Percentage Calculator
Please provide any two values below and click the “Calculate” button to get the third value.
What is a percentage?
In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is one of the ways to represent a dimensionless relationship between two numbers; other methods include ratios, fractions, and decimals. Percentages are often denoted by the symbol “%” written after the number. They can also be denoted by writing “percent” or “pct” after the number. For example, 35% is equivalent to the decimal 0.35, or the fractions 
.
Percentages are computed by multiplying the value of a ratio by 100. For example, if 25 out of 50 students in a classroom are male, 
. The value of the ratio is therefore 0.5, and multiplying this by 100 yields:
0.5 × 100 = 50
In other words, the ratio of 25 males to students in the classroom is equivalent to 50% of students in the classroom being male.
Percentage formula
Although the percentage formula can be written in different forms, it is essentially an algebraic equation involving three values.
P × V1 = V2
P is the percentage, V1 is the first value that the percentage will modify, and V2 is the result of the percentage operating on V1. The calculator provided automatically converts the input percentage into a decimal to compute the solution. However, if solving for the percentage, the value returned will be the actual percentage, not its decimal representation.
Example:
P × 30 = 1.5
P = 1.5⁄30 = 0.05 × 100 = 5%
If solving manually, the formula requires the percentage in decimal form, so the solution for P needs to be multiplied by 100 in order to convert it to a percent. This is essentially what the calculator above does, except that it accepts inputs in percent rather than decimal form.
Percentage difference formula
The percentage difference between two values is calculated by dividing the absolute value of the difference between the two numbers by the average of those two numbers. Multiplying the result by 100 converts it into a percentage. The formula below illustrates this process clearly.
Percentage change formula
Percentage increase and decrease are calculated by computing the difference between two values and comparing that difference to the initial value. Mathematically, this involves using the absolute value of the difference between two values then dividing the result by the initial value, essentially calculating how much the initial value has changed.
The percentage increase calculator above computes an increase or decrease of a specific percentage of the input number. It basically involves converting a percent into its decimal equivalent, and either subtracting (decrease) or adding (increase) the decimal equivalent from and to 1, respectively. Multiplying the original number by this value will result in either an increase or decrease of the number by the given percent. Refer to the example below for clarification.
EX: 500 increased by 10% (0.1)
500 × (1 + 0.1) = 550
500 decreased by 10%
500 × (1 – 0.1) = 450
More Tools By AceCalculator.com
Frequently Asked Questions(FAQs)
A percentage calculator is an online tool that helps you quickly determine percentages, percentage increases or decreases, and the percentage difference between two numbers. It automates the calculations and removes the need for manual math.
To calculate a percentage manually, divide the part value by the total value and multiply by 100.
Example: (25 ÷ 200) × 100 = 12.5%.
The percentage difference shows how much two numbers differ relative to their average. It is calculated by dividing the absolute difference between the two numbers by their average and multiplying by 100.
Percentage refers to a portion out of 100, while percent change measures the relative increase or decrease between two values. Percent change shows growth or decline over time.
Yes. By entering the old and new values into the calculator, you can instantly find how much the value has increased or decreased in percentage terms.
Percentages are used daily in areas such as discounts, finance, taxes, and performance tracking. Understanding them helps you interpret data and make better decisions.
The formula for percentage change is:
(New Value − Old Value) ÷ Old Value × 100
A positive result shows an increase, while a negative result shows a decrease.