How to use the percentage calculator
Choose the calculation that matches the question you are trying to answer. The calculator changes the input labels and formula for each mode so you do not have to translate every percentage problem into the same generic pair of fields.
The four modes cover common percentage calculations: finding a percentage of a number, finding what percent one number is of another, calculating percentage change from an original value to a new value, and working backward from a final value after a percentage increase or decrease.
Percentage formulas
Percent literally means “per hundred.” Converting a percentage such as 18% to decimal form gives 0.18. That decimal can then be multiplied by a base number, used as a ratio, or incorporated into an increase/decrease factor.
The four percentage calculations explained
Percentage of a number
Use this when the percentage and base number are known. Examples include 15% of 80, a 20% discount amount, or a 7.5% commission on a known total.
What percent?
Use this when you know a part and a whole. Divide the part by the whole and convert the ratio to a percentage.
Percentage change
Use an original value and a new value to measure the relative increase or decrease. The original value is the baseline in the denominator.
Reverse percentage
Use this when you know a final value after a percentage increase or decrease and want to recover the original value.
Percentage increase and percentage decrease
Percentage change measures the size of a change relative to the original value. If a price rises from $80 to $100, the change is $20. Divide $20 by the original $80 and multiply by 100: the price increased by 25%.
If a value falls, the numerator becomes negative. For example, a change from 100 to 80 produces -20%, which means a 20% decrease. The direction comes from the sign of the difference between new and original values.
The calculator uses the absolute value of the original amount in the denominator so the direction is determined by the change itself. If the original value is zero, the calculation is undefined because the formula would require division by zero.
Percentage points are not the same as percent change
This distinction matters whenever you compare two rates. A move from 4% to 6% is an increase of 2 percentage points. Relative to the original 4%, however, the rate increased by 50%.
Using “percent” and “percentage points” interchangeably can make a change sound much larger or smaller than it is. When the values themselves are percentages, state clearly whether you mean the direct point difference or the relative percentage change.
Percentage calculator examples
20% of $250
20 ÷ 100 × 250 = 50. The percentage amount is $50.
45 out of 300
45 ÷ 300 × 100 = 15%. So 45 is 15% of 300.
Rent from $1,800 to $1,950
The increase is $150. Divide $150 by the original $1,800 and multiply by 100 to get about 8.33%.
Recover a price after 20% increase
If a value became $120 after a 20% increase, divide $120 by 1.20. The original value was $100.
Common uses for percentage calculations
Percentage math appears in discounts, sales tax, tips, interest rates, markups, commissions, grades, budgets, business metrics, population changes, and many other comparisons. The arithmetic may be identical while the meaning changes with the context.
When a dollar amount is involved, decide whether you want the percentage amount or the final amount after adding or subtracting the percentage. For purchase tax, the Sales Tax Calculator handles subtotal, tax, and total directly. For restaurant bills, the Tip Calculator and Bill Splitter handles gratuity and equal splitting.
Example: Harper compares a rent increase
Harper’s monthly rent rises from $1,800 to $1,950. The $150 increase divided by the original $1,800 gives an increase of approximately 8.33%.
To reverse the calculation, the new rent is divided by 1 plus the percentage change in decimal form. Keep enough decimal places in the percentage if you want to recover the original amount accurately.
The baseline determines percentage change
Percentage change divides the difference by the original value, not by the new value. That makes the starting point part of the meaning of the result.
Moving from 80 to 100 is a 25% increase because the change of 20 is one-quarter of the original 80. Moving back from 100 to 80 is a 20% decrease because the same 20-point change is one-fifth of the new starting value of 100.
Reverse percentages are useful for recovering the original value
If a price, salary, population, or other value is known only after a percentage increase or decrease, reverse-percentage math solves for the starting amount. It is not the same as subtracting the percentage from the final value.
For example, a final price of $120 after a 20% increase came from $100 because $120 is 120% of the original value.
Percentage calculator FAQs
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For example, 20% of 250 is 0.20 × 250 = 50.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. For example, 45 is 15% of 300 because 45 ÷ 300 × 100 = 15%. The whole cannot be zero.
How do I calculate percentage increase or decrease?
Subtract the original value from the new value, divide the difference by the absolute value of the original value, and multiply by 100. A positive result indicates an increase and a negative result indicates a decrease.
How do I reverse a percentage increase or decrease?
Divide the final value by one plus the percentage change written as a decimal. Use a negative percentage for a decrease. For example, after a 20% increase, divide the final value by 1.20 to recover the original.
What is the difference between percentage change and percentage difference?
Percentage change compares a new value with a specific original baseline, so direction matters. Percentage difference usually compares two values without designating one as the original baseline.
What is the difference between percent and percentage points?
Percentage points measure the direct difference between two percentages. If a rate moves from 4% to 6%, that is an increase of 2 percentage points but a 50% increase relative to the original 4%.
Why is percentage change undefined when the original value is zero?
The percentage-change formula divides by the original value. Division by zero is undefined, so there is no finite percentage-change result from a baseline of zero.
For general mathematical use. Percentage results are ratios expressed per hundred; the meaning of any result depends on the quantities and baseline used in the calculation.