The Complete List of Percentage Formulas

The Core Percentage Identity

Everything in percentage math flows from one identity:

Percentage = (Part ÷ Whole) × 100

Rearranging gives two more:

Part  = (Percentage / 100) × Whole
Whole = Part / (Percentage / 100)

These three are the foundation. Every other formula in this guide derives from them.

Basic Calculation Formulas

Find X% of a number

Result = (X / 100) × N

Example: 20% of 150 = (20/100) × 150 = 30

What percent is A of B?

% = (A / B) × 100

Example: 45 is what % of 180? (45/180) × 100 = 25%

Find the whole when you know the part and percentage

Whole = Part / (Percentage / 100)

Example: 30 is 15% of what number? 30 / 0.15 = 200

Change Formulas

Percentage increase

% increase = ((New − Old) / Old) × 100

Percentage decrease

% decrease = ((Old − New) / Old) × 100

Combined percentage change (same formula)

% change = ((New − Old) / Old) × 100

Positive result = increase. Negative result = decrease.

New value after a percentage increase

New = Old × (1 + Rate/100)

Example: 200 increased by 15% = 200 × 1.15 = 230

New value after a percentage decrease

New = Old × (1 − Rate/100)

Example: 200 decreased by 15% = 200 × 0.85 = 170

Find the original value before a percentage change

Original = New / (1 ± Rate/100)

Use + for increase, − for decrease.

Compound Percentage Formulas

Two sequential percentage changes

Combined % = (1 + r1/100) × (1 + r2/100) − 1) × 100

Example: +20% then −10% = (1.20 × 0.90 − 1) × 100 = +8% (not +10%)

Stacked discounts

Combined saving = 1 − (1 − d1/100) × (1 − d2/100)

Example: 20% off then 10% off = 1 − 0.80 × 0.90 = 28% total saving

Business Formulas

Markup (based on cost)

Markup % = ((Price − Cost) / Cost) × 100
Selling price = Cost × (1 + Markup/100)

Gross margin (based on revenue)

Margin % = ((Price − Cost) / Price) × 100

Convert markup to margin

Margin = Markup / (1 + Markup/100)

Convert margin to markup

Markup = Margin / (1 − Margin/100)

Discount formulas

Sale price    = Original × (1 − Discount/100)
Discount %    = ((Original − Sale) / Original) × 100
Original price = Sale / (1 − Discount/100)

Tax Formulas

Add tax

Total = Price × (1 + Rate/100)
Tax amount = Price × (Rate/100)

Remove tax (de-VAT)

Pre-tax price = Total / (1 + Rate/100)
Tax amount    = Total − Pre-tax price

Find the tax rate

Rate = ((Total − Price) / Price) × 100

Percentage Difference vs Percentage Change

These are often confused but measure different things.

Percentage change — how much one value changed relative to its starting point:

% change = ((New − Old) / Old) × 100

Percentage difference — the difference between two values relative to their average:

% difference = (|A − B| / ((A + B) / 2)) × 100

Use change when one value is clearly the “before” and the other is “after.” Use difference when comparing two values with no clear starting point.

Quick Conversion Reference