Percentage Formulas

Every percentage formula you need in one place. Quick reference cards with formulas and examples for calculating percentages, increases, decreases, and more.

Find Percentage of a Number
Result = (Percentage x Number) / 100
Example: What is 25% of 80? (25 x 80) / 100 = 20
Find What Percent X is of Y
Percentage = (X / Y) x 100
Example: 15 is what % of 60? (15 / 60) x 100 = 25%
Percentage Increase
% Increase = ((New – Old) / Old) x 100
Example: 50 to 65 ((65 – 50) / 50) x 100 = 30%
Percentage Decrease
% Decrease = ((Old – New) / Old) x 100
Example: 80 to 60 ((80 – 60) / 80) x 100 = 25%
Increase a Number by Percentage
New Value = Original x (1 + Percentage / 100)
Example: 200 + 15% 200 x 1.15 = 230
Decrease a Number by Percentage
New Value = Original x (1 – Percentage / 100)
Example: 200 – 15% 200 x 0.85 = 170
Find Original After Increase
Original = New Value / (1 + Percentage / 100)
Example: 115 after 15% increase 115 / 1.15 = 100
Percentage Difference
% Diff = (|A – B| / ((A + B) / 2)) x 100
Example: 40 vs 50 (10 / 45) x 100 = 22.2%

This page is your complete reference guide to percentage formulas. Bookmark it for quick access whenever you need to calculate percentages. Each formula includes a clear explanation and practical example.

For live calculations, start with our Percent Calculator. It covers the common “what is X% of Y?” question, reverse percentages, percentage increase, and percentage decrease in one place. You can also read our detailed guide on how to calculate percentages.

Basic Percentage Formulas

These are the three fundamental percentage formulas that form the basis of all percentage calculations:

Formula 1: Find Percentage of a Number

Use this when you need to find what amount a certain percentage represents.

Result = (Percentage x Number) / 100

Alternative form (often easier):

Result = Number x (Percentage / 100)
Examples
20% of 150 = 150 x 0.20 = 30
8.5% of 200 = 200 x 0.085 = 17
125% of 80 = 80 x 1.25 = 100

Formula 2: Find What Percentage One Number is of Another

Use this when you have two numbers and want to express their relationship as a percentage.

Percentage = (Part / Whole) x 100
Examples
30 is what % of 120? = (30 / 120) x 100 = 25%
45 is what % of 60? = (45 / 60) x 100 = 75%
8 is what % of 32? = (8 / 32) x 100 = 25%

Formula 3: Find the Whole from Part and Percentage

Use this when you know a part and what percentage it represents, and need to find the whole.

Whole = (Part / Percentage) x 100
Examples
25 is 20% of what? = (25 / 20) x 100 = 125
15 is 30% of what? = (15 / 30) x 100 = 50
42 is 70% of what? = (42 / 70) x 100 = 60

Percentage Change Formulas

These formulas measure how much a value has changed, either up or down.

Percentage Increase Formula

% Increase = ((New Value – Old Value) / Old Value) x 100
Example: Salary increased from $50,000 to $57,500
Increase = $57,500 – $50,000 = $7,500
% Increase = ($7,500 / $50,000) x 100 = 15%

Try our percentage increase calculator for instant results.

Percentage Decrease Formula

% Decrease = ((Old Value – New Value) / Old Value) x 100
Example: Price dropped from $200 to $150
Decrease = $200 – $150 = $50
% Decrease = ($50 / $200) x 100 = 25%

Percentage Difference Formula

Use this when comparing two values without a clear “before and after” relationship.

% Difference = (|Value1 – Value2| / ((Value1 + Value2) / 2)) x 100
Example: Comparing prices of $80 and $100
Difference = |80 – 100| = 20
Average = (80 + 100) / 2 = 90
% Difference = (20 / 90) x 100 = 22.2%

Applying Percentage Changes

These formulas apply a percentage increase or decrease to a value.

Add Percentage to a Number

New Value = Original x (1 + Percentage / 100)
Examples
$80 + 25% = $80 x 1.25 = $100
$500 + 8% = $500 x 1.08 = $540
150 + 50% = 150 x 1.50 = 225

Subtract Percentage from a Number

New Value = Original x (1 – Percentage / 100)
Examples
$80 – 25% = $80 x 0.75 = $60
$500 – 15% = $500 x 0.85 = $425
200 – 40% = 200 x 0.60 = 120

For discounts and sales, try our discount calculator.

Reverse Percentage Formulas

These formulas work backwards from a result to find the original value.

Find Original Before Percentage Increase

Original = Final Value / (1 + Percentage / 100)
Example: Price is $120 after 20% increase
Original = $120 / (1 + 20/100)
Original = $120 / 1.20 = $100

Find Original Before Percentage Decrease

Original = Final Value / (1 – Percentage / 100)
Example: Sale price is $75 after 25% off
Original = $75 / (1 – 25/100)
Original = $75 / 0.75 = $100

Business Percentage Formulas

These formulas are commonly used in business and finance.

Profit Margin Formula

Profit Margin = ((Selling Price – Cost) / Selling Price) x 100
Example: Cost $60, Sell for $100
Margin = (($100 – $60) / $100) x 100 = 40%

Use our profit margin calculator for business calculations.

Markup Formula

Markup = ((Selling Price – Cost) / Cost) x 100
Example: Cost $60, Sell for $100
Markup = (($100 – $60) / $60) x 100 = 66.67%

Sales Tax / VAT Formula

Total = Price x (1 + Tax Rate / 100)
Example: $50 item with 8% tax
Total = $50 x 1.08 = $54

Try our sales tax calculator for tax calculations.

Conversion Formulas

Percentage to Decimal

Decimal = Percentage / 100
Examples
25% = 25 / 100 = 0.25
7.5% = 7.5 / 100 = 0.075
150% = 150 / 100 = 1.50

Decimal to Percentage

Percentage = Decimal x 100
Examples
0.45 = 0.45 x 100 = 45%
0.08 = 0.08 x 100 = 8%
1.25 = 1.25 x 100 = 125%

Fraction to Percentage

Percentage = (Numerator / Denominator) x 100
Examples
3/4 = (3 / 4) x 100 = 75%
5/8 = (5 / 8) x 100 = 62.5%
1/3 = (1 / 3) x 100 = 33.33%

Use our fraction to percentage calculator for conversions.

All Percentage Formulas Summary

What You NeedFormula
X% of a numberNumber x (X / 100)
What % is A of B(A / B) x 100
A is X% of what(A / X) x 100
% increase((New - Old) / Old) x 100
% decrease((Old - New) / Old) x 100
Add X% to numberNumber x (1 + X / 100)
Subtract X% from numberNumber x (1 - X / 100)
Original before increaseFinal / (1 + X / 100)
Original before decreaseFinal / (1 - X / 100)
% difference|A - B| / ((A + B) / 2) x 100
Profit margin(Profit / Revenue) x 100
Markup(Profit / Cost) x 100
% to decimal% / 100
Decimal to %Decimal x 100
Fraction to %(Top / Bottom) x 100

Frequently Asked Questions

What is the basic percentage formula?

The most basic percentage formula is: Result = (Percentage x Number) / 100. This finds what amount a certain percentage represents. For example, 20% of 50 = (20 x 50) / 100 = 10.

How do I calculate percentage increase?

Use: % Increase = ((New Value – Old Value) / Old Value) x 100. Subtract the old from the new, divide by the old, multiply by 100. For example, 80 to 100: ((100-80)/80) x 100 = 25% increase.

What is the difference between margin and markup?

Margin divides profit by selling price. Markup divides profit by cost. Same profit, different percentages. A $40 profit on $100 sale is 40% margin but 66.7% markup (if cost was $60).

How do I reverse a percentage?

To find original before increase: Original = Final / (1 + %/100). Before decrease: Original = Final / (1 – %/100). For example, $115 after 15% increase: $115 / 1.15 = $100 original.

How do I convert percentage to decimal?

Divide by 100 (or move decimal two places left). 25% = 0.25, 8% = 0.08, 150% = 1.50. To convert back, multiply by 100.

What formula calculates what percent one number is of another?

Percentage = (Part / Whole) x 100. Divide the part by the whole, multiply by 100. For example, 15 is what % of 60? (15/60) x 100 = 25%.

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