Percentage Calculator

Defining Percentage in Mathematics

In the realm of mathematics, percentages represent numbers or ratios as a fraction of 100. They serve as a tool to showcase a dimensionless relationship between two distinct numbers, standing alongside other methods such as ratios, fractions, and decimals. The symbol "%" typically denotes percentages, but terms like "percent" or "pct" can be used as well. To put it in context, 35% is the same as the decimal 0.35 or the fraction 35/100.

Calculation of Percentages

To determine a percentage, you multiply the ratio's value by 100. Taking an example, if a classroom of 50 students has 25 males, then the ratio for male students is 25/50 or 0.5. Converting this ratio to a percentage:

0.5 × 100 = 50

This implies that 50% of the students in the classroom are male.

The Percentage Formula

While there are various formats to express the percentage formula, its core remains an algebraic equation involving three variables:

$P\times V1=V2$

Here:

• P represents the percentage.
• V1 is the initial value that the percentage modifies.
• V2 denotes the outcome after applying the percentage to V1.

The above calculator seamlessly transforms the input percentage into its decimal equivalent to compute the result. But, when calculating the percentage, the answer is in its percentage form, not in decimal.

An Example

Given: $P\times 30=1.5$

To find P: P=1.5/30=0.05  $=5$

When calculating manually, one must convert the formula's percentage to its decimal form, so the P result should be multiplied by 100 to get its percentage value. This approach is exactly what the above calculator adopts but accepts values in percentage instead of decimals.

Formula for Percentage Difference

To determine the percentage difference between two numbers, one must take the absolute value of the difference between them, divide it by the average of the two numbers, and then multiply by 100. The formula is illustrated as:

Percentage Difference=2V1+V2​∣V1−V2∣​×100

Example:

Considering the numbers 10 and 6: ∣10−6∣10+62=48=0.5210+6​∣10−6∣​=84​=0.5 Converted to percentage: $0.5\times 100=50$

Formula for Percentage Change

To calculate the percentage increase or decrease, you'll need to find the difference between two values and then compare this difference to the initial value. This provides insight into the proportion by which the initial value has shifted.

For percentage increase or decrease: Percentage Change=DifferenceInitial Value×100Percentage Change=Initial ValueDifference​×100

The above percentage increase calculator determines the rise or fall in percentage of an input number. This involves converting the percentage into its decimal form and adding it to (for increase) or subtracting it from (for decrease) the number 1. When the original number is then multiplied by this resultant value, it gives the increased or decreased number.

Examples:

1. To increase 500 by 10% (0.1): $500\times (1+0.1)=550$

2. To decrease 500 by 10%: $500\times (1-0.1)=450$