The Complete Everyday Math Guide: Percentages, Discounts, Taxes, Tips, Raises, Profit, Interest, And More

Everyday life is full of calculations: a 25% discount, a 7.5% sales tax, a 20% restaurant tip, a 4% salary raise, a 60% test score, a 35% profit margin, or a savings goal that asks you to set aside 15% of your income. The good news is that most of these problems use the same small set of ideas. Once you understand how percentages, ratios, changes, and totals work, you can solve a huge range of practical math problems with confidence.

This guide is designed to be a complete, plain-English reference for common calculations people run into in daily life. You will learn the formulas, see examples, and understand the difference between similar ideas such as markup and margin, or percentage points and percentages. Keep it handy whenever you need to check a sale price, compare prices, estimate taxes, calculate a raise, evaluate a budget, or understand growth over time.

1. What Is A Percentage?

A percentage is a way to express a number as a part of 100. The word percent means “per hundred.” So 25% means 25 out of 100, 50% means 50 out of 100, and 100% means the whole amount.

Percentages are useful because they make comparisons easier. Saying that you saved $20 is helpful, but saying you saved 20% tells you how large that saving is compared with the original price. A $20 saving on a $100 item is big. A $20 saving on a $2,000 item is much smaller.

1.1 How To Convert Between Percentages, Decimals, And Fractions

Most percentage calculations become easier when you convert the percentage to a decimal. To convert a percentage to a decimal, divide by 100.

• 10% becomes 0.10
• 25% becomes 0.25
• 50% becomes 0.50
• 7.5% becomes 0.075
• 125% becomes 1.25

To convert a decimal back to a percentage, multiply by 100.

• 0.20 becomes 20%
• 0.375 becomes 37.5%
• 1.40 becomes 140%

Some common fractions are worth memorizing because they appear often in daily life.

• 1/2 equals 50%
• 1/4 equals 25%
• 3/4 equals 75%
• 1/5 equals 20%
• 1/10 equals 10%
• 1/3 is about 33.33%
• 2/3 is about 66.67%

2. How To Calculate A Percentage Of A Number

This is one of the most common percentage calculations. You use it for discounts, tips, tax, savings contributions, interest, grades, and more.

The formula is:

Percentage of a number = number × percentage as a decimal

For example, to calculate 20% of 80:

80 × 0.20 = 16

So 20% of 80 is 16.

2.1 Examples Of Finding A Percentage Of A Number

• 15% of 200 = 200 × 0.15 = 30
• 8% of 50 = 50 × 0.08 = 4
• 35% of 120 = 120 × 0.35 = 42
• 2.5% of 1,000 = 1,000 × 0.025 = 25

This same formula powers many everyday calculations. A 15% tip on a $60 meal is $60 × 0.15 = $9. A 30% discount on a $90 jacket is $90 × 0.30 = $27. A 6% tax on a $200 purchase is $200 × 0.06 = $12.

2.2 Mental Math Tricks For Percentages

You do not always need a calculator. Many percentages can be built from easier ones.

• 10% is found by moving the decimal one place left. 10% of 80 is 8.
• 5% is half of 10%. 5% of 80 is 4.
• 1% is found by dividing by 100. 1% of 80 is 0.80.
• 20% is double 10%. 20% of 80 is 16.
• 25% is one quarter. 25% of 80 is 20.
• 50% is half. 50% of 80 is 40.

For example, to find 15% of 80, find 10% and 5%, then add them: 8 + 4 = 12.

3. How To Find What Percentage One Number Is Of Another

Sometimes you know two numbers and want to find the percentage relationship between them. This is common for test scores, budgets, sales performance, attendance, completion rates, and progress goals.

The formula is:

Percentage = part ÷ whole × 100

For example, if you scored 45 points out of 60, then:

45 ÷ 60 × 100 = 75%

So 45 is 75% of 60.

3.1 Examples Of One Number As A Percentage Of Another

• 30 out of 50 = 30 ÷ 50 × 100 = 60%
• 18 out of 20 = 18 ÷ 20 × 100 = 90%
• 12 out of 80 = 12 ÷ 80 × 100 = 15%
• 250 out of 1,000 = 250 ÷ 1,000 × 100 = 25%

The key is knowing which number is the part and which number is the whole. In “what percentage is 12 of 80,” the part is 12 and the whole is 80. In “what percentage of your income is rent,” rent is the part and income is the whole.

4. How To Calculate Percentage Increase

Percentage increase tells you how much something grew compared with where it started. You use it for price increases, salary raises, investment growth, rent increases, business revenue, weight gain, and population growth.

The formula is:

Percentage increase = increase ÷ original amount × 100

Where:

Increase = new amount - original amount

Example: A price rises from $80 to $100.

• Increase = 100 - 80 = 20
• Percentage increase = 20 ÷ 80 × 100 = 25%

The price increased by 25%.

4.1 Percentage Increase Examples

• A salary rises from $50,000 to $55,000. Increase = $5,000. Percentage increase = 5,000 ÷ 50,000 × 100 = 10%.
• A bill rises from $120 to $150. Increase = $30. Percentage increase = 30 ÷ 120 × 100 = 25%.
• Your savings grow from $2,000 to $2,500. Increase = $500. Percentage increase = 500 ÷ 2,000 × 100 = 25%.

Always divide by the original amount, not the new amount. This is one of the most common percentage mistakes.

5. How To Calculate Percentage Decrease

Percentage decrease tells you how much something fell compared with where it started. You use it for discounts, price drops, weight loss, lower expenses, reduced debt, and declining sales.

The formula is:

Percentage decrease = decrease ÷ original amount × 100

Where:

Decrease = original amount - new amount

Example: A price drops from $100 to $75.

• Decrease = 100 - 75 = 25
• Percentage decrease = 25 ÷ 100 × 100 = 25%

The price decreased by 25%.

5.1 Percentage Decrease Examples

• A bill falls from $200 to $160. Decrease = $40. Percentage decrease = 40 ÷ 200 × 100 = 20%.
• Weight falls from 180 lb to 171 lb. Decrease = 9 lb. Percentage decrease = 9 ÷ 180 × 100 = 5%.
• A product price falls from $50 to $35. Decrease = $15. Percentage decrease = 15 ÷ 50 × 100 = 30%.

Again, divide by the original amount. If something goes from 100 to 75, the decrease is 25% because 25 is 25% of the original 100.

6. How To Reverse A Percentage

Reversing a percentage means working backward from a final amount to find the original amount. This comes up when you know the price after tax, after a discount, after a raise, or after a markup.

The basic idea is to divide by the final multiplier.

6.1 Reversing A Percentage Increase

If an amount has increased by a percentage, the final amount equals:

Original amount × (1 + percentage as a decimal)

To reverse it:

Original amount = final amount ÷ (1 + percentage as a decimal)

Example: A price after a 20% increase is $120. What was the original price?

120 ÷ 1.20 = 100

The original price was $100.

6.2 Reversing A Percentage Decrease

If an amount has decreased by a percentage, the final amount equals:

Original amount × (1 - percentage as a decimal)

To reverse it:

Original amount = final amount ÷ (1 - percentage as a decimal)

Example: A sale price after 25% off is $75. What was the original price?

75 ÷ 0.75 = 100

The original price was $100.

A common mistake is to add 25% back to $75. That gives $93.75, not $100. Why? Because 25% off was calculated from the original price, not the discounted price.

7. Discounts And Sale Prices

Discounts are percentage decreases. To calculate a discount, first find the discount amount, then subtract it from the original price.

The formula is:

Sale price = original price × (1 - discount percentage as a decimal)

Example: A $120 item is 30% off.

120 × (1 - 0.30) = 120 × 0.70 = 84

The sale price is $84.

7.1 Discount Examples

• $80 item at 25% off: 80 × 0.75 = $60
• $50 item at 10% off: 50 × 0.90 = $45
• $200 item at 40% off: 200 × 0.60 = $120
• $35 item at 15% off: 35 × 0.85 = $29.75

7.2 Stacked Discounts

Stacked discounts do not usually add directly. If an item is 20% off and then an extra 10% off, the total discount is not 30%. The second discount applies to the already discounted price.

Example: $100 item, 20% off, then 10% off.

• After 20% off: 100 × 0.80 = $80
• After another 10% off: 80 × 0.90 = $72

The final price is $72, which is a 28% total discount from $100.

8. Sales Tax And VAT

Sales tax and value-added tax are percentage increases added to a price. Depending on where you live, tax may be shown separately at checkout or included in the listed price.

If tax is added to the price, use:

Total price = pre-tax price × (1 + tax rate as a decimal)

Example: A $100 purchase with 8% sales tax:

100 × 1.08 = 108

The total is $108.

8.1 Finding The Tax Amount

To find only the tax amount:

Tax amount = pre-tax price × tax rate as a decimal

Example: $250 purchase with 6.5% tax:

250 × 0.065 = 16.25

The tax is $16.25, and the total is $266.25.

8.2 Removing Tax From A Tax-Included Price

If a total price already includes tax and you want the pre-tax price, reverse the percentage increase.

Pre-tax price = tax-included price ÷ (1 + tax rate as a decimal)

Example: A price including 20% VAT is $120.

120 ÷ 1.20 = 100

The pre-tax price is $100, and the tax amount is $20.

9. Tips And Service Charges

Tips are usually calculated as a percentage of a bill. In restaurants, people often calculate tips before tax, but practices vary by location and personal preference. Service charges may be mandatory, while tips may be optional. Always check the bill carefully.

The tip formula is:

Tip = bill amount × tip percentage as a decimal

Example: 20% tip on a $75 bill:

75 × 0.20 = 15

The tip is $15, and the total is $90.

9.1 Fast Tip Calculations

• 10% tip: move the decimal one place left.
• 15% tip: calculate 10% plus 5%.
• 20% tip: calculate 10% and double it.
• 25% tip: divide the bill by 4.

For a $64 bill, 20% is 12.80 because 10% is 6.40 and double that is 12.80.

10. Price Increases And Inflation-Style Calculations

Price increases are percentage increases. If your rent, utilities, groceries, insurance, or subscription costs rise, you can calculate both the dollar increase and the percentage increase.

Example: A monthly subscription rises from $12 to $15.

• Dollar increase = 15 - 12 = $3
• Percentage increase = 3 ÷ 12 × 100 = 25%

A $3 increase may sound small, but a 25% increase is substantial. Percentages help reveal the scale of the change.

10.1 Comparing Price Increases Fairly

Suppose your phone bill rises by $5 and your streaming subscription rises by $5. Are those increases equally large? Not necessarily.

• Phone bill: $100 to $105 = 5% increase
• Streaming subscription: $10 to $15 = 50% increase

The dollar increase is the same, but the percentage increase is very different.

11. Salary Raises And Pay Changes

Salary raises are another form of percentage increase. To calculate your new salary after a raise, multiply your current salary by 1 plus the raise percentage.

New salary = current salary × (1 + raise percentage as a decimal)

Example: $60,000 salary with a 5% raise:

60,000 × 1.05 = 63,000

The new salary is $63,000.

11.1 Calculating The Raise Amount

To find only the raise amount:

Raise amount = current salary × raise percentage as a decimal

Example: 4% raise on $48,000:

48,000 × 0.04 = 1,920

The raise is $1,920 per year.

11.2 Hourly Wage Raises

The same method works for hourly wages. If your hourly rate increases from $20 to $22:

• Increase = 22 - 20 = 2
• Percentage increase = 2 ÷ 20 × 100 = 10%

Your hourly wage increased by 10%.

12. Profit Margin

Profit margin tells you what percentage of revenue is profit. It is commonly used in business, freelancing, retail, and investing. The basic formula is:

Profit margin = profit ÷ revenue × 100

Where:

Profit = revenue - cost

Example: You sell a product for $100 and it costs you $60.

• Profit = 100 - 60 = $40
• Profit margin = 40 ÷ 100 × 100 = 40%

Your profit margin is 40%.

12.1 Why Profit Margin Matters

Profit margin shows how much of each sales dollar remains after costs. A 40% margin means that for every $1 of revenue, $0.40 is profit before considering any additional expenses not included in your cost calculation.

Be clear about what costs are included. Gross margin considers the cost of goods sold. Net margin considers broader expenses such as overhead, taxes, interest, and operating costs.

13. Markup

Markup tells you how much you add to cost to set a selling price. It is related to margin, but it is not the same thing.

The formula is:

Markup = profit ÷ cost × 100

Example: An item costs $60 and sells for $100.

• Profit = 100 - 60 = $40
• Markup = 40 ÷ 60 × 100 = 66.67%

The markup is 66.67%.

13.1 Margin Vs Markup

Margin divides profit by selling price. Markup divides profit by cost. That difference matters.

• Cost: $60
• Selling price: $100
• Profit: $40
• Margin: 40 ÷ 100 = 40%
• Markup: 40 ÷ 60 = 66.67%

Many pricing mistakes happen when people confuse margin and markup. A 50% markup does not mean a 50% profit margin. If cost is $100 and markup is 50%, the selling price is $150. Profit is $50. Margin is 50 ÷ 150 = 33.33%.

14. Grades And Test Scores

Most test score percentages use the part-over-whole formula:

Score percentage = points earned ÷ total possible points × 100

Example: You earned 42 points out of 50.

42 ÷ 50 × 100 = 84%

Your score is 84%.

14.1 Weighted Grades

Weighted grades are more complex because different categories count for different percentages of the final grade. For example:

• Homework: 20%
• Quizzes: 30%
• Final exam: 50%

If your category scores are 90%, 80%, and 70%, calculate:

• Homework: 90 × 0.20 = 18
• Quizzes: 80 × 0.30 = 24
• Final exam: 70 × 0.50 = 35

Add them: 18 + 24 + 35 = 77. Your weighted grade is 77%.

15. Budget Percentages

Budget percentages help you understand where your money goes. The formula is:

Category percentage = category spending ÷ total income or total spending × 100

Example: You earn $4,000 per month and spend $1,200 on rent.

1,200 ÷ 4,000 × 100 = 30%

Rent is 30% of your monthly income.

15.1 Common Budget Categories

• Housing
• Food
• Transportation
• Insurance
• Debt payments
• Savings
• Entertainment
• Utilities
• Giving

There is no single perfect budget for everyone. Percentages are most useful because they let you compare your spending to your goals. If dining out is 18% of your income and savings is 3%, that may reveal an opportunity to adjust.

16. Savings Goals

Percentages make savings goals easier to plan. You might save a percentage of income, calculate progress toward a target, or determine how much more you need.

To calculate savings rate:

Savings rate = amount saved ÷ income × 100

Example: You save $600 from a $4,000 monthly income.

600 ÷ 4,000 × 100 = 15%

Your savings rate is 15%.

16.1 Progress Toward A Savings Goal

To calculate progress:

Progress percentage = amount saved ÷ goal amount × 100

Example: You have saved $3,000 toward a $10,000 goal.

3,000 ÷ 10,000 × 100 = 30%

You are 30% of the way to your goal.

16.2 How Much To Save Each Month

If you know your goal and deadline, divide the remaining amount by the number of months.

Example: You want $6,000 in 12 months and already have $1,200.

• Remaining amount = 6,000 - 1,200 = $4,800
• Monthly savings needed = 4,800 ÷ 12 = $400

You need to save $400 per month.

17. Weight Loss And Weight Gain Percentages

Weight change percentages use the same increase and decrease formulas. They can help track progress, but they should be interpreted carefully because health is not just a number.

For weight loss:

Weight loss percentage = weight lost ÷ starting weight × 100

Example: You go from 200 lb to 190 lb.

• Weight lost = 10 lb
• Percentage lost = 10 ÷ 200 × 100 = 5%

You lost 5% of your starting weight.

For weight gain:

Weight gain percentage = weight gained ÷ starting weight × 100

Example: You go from 150 lb to 165 lb.

• Weight gained = 15 lb
• Percentage gained = 15 ÷ 150 × 100 = 10%

You gained 10% of your starting weight.

18. Simple Interest

Simple interest is interest calculated only on the original principal. It is commonly used in basic finance examples and some short-term lending situations.

The formula is:

Simple interest = principal × rate × time

Rate should be written as a decimal, and time is usually in years.

Example: $1,000 at 5% simple interest for 3 years:

1,000 × 0.05 × 3 = 150

The interest is $150. The final amount is $1,150.

18.1 Simple Interest With Partial Years

If time is less than one year, write it as a fraction or decimal. Six months is 0.5 years.

Example: $2,000 at 6% simple interest for 6 months:

2,000 × 0.06 × 0.5 = 60

The interest is $60.

19. Compound Growth Basics

Compound growth means growth is calculated on the original amount plus previous growth. It matters for savings, investing, debt, inflation, and population growth.

The basic compound growth formula is:

Final amount = starting amount × (1 + growth rate) ^ number of periods

Example: $1,000 grows by 5% per year for 3 years.

1,000 × 1.05 ^ 3 = 1,157.625

The final amount is about $1,157.63.

19.1 Why Compound Growth Is Different From Simple Growth

With simple growth, 5% of $1,000 is $50 each year. Over 3 years, that would be $150, for a total of $1,150.

With compound growth, the second year’s growth is calculated on $1,050, not just $1,000. The third year’s growth is calculated on the new larger amount. That is why the compound result is $1,157.63 instead of $1,150.

19.2 Compound Decrease

Compound decrease works the same way, but the multiplier is less than 1.

Example: A value decreases by 10% each year for 3 years, starting at $1,000.

1,000 × 0.90 ^ 3 = 729

After 3 years, the value is $729.

Notice that three decreases of 10% do not equal a 30% decrease in the simple sense. The final amount is 72.9% of the original, so the total decrease is 27.1%.

20. Percentage Points Vs Percentages

Percentage points and percentages are often confused, especially in news, finance, polling, interest rates, and school data.

A percentage point is the simple difference between two percentages. A percent change compares that difference with the starting percentage.

Example: An interest rate rises from 4% to 5%.

• The increase is 1 percentage point.
• The percentage increase is 1 ÷ 4 × 100 = 25%.

Both statements are true, but they mean different things. Saying the rate rose by 1% would be unclear and often incorrect. It rose by 1 percentage point, or by 25% relative to its previous level.

20.1 Another Percentage Points Example

If a test pass rate rises from 80% to 90%, it increased by 10 percentage points. The relative percentage increase is:

10 ÷ 80 × 100 = 12.5%

So the pass rate rose by 10 percentage points, which is a 12.5% increase relative to the original pass rate.

21. Ratios, Rates, And Unit Prices

Not every everyday calculation is a percentage. Ratios and rates also help you compare quantities.

A ratio compares two quantities. For example, if a recipe uses 2 cups of flour and 1 cup of sugar, the flour-to-sugar ratio is 2:1.

A rate compares quantities with different units. For example, miles per hour, dollars per pound, and words per minute are rates.

21.1 Unit Price

Unit price helps you compare shopping options.

The formula is:

Unit price = total price ÷ number of units

Example: A 12-pack costs $6.

6 ÷ 12 = 0.50

The unit price is $0.50 each.

If a 20-pack costs $9, then:

9 ÷ 20 = 0.45

The 20-pack is cheaper per item.

22. A Quick Formula Cheat Sheet

Here are the most useful everyday calculation formulas in one place.

• Percentage of a number: number × percentage as decimal
• What percentage one number is of another: part ÷ whole × 100
• Percentage increase: increase ÷ original × 100
• Percentage decrease: decrease ÷ original × 100
• New amount after increase: original × (1 + percentage as decimal)
• New amount after decrease: original × (1 - percentage as decimal)
• Reverse an increase: final ÷ (1 + percentage as decimal)
• Reverse a decrease: final ÷ (1 - percentage as decimal)
• Tip: bill × tip percentage as decimal
• Sales tax: pre-tax price × tax rate as decimal
• Total with tax: pre-tax price × (1 + tax rate)
• Profit margin: profit ÷ revenue × 100
• Markup: profit ÷ cost × 100
• Simple interest: principal × rate × time
• Compound growth: starting amount × (1 + rate) ^ periods
• Unit price: total price ÷ units

23. Common Mistakes People Make

Most percentage mistakes come from using the wrong base, mixing up similar concepts, or adding percentages when they should be compounded. Here are the biggest pitfalls to watch for.

23.1 Dividing By The Wrong Number

For percentage increase or decrease, always divide by the original amount. If a price rises from $50 to $60, the increase is $10. Divide by $50, not $60.

10 ÷ 50 × 100 = 20%

23.2 Thinking A Percentage Increase And Decrease Cancel Out

A 20% increase followed by a 20% decrease does not return you to the original amount.

Example: Start with $100.

• Increase by 20%: 100 × 1.20 = $120
• Decrease by 20%: 120 × 0.80 = $96

You end at $96, not $100.

23.3 Adding Stacked Discounts Incorrectly

A 30% discount followed by another 20% discount is not a 50% discount. On a $100 item:

• First discount: 100 × 0.70 = $70
• Second discount: 70 × 0.80 = $56

The total discount is 44%, not 50%.

23.4 Confusing Markup With Margin

Markup is based on cost. Margin is based on selling price. If you need a 40% margin, you cannot simply add 40% to cost. Adding 40% to a $100 cost gives a $140 price and a $40 profit, but the margin is 40 ÷ 140 = 28.57%.

23.5 Moving The Decimal The Wrong Way

To convert a percentage to a decimal, divide by 100. That means 8% is 0.08, not 0.8. This mistake can make your answer ten times too large.

23.6 Ignoring Rounding

Rounding can affect money calculations. If you calculate taxes, tips, or loan payments, small rounding differences may appear. For estimates, rounding is fine. For bills, accounting, payroll, taxes, or legal documents, use exact rules required by the relevant institution or authority.

24. How To Choose The Right Calculation

If you are not sure which formula to use, ask yourself what the problem is really asking.

• If you need part of a number, multiply by the percentage.
• If you need to compare a part to a whole, divide part by whole and multiply by 100.
• If something changed from old to new, subtract first, then divide by the original.
• If you need the final price after an increase, multiply by more than 1.
• If you need the final price after a decrease, multiply by less than 1.
• If you need to work backward, divide by the multiplier.
• If growth happens repeatedly over time, use compound growth.

The fastest way to avoid mistakes is to write down what each number represents. Label the original amount, new amount, part, whole, cost, price, profit, rate, and time before calculating.

25. Final Thoughts

Basic calculations are not just school math. They help you make better decisions with money, shopping, work, health, education, and long-term planning. The same core formulas appear again and again: multiply to find a percentage of a number, divide to compare a part with a whole, use the original amount for percentage change, and use multipliers to apply or reverse increases and decreases.

Once you understand the logic behind the formulas, everyday math becomes much less intimidating. You can check whether a sale is really a bargain, understand how much a raise is worth, compare unit prices, calculate taxes and tips, measure progress toward a savings goal, and avoid common traps such as confusing percentage points with percentages or margin with markup. The more you practice these calculations, the more natural they become.