Calculate percentages of numbers, determine percentage increase or decrease, and find percentage difference with step-by-step formula breakdowns.
Find the exact value that represents a given percentage of a total amount.
Determine the proportion or percentage that one number represents of another.
Calculate how much a value has grown compared to its initial starting baseline.
Calculate how much a value has dropped from its initial starting baseline.
Compare two arbitrary quantities where neither value is considered the starting baseline.
Understand the mathematical principles behind percentage calculations with our clear, standardized formulas and explanations.
The word percentage originates from the Latin per centum, meaning "by the hundred." A percentage is simply a ratio or fraction expressed with a denominator of 100, represented by the symbol %.
1% = 1 ÷ 100 = 0.0150% = 50 ÷ 100 = 0.50100% = 100 ÷ 100 = 1.00
To calculate X% of Y, divide the percentage by 100 to convert it into a decimal fraction, and then multiply by the total number.
Result = (X ÷ 100) × Y
To find the proportion that X represents of a total Y, divide X by Y to get a decimal fraction, then multiply by 100.
Percentage = (X ÷ Y) × 100
Subtract the original starting value from the new value, divide the net difference by the original value, and multiply by 100.
Increase = ((New - Original) ÷ Original) × 100
Subtract the new value from the original value, divide the difference by the original value, and multiply by 100.
Decrease = ((Original - New) ÷ Original) × 100
Used when comparing two values without an established reference baseline. Divide the absolute difference by the average of the two numbers.
Difference = (|A - B| ÷ ((A + B) ÷ 2)) × 100
Discover how percentage calculations are applied in finance, commerce, nutrition, and everyday life.
Your dinner bill total comes to $150.00 and you want to leave a 20% tip for courteous service.
A winter jacket originally priced at $150.00 is marked down on sale for $100.00.
An employee receives a salary bump from $100,000 per year to $150,000 per year.
A student answers 30 questions correctly out of a total of 150 questions on an exam.
Store A sells a tablet for $100 while Store B sells an equivalent model for $120.
A local city levies an 8.25% sales tax on an electronics purchase priced at $240.00.
Get direct answers to common questions regarding percentage formulas, decimal handling, and calculations.
To calculate what percentage one number (X) represents of another (Y), divide X by Y, then multiply the quotient by 100:
Percentage = (X ÷ Y) × 100
Conversely, to find what X% of a number Y is, convert the percentage into a decimal by dividing by 100, then multiply by Y: (X ÷ 100) × Y.
20% of 100 is 20.
Because percentages are parts per hundred, any percentage of 100 is equal to the percentage number itself. Mathematically: (20 ÷ 100) × 100 = 0.20 × 100 = 20.
To calculate percentage increase between an original value and a new higher value:
New - Original.Gain ÷ Original.((New - Original) ÷ Original) × 100.
For example, if rent increases from $1,000 to $1,150, the increase is ((1,150 - 1,000) ÷ 1,000) × 100 = 15%.
To calculate percentage decrease between an original starting value and a new lower value:
Original - New.Reduction ÷ Original.((Original - New) ÷ Original) × 100.
For example, if an item drops from $150 to $100, the percentage decrease is ((150 - 100) ÷ 150) × 100 = 33.33%.
Percentage Change (increase or decrease) is directional and requires a definitive starting baseline (an "original" vs. a "new" value). The denominator is always the starting value.
Percentage Difference is non-directional. It is used when comparing two concurrent values where neither is considered the baseline (such as product prices at two competing stores, or heights of two buildings). The denominator is the average of the two numbers:
Percentage Difference = (|A - B| ÷ ((A + B) ÷ 2)) × 100
Yes! All 5 modes on this calculator support decimal numbers (such as 12.5% or $89.95) and negative inputs. Our calculation engine handles floating-point math cleanly, rounding accurately to up to 4 decimal places without computer binary rounding artifacts.