how to find percentage of a number

Per centum Reckoner

Calculator Use

Find a percentage or piece of work out the percentage given numbers and percent values. Use percentage formulas to figure out percentages and unknowns in equations. Add or subtract a pct from a number or solve the equations.

How to Calculate Percentages

There are many formulas for per centum bug. You can call back of the most basic as X/Y = P x 100. The formulas below are all mathematical variations of this formula.

Let's explore the three basic per centum problems. 10 and Y are numbers and P is the percentage:

Find P percent of X
Find what percent of X is Y
Find X if P per centum of information technology is Y

Read on to learn more than almost how to effigy percentages.

1. How to calculate percent of a number. Use the percentage formula: P% * X = Y

Example: What is 10% of 150?

Convert the problem to an equation using the percentage formula: P% * X = Y
P is 10%, X is 150, so the equation is ten% * 150 = Y
Catechumen 10% to a decimal by removing the percentage sign and dividing past 100: 10/100 = 0.ten
Substitute 0.x for ten% in the equation: x% * 150 = Y becomes 0.x * 150 = Y
Do the math: 0.10 * 150 = 15
Y = fifteen
So 10% of 150 is 15
Double check your answer with the original question: What is 10% of 150? Multiply 0.x * 150 = xv

2. How to find what per centum of 10 is Y. Utilize the percentage formula: Y/X = P%

Example: What percent of 60 is 12?

Convert the problem to an equation using the percent formula: Y/X = P%
10 is 60, Y is 12, so the equation is 12/60 = P%
Exercise the math: 12/lx = 0.20
Important! The result will always be in decimal form, not percent class. You need to multiply the effect by 100 to get the percent.
Converting 0.20 to a per centum: 0.twenty * 100 = 20%
So 20% of 60 is 12.
Double check your reply with the original question: What per centum of 60 is 12? 12/lx = 0.xx, and multiplying by 100 to get percentage, 0.20 * 100 = twenty%

three. How to find 10 if P percent of it is Y. Employ the percentage formula Y/P% = X

Example: 25 is twenty% of what number?

Catechumen the problem to an equation using the percentage formula: Y/P% = X
Y is 25, P% is 20, so the equation is 25/20% = X
Convert the percentage to a decimal by dividing past 100.
Converting twenty% to a decimal: twenty/100 = 0.20
Substitute 0.twenty for 20% in the equation: 25/0.20 = X
Practise the math: 25/0.20 = X
Ten = 125
And then 25 is xx% of 125
Double check your answer with the original question: 25 is 20% of what number? 25/0.20 = 125

Remember: How to convert a pct to a decimal

Remove the percentage sign and divide by 100
15.vi% = xv.6/100 = 0.156

Remember: How to convert a decimal to a percentage

Multiply past 100 and add together a per centum sign
0.876 = 0.876 * 100 = 87.6%

Percentage Problems

There are nine variations on the 3 basic bug involving percentages. See if you lot can match your problem to 1 of the samples below. The problem formats match the input fields in the calculator higher up. Formulas and examples are included.

What is P percentage of X?

Written as an equation: Y = P% * X
The 'what' is Y that nosotros desire to solve for
Remember to first convert percentage to decimal, dividing by 100
Solution: Solve for Y using the percentage formula
Y = P% * 10

Case: What is 10% of 25?

Written using the per centum formula: Y = 10% * 25
Commencement convert percentage to a decimal 10/100 = 0.1
Y = 0.1 * 25 = 2.v
So ten% of 25 is 2.5

Y is what percentage of X?

Written every bit an equation: Y = P% ? Ten
The 'what' is P% that we want to solve for
Split both sides by 10 to get P% on one side of the equation
Y ÷ X = (P% ? Ten) ÷ X becomes Y ÷ Ten = P%, which is the same as P% = Y ÷ 10
Solution: Solve for P% using the percentage formula
P% = Y ÷ 10

Example: 12 is what per centum of 40?

Written using the formula: P% = 12 ÷ twoscore
P% = 12 ÷ forty = 0.three
Convert the decimal to percent
P% = 0.three × 100 = 30%
And then 12 is xxx% of 40

Y is P percent of what?

Written as an equation: Y = P% * Ten
The 'what' is X that nosotros want to solve for
Dissever both sides by P% to get X on one side of the equation
Y ÷ P% = (P% × X) ÷ P% becomes Y ÷ P% = 10, which is the aforementioned as X = Y ÷ P%
Solution: Solve for X using the percentage formula
Ten = Y ÷ P%

Instance: nine is threescore% of what?

Writen using the formula: X = 9 ÷ lx%
Convert percent to decimal
60% ÷ 100 = 0.half-dozen
X = 9 ÷ 0.6
X = 15
And then 9 is lx% of 15

What per centum of X is Y?

Written as an equation: P% * 10 = Y
The 'what' is P% that we want to solve for
Split up both sides past X to go P% on one side of the equation
(P% * X) ÷ X = Y ÷ 10 becomes P% = Y ÷ Ten
Solution: Solve for P% using the percent formula
P% = Y ÷ X

Example: What percent of 27 is half dozen?

Written using the formula: P% = 6 ÷ 27
6 ÷ 27 = 0.2222
Catechumen decimal to percentage
P% = 0.2222 × 100
P% = 22.22%
So 22.22% of 27 is vi

P percent of what is Y?

Written as an equation: P% × X = Y
The 'what' is Ten that nosotros want to solve for
Dissever both sides by P% to get X on 1 side of the equation
(P% × X) ÷ P% = Y ÷ P% becomes X = Y ÷ P%
Solution: Solve for Ten using the percent formula
X = Y ÷ P%

Example: xx% of what is 7?

Written using the formula: X = 7 ÷ 20%
Catechumen the percent to a decimal
20% ÷ 100 = 0.2
10 = 7 ÷ 0.2
X = 35
Then 20% of 35 is 7.

P percentage of 10 is what?

Written as an equation: P% * X = Y
The 'what' is Y that we desire to solve for
Solution: Solve for Y using the percent formula
Y = P% * Ten

Example: v% of 29 is what?

Written using the formula: 5% * 29 = Y
Convert the percent to a decimal
5% ÷ 100 = 0.05
Y = 0.05 * 29
Y = 1.45
And so 5% of 29 is 1.45

Y of what is P pct?

Written as an equation: Y / X = P%
The 'what' is X that nosotros want to solve for
Multiply both sides by X to get X out of the denominator
(Y / X) * 10 = P% * X becomes Y = P% * X
Divide both sides by P% so that Ten is on ane side of the equation
Y ÷ P% = (P% * Ten) ÷ P% becomes Y ÷ P% = X
Solution: Solve for X using the percentage formula
10 = Y ÷ P%

Example: 4 of what is 12%?

Written using the formula: X = 4 ÷ 12%
Solve for X: X = Y ÷ P%
Catechumen the percent to a decimal
12% ÷ 100 = 0.12
Ten = four ÷ 0.12
X = 33.3333
4 of 33.3333 is 12%

What of X is P pct?

Written as an equation: Y / X = P%
The 'what' is Y that we want to solve for
Multiply both sides by 10 to get Y on one side of the equation
(Y ÷ X) * X = P% * X becomes Y = P% * X
Solution: Solve for Y using the per centum formula
Y = P% * Ten

Example: What of 25 is 11%?

Written using the formula: Y = 11% * 25
Convert the pct to a decimal
11% ÷ 100 = 0.11
Y = 0.xi * 25
Y = ii.75
So ii.75 of 25 is eleven%

Y of X is what per centum?

Written as an equation: Y / X = P%
The 'what' is P% that nosotros want to solve for
Solution: Solve for P% using the percentage formula
P% = Y / X

Instance: 9 of thirteen is what percent?

Written using the formula: P% = Y / X
9 ÷ 13 = P%
nine ÷ 13 = 0.6923
Convert decimal to percent by multiplying by 100
0.6923 * 100 = 69.23%
ix ÷ 13 = 69.23%
So 9 of thirteen is 69.23%

Related Calculators

Discover the change in pct as an increase or decrease using the Pct Change Calculator.

Solve decimal to percentage conversions with our Decimal to Percent Figurer.

Catechumen from percent to decimals with the Percent to Decimal Calculator.

If you need to convert betwixt fractions and percents come across our Fraction to Percent Calculator, or our Pct to Fraction Figurer.

References

Weisstein, Eric West. "Per centum." From MathWorld -- A Wolfram Spider web Resource.

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