Percentage Calculator in Common Phrases
Percentage Difference Calculator
Percentage Change Calculator
What is a Percentage?
In mathematics, a percentage represents a fraction of 100. It is a way to express the relationship between two numbers, similar to ratios, fractions, and decimals. The % symbol is commonly used to denote percentages, but they can also be written as “percent” or “pct.” For example, 35% is equivalent to 0.35 in decimal form or 35/100 as a fraction.
To calculate a percentage, multiply the ratio by 100. For example, if 25 out of 50 students in a class are male:2550=0.5\frac{25}{50} = 0.55025​=0.5 0.5×100=50%0.5 \times 100 = 50\%0.5×100=50%
This means 50% of the students in the classroom are male.
Percentage Formula
The percentage formula is a basic algebraic equation involving three variables:P×V1=V2P \times V1 = V2P×V1=V2
Where:
- P = Percentage
- V1 = Initial value
- V2 = Result after applying the percentage
For example, solving for P in the equation:P×30=1.5P \times 30 = 1.5P×30=1.5 P=1.530=0.05P = \frac{1.5}{30} = 0.05P=301.5​=0.05 0.05×100=5%0.05 \times 100 = 5\%0.05×100=5%
When solving manually, the percentage should be converted to decimal form first, then multiplied by 100 to express it as a percentage.
Percentage Difference Formula
The percentage difference between two values is calculated as:∣V1−V2∣(V1+V2)/2×100\frac{|V1 – V2|}{(V1 + V2)/2} \times 100(V1+V2)/2∣V1−V2∣​×100
For example, comparing 10 and 6:∣10−6∣(10+6)/2=48=0.5=50%\frac{|10 – 6|}{(10 + 6)/2} = \frac{4}{8} = 0.5 = 50\%(10+6)/2∣10−6∣​=84​=0.5=50%
Percentage Change Formula
Percentage increase or decrease is determined by comparing the difference between two values to the original value. The formula is:∣V1−V2∣V1×100\frac{|V1 – V2|}{V1} \times 100V1∣V1−V2∣​×100
For an increase of 10% on 500:500×(1+0.1)=550500 \times (1 + 0.1) = 550500×(1+0.1)=550
For a decrease of 10% on 500:500×(1−0.1)=450500 \times (1 – 0.1) = 450500×(1−0.1)=450
This formula is useful for calculating price changes, population growth, and other real-world applications.