X% of a value
result = V × X ÷ 100
Share matching a percentage.
Percentage calculator: X% of Y, proportion, percent change
The all-in-one percentage calculator: X% of a number, what percentage one value is of another, percent change between two values and the original value before an increase or decrease. Formulas, growth factor, percentage points and common pitfalls explained.
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How does this tool work?
This calculator brings the four everyday percentage calculations together in one place: taking X% of a value, finding what percentage a value is of a total, measuring the change between two values and recovering the original value before an increase or a decrease. Choose the type of calculation, enter two numbers, and the result appears immediately with the matching operation.
X% of Y: multiply Y by X, then divide by 100. 20% of 150 = 30. This is how you calculate sales tax, a commission, a deposit or a tip.
What percentage? Divide the part by the total, then multiply by 100. 30 out of 150 = 20%. This is how you turn a test score into a percentage, get a success rate or measure how much of a budget one expense takes.
Change between two values: (final value − starting value) ÷ starting value × 100. From 80 to 100, the change is +25%; from 100 to 80, it is −20%. The starting value is always the reference, which is why an increase and a decrease of the same amount do not have the same percentage.
Finding the original value: divide the result by the growth factor 1 + t ÷ 100, with t negative for a decrease. 120 after a 20% increase comes from 120 ÷ 1.2 = 100; 68 after a 15% decrease comes from 68 ÷ 0.85 = 80. Taking off or adding back the same percentage gives the wrong figure.
All four operations rest on the same idea: a percentage is a fraction with a denominator of 100, and a t% change means multiplying by 1 + t ÷ 100. Successive changes therefore combine by multiplying the factors, not by adding the percentages.
How to use this tool
Choose the type of calculation
X% of Y, What percentage, Change between two values or Find the original value.
Enter the two numbers
The labels adapt to the chosen calculation; decimals and negative percentages (decreases) are accepted.
Read and copy the result
The result is shown with the operation spelled out; the copy button copies it as text.
Percentage formulas
Four calculations, one idea: a percentage is a fraction out of 100.
Proportion as a percentage
p = part ÷ total × 100
Weight of a value within a total.
Percent change
t = (VA − VD) ÷ VD × 100
Relative change between two values.
Original value
VD = VA ÷ (1 + t ÷ 100)
Reverse percentage, t negative for a decrease.
- V, X
- reference value and percentage applied
- part, total
- value being measured and value that equals 100%
- VD, VA
- starting (original) value and final value
- t
- rate of change, in %
Example: from 40 to 50, t = 10 ÷ 40 × 100 = +25%, and 50 ÷ 1.25 gives back 40.
Use cases
Shopping and bills
Calculate sales tax or VAT, a discount or a tip, or work back to the price before tax.
Salaries and personal finance
Put a figure on a raise, compare two paychecks or measure the share of one expense in your budget.
Data analysis
Express counts as proportions, measure how a metric changed between two periods or compare groups.
School and exams
Review percentages, growth factors and reverse percentages from middle school to high school.
Examples
X% of Y
250 × 18 ÷ 100 = 45.
Input
18% of 250Result
45What percentage
45 ÷ 180 × 100 = 25%.
Input
45 out of 180Result
25%Increase
150 ÷ 1,250 × 100 = 12%.
Input
from 1,250 to 1,400Result
+12%Decrease
−15 ÷ 60 × 100 = −25%.
Input
from 60 to 45Result
−25%Original value
1,012 ÷ 1.10 = 920.
Input
1,012 after +10%Result
920Price before VAT
VAT is a 20% increase applied to the net price: 96 ÷ 1.2 = £80.
Input
£96 including 20% VATResult
£80 excluding VATTips and best practices
- Identify the reference value: it is the one that equals 100% and goes in the denominator.
- A t% increase followed by a t% decrease does not bring you back to the starting value.
- To undo a change, divide by the growth factor instead of subtracting the percentage.
- A gap between two rates is expressed in percentage points: from 4% to 5% is +1 point but +25%.
- For an average change over several years, use a compound annual growth rate (CAGR).
Sources and references
- Weisstein E.W., Percent (opens in a new tab), Wolfram MathWorldPage in English
- Weisstein E.W., Percentage Change (opens in a new tab), Wolfram MathWorldPage in English
- Programme de mathématiques pour le cycle 4 (annexe 2) (opens in a new tab), Ministère de l’Éducation nationalePage in French
Frequently asked questions
What is the formula for a percentage?
A percentage is a part expressed per 100: p = part ÷ total × 100. Conversely, X% of a value V is V × X ÷ 100.
How do I calculate percent change?
Work out (final value − starting value) ÷ starting value × 100. A positive result means an increase, a negative result a decrease.
How do I find a price before an increase or a discount?
Divide the final price by 1 + t for an increase, or by 1 − t for a decrease, with t written as a decimal. After a 30% discount, a $35 item was originally 35 ÷ 0.7 = $50.
What is the difference between a percentage and a percentage point?
A percentage point measures the absolute gap between two rates, a percentage the relative gap. An interest rate that goes from 2% to 3% rises by one point, which is a 50% increase in the rate.
Why don't +10% then −10% add up to 0%?
The decrease applies to a value larger than the starting value. 100 × 1.1 × 0.9 = 99: an overall decrease of 1% remains.
What does a percentage above 100% mean?
That the part exceeds the reference. 150% of a value is one and a half times that value; a change of +150% means the value was multiplied by 2.5.
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