other words, a percentage indicates the quantity of something in terms of 100. The word ‘percent’ essentially means ‘per hundred’. Percentages are extremely useful in mathematical calculations, and for finding and comparing ratios. The symbol for percentage is %. For example, the ratio 15/16 as a percentage is 93.75%.

The simplest way of expressing a fraction (or ratio) as a percentage is A/B = P × 100, where ‘A’ is the numerator of the fraction, ‘B’ is the denominator and ‘P’ is the percentage. In a percentage calculation, the denominator denotes the total value of a quantity, and the numerator denotes some part of the total value. The percentage simply expresses this ratio in terms of 100.

The percentage growth (or increase) indicates the increase in the value of some quantity, when the initial and final values, and the change in the number of years is known to us. In other words, the calculator measures the increase from one value to another, of a given quantity, for a given period of time. For example, a percentage increase of 6% over one year means that, if the original value was divided into 100 equal parts, then after one year, that value would increase by 6 parts. If the original value was divided into 200 units, the value would increase by 12 parts; for 300 units, there would be an increase by 18 parts, and so on.

If A = initial value, B = final value, then the formula for percentage growth (P) is

$$ Percentage \; growth, P = {{Final \; value − initial \; value} \over {|initial \; value|}} * 100 $$

$$ or, P = {{B-A}\over A}*100 $$

To find the percentage growth over a number of years n (or the annual percentage growth), the formula is

$$ Annual \; percentage \; growth = {{percentage \; growth}\over{number \; of \; years}} $$

$$ or, \; Annual \; percentage \; growth = {P \over n} $$

The annual percentage growth is expressed as percentage per unit time (%/time). The unit of time may be years, hours, minutes, etc.

If A = initial value, B = final value, then the steps for calculating percentage growth (P) are

     i) First subtract the initial value from the final value.

     ii) Divide this difference by the absolute value of the initial value.

     iii) After performing the division, multiply the result with 100. This gives the percentage growth.

     iv) If the percentage growth turns out to be a negative number, it would mean that the final value is lesser than the initial value, and hence, there was a percentage decrease instead of an increase.

Consider this example. One litre of milk was worth INR 50 in the beginning of 2020. In the beginning of 2021, the cost of one litre milk became INR 55. What is the percentage increase in the price of milk?

In this case, the initial value (A) = 50, final value (B) = 55. Hence,

$$ P = {{B-A}\over A}*100 \\ P = {{55-50}\over 50}*100 \\ P = {5\over50}*100 = {1\over10}*100 = 10\%$$

Hence, there was a 10% increase in the cost of milk.

Calculating the percentage decrease follows a very similar process to percentage increase. There is a slight modification in the formula.

If A = initial value, B = final value, then the formula for percentage growth (Q) is

$$ Percentage \; decrease, Q = {{initial \; value − final \; value} \over {|initial \; value|}}*100 $$

$$ or,\; Q = {{A-B}\over A} * 100 $$

To find the percentage growth over a number of years n (or the annual percentage growth), the formula is

$$ Annual \; percentage \; decrease = {{percentage \; decrease} \over {number \; of \; years}} $$

$$ or, \; Annual \; percentage \; growth = {Q \over n} $$

The steps for calculating this are,

     i) First subtract the final value from the initial value.

     ii) Divide this difference by the absolute value of the initial value.

     iii) After performing the division, multiply the result with 100. This gives the percentage decrease.

     iv) If the percentage decrease turns out to be a negative number, it would mean that the final value is greater than the initial value, and hence, there was a percentage increase instead of a decrease.

Percentage increases and decreases find numerous applications in mathematics and science, and also in various walks of life. They can be used to calculate the rates of inflation, or the rates of interest in a bank. In chemistry, percentage increase in the mass of a chemical compound is calculated, and in the case of radioactive decay, the percentage decay of the mass of a radioactive substance can be found once the initial and present values of the mass are known for some period of time. In polls, the percentage of people preferring a particular candidate is useful to check if the difference is significant. In general, percentage changes can be used to analyse how a particular value changes over time. For studying statistical data, the percentage increase is a very common way of measuring growth.

Given below is a problem describing percentage growth in real life.

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