Percentage Formulas Cheat Sheet

Every percentage formula you need, with examples and links to free calculators. Bookmark this page for quick reference.

Percent of a Number

Result = (Percentage × Value) ÷ 100

Find a percentage of any number. Used for tips, discounts, taxes, and commissions.

Example: 25% of 200 = (25 × 200) ÷ 100 = 50

Try: What is 25% of 200? →

What Percent is X of Y

Percentage = (Part ÷ Whole) × 100

Find what percentage one number is of another. Used for test scores, budget tracking, and comparisons.

Example: 50 is what % of 200? = (50 ÷ 200) × 100 = 25%

Try: 50 is what % of 200? →

Percentage Change

% Change = ((New − Old) ÷ |Old|) × 100

Measure how much a value increased or decreased. Used for price changes, salary raises, and growth metrics.

Example: 100 to 150 = ((150 − 100) ÷ 100) × 100 = 50%

Try: % change from 100 to 150 →

Reverse Percentage

Whole = Part ÷ (Percentage ÷ 100)

Find the original number when you know the part and percentage. Used for finding pre-tax prices and original values.

Example: 50 is 25% of what? = 50 ÷ 0.25 = 200

Try: 50 is 25% of what? →

Percentage Difference

% Diff = (|A − B| ÷ ((A + B) ÷ 2)) × 100

Compare two values symmetrically without a before/after relationship. Used for price comparisons and benchmarking.

Example: 100 and 150 = (50 ÷ 125) × 100 = 40%

Try: % difference 100 and 150 →

Profit Margin

Margin = ((Revenue − Cost) ÷ Revenue) × 100

Calculate profit as a percentage of revenue. Different from markup, which uses cost as the base.

Example: Revenue $150, Cost $100: ((150 − 100) ÷ 150) × 100 = 33.33%

Try: Margin Calculator →

Markup

Markup = ((Selling Price − Cost) ÷ Cost) × 100

Calculate how much you've added to cost to get selling price. A 50% markup on $100 = $150 selling price.

Example: Cost $100, Sell $150: ((150 − 100) ÷ 100) × 100 = 50%

Try: Markup Calculator →

Compound Interest

A = P(1 + r/n)^(nt)

Calculate how money grows when interest earns interest. P = principal, r = rate, n = compounds/year, t = years.

Example: $1,000 at 5% for 10 years (annual): $1,000 × (1.05)^10 = $1,628.89

Try: Compound Interest Calculator →

Loan Payment

M = P × [r(1+r)^n] ÷ [(1+r)^n − 1]

Calculate monthly loan payments. P = principal, r = monthly rate (annual/12), n = total months.

Example: $10,000 at 5% for 5 years: M = $188.71/month

Try: Loan Calculator →

ROI (Return on Investment)

ROI = ((Final Value − Cost) ÷ Cost) × 100

Measure the return on an investment as a percentage of the original cost.

Example: Invested $1,000, now worth $1,500: ((1500 − 1000) ÷ 1000) × 100 = 50%

Try: ROI Calculator →

Sales Tax

Tax = Price × (Tax Rate ÷ 100)

Calculate tax amount and total price. Reverse: Pre-tax = Total ÷ (1 + Rate/100).

Example: $100 at 8% tax: $100 × 0.08 = $8 tax, $108 total

Try: Sales Tax Calculator →

Tip

Tip = Bill × (Tip Rate ÷ 100)

Calculate tip amount and total. Split: Per person = Total ÷ Number of people.

Example: $50 bill at 18% tip: $50 × 0.18 = $9 tip, $59 total

Try: Tip Calculator →

Discount

Sale Price = Original × (1 − Discount ÷ 100)

Calculate sale price after a percentage discount. Savings = Original × (Discount ÷ 100).

Example: $80 at 25% off: $80 × 0.75 = $60 (save $20)

Try: Discount Calculator →

Mental Math Shortcuts

Percentages are reversible8% of 25 = 25% of 8 = 2. Swap if one is easier to calculate.
Finding 10%Move the decimal one place left. 10% of 450 = 45.
Finding 5%Find 10%, then halve it. 5% of 450 = 22.50.
Finding 15%Find 10% + 5%. 15% of 450 = 45 + 22.50 = 67.50.
Finding 20%Find 10% and double it. 20% of 450 = 90.
Finding 25%Divide by 4. 25% of 450 = 112.50.
Finding 50%Divide by 2. 50% of 450 = 225.
Finding 1%Move decimal two places left. 1% of 450 = 4.50. Then multiply for any %.
Rule of 72Divide 72 by the interest rate to estimate doubling time. At 6%, money doubles in ~12 years.

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