Calculating a percentage becomes much easier once you identify the part being compared and the total or reference value. The basic percentage formula is **Percentage = Part ÷ Whole × 100**. For example, if 30 students out of a class of 50 pass an exam, divide 30 by 50 to get 0.60, then multiply by 100. The result is 60%, meaning 60% of the students passed. This same relationship can be adapted to calculate discounts, grades, price changes, taxes, tips, growth rates, survey results, profit margins, and many other everyday values.
What Is a Percentage?
A percentage expresses a number as a portion of 100. The word percent means "per hundred," so 1% means 1 out of 100, 25% means 25 out of 100, 50% means half of the total, and 100% means the complete amount. A percentage can also be greater than 100%. For example, 150% represents one and a half times the reference amount, while 200% represents twice the original amount.
Percentages can be written as decimals and fractions. Twenty-five percent is the same as 0.25 and the same as 25/100, which simplifies to 1/4. Seventy-five percent is 0.75 or 3/4. Understanding these equivalent forms makes percentage calculations much easier because most formulas use the percentage as a decimal.
A percentage has meaning only when the reference amount is clear. A score of 40 points could represent 80% of a 50-point test, 40% of a 100-point test, or 20% of a 200-point test. The number 40 stays the same, but the percentage changes because the whole changes.
The Basic Percentage Formula
To determine what percentage one quantity represents of another, use:
**Percentage = Part ÷ Whole × 100**
The part is the amount being compared, and the whole is the total or reference amount. Dividing the part by the whole produces a decimal. Multiplying that decimal by 100 converts it into a percentage.
Suppose 18 employees out of a total of 24 complete a workplace survey. Divide 18 by 24 to get 0.75. Multiplying 0.75 by 100 gives 75%, so 75% of the employees completed the survey.
This basic formula is the foundation of most percentage calculations. The main challenge is usually not the arithmetic but choosing the correct part and whole.
How to Find What Percentage One Number Is of Another
When the question asks what percentage one number is of another, divide the first number by the second and multiply by 100.
For example, to find what percentage 20 is of 80, calculate 20 ÷ 80 × 100. The division produces 0.25, and multiplying by 100 gives 25%. Therefore, 20 is 25% of 80.
To determine what percentage 45 is of 60, calculate 45 ÷ 60 × 100. The answer is 75%, so 45 is 75% of 60.
To find what percentage 7 is of 40, calculate 7 ÷ 40 × 100. The result is 17.5%, meaning 7 represents 17.5% of 40.
In this type of question, the word "of" often identifies the whole. In "20 is what percentage of 80," the number 80 is the reference amount and therefore belongs in the denominator.
How to Calculate a Percentage of a Number
To find a particular percentage of a number, convert the percentage into a decimal and multiply it by the number.
Use:
**Percentage amount = Percentage ÷ 100 × Number**
To calculate 20% of 150, convert 20% to 0.20 and multiply by 150. The result is 30, so 20% of 150 is 30.
To calculate 35% of 80, multiply 0.35 by 80. The result is 28.
To calculate 7.5% of 240, multiply 0.075 by 240. The result is 18.
You can also write these calculations directly as 20 ÷ 100 × 150, 35 ÷ 100 × 80, and 7.5 ÷ 100 × 240.
How to Find the Whole When the Percentage Is Known
Sometimes the part and percentage are known, but the original total is missing. In that case, divide the part by the percentage written as a decimal.
Use:
**Whole = Part ÷ Percentage as a decimal**
If 30 is 20% of an unknown number, convert 20% to 0.20 and calculate 30 ÷ 0.20. The result is 150, so 30 is 20% of 150.
If 45 is 75% of an unknown total, divide 45 by 0.75. The answer is 60.
If 12 is 7.5% of an unknown number, divide 12 by 0.075. The result is 160.
This calculation is sometimes called a reverse percentage because it works backward from a known percentage amount to the original whole.
The Relationship Between Part, Percentage, and Whole
The three most important percentage calculations come from one relationship:
**Part = Percentage × Whole**
The percentage must be written as a decimal. If you know any two of these values, you can find the third.
To find the part, multiply the percentage by the whole. To find the percentage, divide the part by the whole. To find the whole, divide the part by the percentage.
For example, if the whole is 200 and the percentage is 15%, convert 15% to 0.15 and multiply 0.15 by 200. The part is 30.
If the part is 30 and the whole is 200, divide 30 by 200 to get 0.15, which becomes 15%.
If the part is 30 and the percentage is 15%, divide 30 by 0.15 to get 200.
How to Convert a Percentage to a Decimal
Divide the percentage by 100 or move the decimal point two places to the left. Seventy-five percent becomes 0.75, 25% becomes 0.25, 8% becomes 0.08, and 2.5% becomes 0.025.
Percentages greater than 100 become decimals greater than 1. For example, 125% becomes 1.25, while 200% becomes 2.00.
A small percentage such as 0.5% becomes 0.005. This is a common source of mistakes because 0.5% is not the same as 0.5. The decimal 0.5 represents 50%, while 0.005 represents 0.5%.
How to Convert a Decimal to a Percentage
Multiply the decimal by 100 or move the decimal point two places to the right. The decimal 0.4 becomes 40%, 0.75 becomes 75%, 0.025 becomes 2.5%, and 1.2 becomes 120%.
For example, to convert 0.375 into a percentage, multiply it by 100. The answer is 37.5%.
How to Convert a Fraction to a Percentage
Divide the numerator by the denominator and multiply the result by 100.
Use:
**Percentage = Numerator ÷ Denominator × 100**
To convert 3/4 to a percentage, divide 3 by 4 to get 0.75 and multiply by 100. The answer is 75%.
To convert 2/5, divide 2 by 5 to get 0.4. Multiplying by 100 produces 40%.
To convert 7/8, divide 7 by 8 to get 0.875, which becomes 87.5%.
Several common fractions are useful to remember. One-half is 50%, one-third is approximately 33.33%, two-thirds is approximately 66.67%, one-quarter is 25%, three-quarters is 75%, one-fifth is 20%, one-eighth is 12.5%, and one-tenth is 10%.
How to Convert a Percentage to a Fraction
Write the percentage over 100 and simplify.
Forty percent can be written as 40/100. Dividing the numerator and denominator by 20 gives 2/5, so 40% equals 2/5.
Seventy-five percent becomes 75/100, which simplifies to 3/4.
For a decimal percentage such as 12.5%, write 12.5/100 and multiply both numbers by 10 to remove the decimal. This produces 125/1000, which simplifies to 1/8.
How to Calculate Percentage Increase
Percentage increase measures how much a value has grown compared with its original value.
Use:
**Percentage increase = (New value − Original value) ÷ Original value × 100**
If a price rises from $80 to $100, the increase is $20. Divide 20 by the original price of 80 to get 0.25, then multiply by 100. The price increased by 25%.
If sales rise from 250 units to 325 units, the increase is 75. Divide 75 by 250 and multiply by 100. The result is 30%, so sales increased by 30%.
The original value must be used as the denominator. Dividing by the new value answers a different question and produces an incorrect percentage increase.
How to Calculate Percentage Decrease
Percentage decrease measures how much a value has fallen relative to its original level.
Use:
**Percentage decrease = (Original value − New value) ÷ Original value × 100**
If a price falls from $120 to $90, the decrease is $30. Divide 30 by 120 and multiply by 100. The price decreased by 25%.
If website errors fall from 500 to 350, the reduction is 150. Dividing 150 by 500 and multiplying by 100 gives 30%, so the number of errors decreased by 30%.
How to Calculate Percentage Change
Percentage change can represent either an increase or a decrease.
Use:
**Percentage change = (New value − Original value) ÷ Original value × 100**
If a value changes from 60 to 75, subtract 60 from 75 to get 15. Divide 15 by 60 and multiply by 100. The result is +25%, indicating an increase.
If the value changes from 60 to 45, the change is -15. Dividing -15 by 60 and multiplying by 100 gives -25%, indicating a decrease of 25%.
A positive result represents growth, while a negative result represents decline.
Why Percentage Increases and Decreases Are Not Symmetrical
An increase and decrease of the same percentage do not cancel each other because they are applied to different base values.
Suppose a price begins at $100 and increases by 50%. The new price is $150. If that price then decreases by 50%, the reduction is calculated from $150, not from the original $100. Half of $150 is $75, so the final value becomes $75 rather than returning to $100.
To return from $150 to $100, the required decrease is 33.33%, not 50%. This illustrates why the reference amount matters in every percentage calculation.
How to Calculate Percentage Difference
Percentage difference is commonly used to compare two values when neither one is treated as the original or reference amount.
Use:
**Percentage difference = Absolute difference ÷ Average of the two values × 100**
To compare 40 and 50, first find the absolute difference, which is 10. Next, calculate the average: 40 + 50 = 90, and 90 ÷ 2 = 45. Divide 10 by 45 and multiply by 100. The percentage difference is approximately 22.22%.
Use percentage change when one value clearly comes before the other or serves as the original value. Use percentage difference when the comparison is symmetrical and neither value is considered the starting point.
Percentage Points Versus Percentage Change
A movement between two percentages can be expressed in percentage points or as a relative percentage change, but these are not the same.
Suppose a rate rises from 20% to 30%. The direct difference is 10 percentage points. To find the relative increase, subtract 20 from 30, divide the difference by the original 20, and multiply by 100. The relative increase is 50%.
The rate therefore increased by 10 percentage points, which is equivalent to a 50% increase relative to its original level.
How to Calculate a Discount
To calculate the discount amount, multiply the original price by the discount rate written as a decimal.
Use:
**Discount amount = Original price × Discount percentage ÷ 100**
To find the final sale price, subtract the discount amount from the original price. You can also multiply the original price by the percentage that remains.
Use:
**Sale price = Original price × (1 − Discount rate)**
If an $80 product is discounted by 20%, the discount is 80 × 0.20 = $16. Subtracting $16 from $80 gives a sale price of $64.
If a $240 product is discounted by 35%, the discount is $84. The sale price is $156.
How to Find the Original Price After a Discount
When the sale price and discount percentage are known, divide the sale price by the proportion of the original price that remains.
Use:
**Original price = Sale price ÷ (1 − Discount rate)**
Suppose an item costs $60 after a 25% discount. A 25% discount means 75% of the original price remains. Convert 75% to 0.75 and divide 60 by 0.75. The original price was $80.
Do not simply add 25% to the sale price. The discount was calculated from the larger original amount, so reversing it requires division.
How to Calculate Multiple Discounts
Successive discounts must be applied one after another. They should not normally be added together.
Suppose a $100 product receives a 20% discount followed by another 10% discount. After the first discount, the price becomes $80. The second 10% discount is calculated from $80, reducing the price by $8. The final price is $72.
The total reduction is $28, which represents 28% of the original $100. A 20% discount followed by a 10% discount therefore produces an overall discount of 28%, not 30%.
How to Add a Percentage to a Number
To increase a value by a percentage, multiply the original amount by one plus the percentage written as a decimal.
Use:
**New amount = Original amount × (1 + Percentage rate)**
To increase 200 by 15%, multiply 200 by 1.15. The result is 230.
This multiplier includes both the original 100% and the additional 15%.
How to Subtract a Percentage From a Number
To reduce a number by a percentage, multiply it by one minus the percentage rate.
Use:
**New amount = Original amount × (1 − Percentage rate)**
To reduce 500 by 30%, multiply 500 by 0.70. The result is 350.
The multiplier 0.70 represents the 70% that remains after removing 30%.
How to Calculate a Reverse Percentage
Reverse percentage calculations recover an original value after an increase or decrease.
When the final value includes an increase, use:
**Original value = Final value ÷ (1 + Increase rate)**
If a salary becomes $57,500 after a 15% increase, divide $57,500 by 1.15. The original salary was $50,000.
When the final value follows a decrease, use:
**Original value = Final value ÷ (1 − Decrease rate)**
If a price becomes $72 after a 20% reduction, divide $72 by 0.80. The original price was $90.
How to Calculate a Grade Percentage
To calculate a test or assignment percentage, divide the points earned by the total possible points and multiply by 100.
Use:
**Grade percentage = Points earned ÷ Total possible points × 100**
If a student earns 42 points out of 50, calculate 42 ÷ 50 × 100. The grade is 84%.
If a student earns 73 points out of 80, the result is 91.25%.
How to Calculate a Weighted Grade
Weighted grades give different categories different levels of importance. Convert each weight to a decimal, multiply each score by its weight, and add the results.
Suppose homework is worth 20%, a midterm is worth 30%, and a final exam is worth 50%. If the scores are 90%, 80%, and 70%, the weighted contributions are 90 × 0.20 = 18, 80 × 0.30 = 24, and 70 × 0.50 = 35. Adding them gives a final weighted grade of 77%.
The weights should total 100%, or 1.00 when written as decimals.
How to Calculate Attendance Percentage
Divide the number of sessions attended by the total number of sessions and multiply by 100.
If a student attends 36 of 40 classes, calculate 36 ÷ 40 × 100. The attendance rate is 90%.
The same formula can be used for work attendance, event participation, completed appointments, and similar records.
How to Calculate Survey Percentages
Divide the number of respondents choosing a particular answer by the relevant total number of responses and multiply by 100.
If 185 people out of 500 select option A, calculate 185 ÷ 500 × 100. The result is 37%.
The denominator must match the group being described. If some people skipped the question, decide whether the percentage should be based on all participants, only valid responses, or a specific subgroup. Different denominators produce different results.
How to Calculate a Tip
Multiply the bill by the tip percentage written as a decimal.
Use:
**Tip = Bill amount × Tip rate**
For an 18% tip on a $50 bill, multiply 50 by 0.18. The tip is $9, and the total payment becomes $59.
For a quick 20% tip, find 10% of the bill and double it. Ten percent of $65 is $6.50, so 20% is $13.
How to Calculate Tax
Multiply the pre-tax price by the tax rate written as a decimal.
Use:
**Tax amount = Price × Tax rate**
If a purchase costs $250 and the tax rate is 8%, multiply 250 by 0.08. The tax is $20, making the final price $270.
Tax rules, exemptions, and whether displayed prices already include tax depend on the jurisdiction and transaction.
How to Remove Tax From a Tax-Inclusive Price
Do not subtract the tax percentage directly from the final total. Divide the tax-inclusive amount by one plus the tax rate.
Use:
**Pre-tax price = Final price ÷ (1 + Tax rate)**
If the final price is $108 and includes 8% tax, divide 108 by 1.08. The pre-tax amount is $100, and the tax portion is $8.
How to Calculate Markup
Markup compares profit with the cost of the product.
Use:
**Markup percentage = (Selling price − Cost) ÷ Cost × 100**
If a product costs $50 and sells for $75, the profit is $25. Divide 25 by the cost of 50 and multiply by 100. The markup is 50%.
How to Calculate Profit Margin
Profit margin compares profit with the selling price.
Use:
**Margin percentage = (Selling price − Cost) ÷ Selling price × 100**
Using the same product that costs $50 and sells for $75, the profit is $25. Divide 25 by the selling price of 75 and multiply by 100. The margin is approximately 33.33%.
Markup and margin are not interchangeable. Markup uses cost as the denominator, while margin uses selling price. Confusing them can produce incorrect pricing decisions.
How to Calculate Growth
Growth rate uses the standard percentage-change formula.
Use:
**Growth rate = (New value − Old value) ÷ Old value × 100**
If subscribers grow from 2,000 to 2,600, the increase is 600. Divide 600 by 2,000 and multiply by 100. Subscriber growth is 30%.
For year-over-year growth, compare the current period with the same period one year earlier. If annual revenue rises from $350,000 to $420,000, the increase is $70,000. Dividing $70,000 by $350,000 and multiplying by 100 gives 20% year-over-year growth.
How to Calculate Completion Percentage
Divide the completed amount by the total amount and multiply by 100.
If a project has completed 36 of 60 tasks, calculate 36 ÷ 60 × 100. The project is 60% complete.
This formula can be used for reading goals, construction milestones, training programs, data processing, and many other progress measurements.
How to Calculate an Error Rate
One common error-rate formula is:
**Error rate = Number of errors ÷ Total opportunities × 100**
If a production line creates 12 defective items out of 2,000, calculate 12 ÷ 2,000 × 100. The defect rate is 0.6%.
The denominator should represent the total number of opportunities for an error to occur.
How to Calculate Percentage Error
Percentage error compares a measured value with an accepted or expected value.
Use:
**Percentage error = |Measured value − Accepted value| ÷ |Accepted value| × 100**
The vertical bars indicate absolute value, meaning the difference is treated as positive.
If the measured value is 98 and the accepted value is 100, the difference is 2. Divide 2 by 100 and multiply by 100. The percentage error is 2%.
How to Calculate Percentages on a Calculator
A dedicated percentage button is not required. You can enter the formula directly.
To find what percentage 30 is of 120, enter 30 ÷ 120 × 100. The result is 25, so 30 is 25% of 120.
To calculate 15% of 200, enter 0.15 × 200 or 15 ÷ 100 × 200. The answer is 30.
To add 15% to 200, multiply 200 by 1.15. The result is 230.
To subtract 15% from 200, multiply 200 by 0.85. The result is 170.
Percentage-button behavior varies between calculator models and applications. For reliable results, decimal multiplication is often clearer than relying on a `%` key whose behavior may change depending on the operation.
How to Calculate Percentages Mentally
Several benchmark percentages make mental calculation much faster. To find 10%, move the decimal point one place to the left. Ten percent of 250 is 25, while 10% of 1,200 is 120.
To find 1%, move the decimal point two places to the left. One percent of 500 is 5, and 1% of 2,400 is 24.
To find 5%, calculate 10% and divide by two. Ten percent of 240 is 24, so 5% is 12.
To find 20%, calculate 10% and double it. Ten percent of 90 is 9, so 20% is 18.
To find 25%, divide the number by four. Twenty-five percent of 200 is 50.
To find 50%, divide the number by two. Fifty percent of 140 is 70.
To find 75%, combine 50% and 25%. Half of 80 is 40, one-quarter is 20, and together they equal 60.
To find 15%, combine 10% and 5%. Ten percent of 300 is 30, and 5% is 15, producing a total of 45.
To find 12.5%, divide by eight. Twelve and a half percent of 160 is 20.
A useful mental shortcut is that X% of Y equals Y% of X. For example, 4% of 75 equals 75% of 4. Since 75% of 4 is 3, 4% of 75 is also 3.
How to Calculate Percentage in Excel
If cell A2 contains the part and cell B2 contains the whole, enter:
`=A2/B2`
Then format the result cell as a percentage. Do not multiply the formula by 100 when the cell is already formatted as Percentage because Excel applies the percentage display automatically.
If A2 contains 30 and B2 contains 50, the formula returns 0.6, which displays as 60% after percentage formatting.
To find a percentage of a number when A2 contains 20% and B2 contains 150, use:
`=A2*B2`
The result is 30.
When A2 contains the number 20 rather than the actual percentage value 20%, use:
`=A2/100*B2`
To calculate percentage change when A2 contains the original value and B2 contains the new value, use:
`=(B2-A2)/A2`
Format the result as a percentage. A positive result shows an increase, while a negative result shows a decrease.
To increase A2 by the percentage in B2, use:
`=A2*(1+B2)`
To reduce A2 by the percentage in B2, use:
`=A2*(1-B2)`
How to Calculate Percentage in Google Sheets
Google Sheets uses the same basic formulas as Excel. Use `=A2/B2` for a percentage of a total, `=(B2-A2)/A2` for percentage change, `=A2*B2` for a percentage of a number, `=A2*(1+B2)` to increase a value, and `=A2*(1-B2)` to reduce it.
Apply percentage formatting to cells that contain decimal percentage values. Avoid multiplying by 100 inside the formula when the result will also receive percentage formatting.
How to Calculate Percentages in Code
The mathematical relationship is the same in any programming language:
`percentage = (part / whole) * 100`
Always check whether the whole is zero before dividing. Division by zero is undefined and can cause errors or invalid results.
Keep sufficient decimal precision during intermediate calculations and round only the final displayed value. Rounding too early can create noticeable errors when several calculations depend on one another.
How to Round Percentages
The correct number of decimal places depends on the context. A general explanation may use a whole percentage, while grades, surveys, scientific measurements, and financial reports may require one, two, or more decimal places.
A raw result of 33.333333% could be displayed as 33%, 33.3%, or 33.33%. Keep the unrounded value during the calculation and round only the final presentation.
Rounded percentages may not total exactly 100%. If three exact values are 33.33%, 33.33%, and 33.34%, they total 100%. Rounding each to the nearest whole number produces 33%, 33%, and 33%, which total 99%. Similar rounding can produce 101%.
Percentages With Negative Numbers
Percentage change can become difficult to interpret when values are negative or cross zero. The usual formula still uses the original value, but the result may not communicate the situation clearly.
A change from -10 to +10 crosses zero. Describing it as an ordinary percentage increase can be misleading because the denominator is negative and the underlying quantity has changed sign.
In these situations, report the original value, final value, absolute change, and any domain-specific measure that explains the result more clearly.
Can a Percentage Be Greater Than 100%?
Yes. A percentage above 100% means the amount is larger than the reference whole.
To find what percentage 150 is of 100, divide 150 by 100 and multiply by 100. The result is 150%, meaning the amount is one and a half times the reference.
Two hundred percent means twice the original amount, while 300% means three times the original amount.
Can a Percentage Be Negative?
Yes. Negative percentages commonly describe declines, losses, negative returns, or reductions.
A percentage change of -20% means the value decreased by 20% relative to its original level. The meaning depends on the type of quantity being measured.
Why Division by Zero Is Undefined
Percentage formulas require dividing by a whole or original value. When that value is zero, the result is undefined.
For example, asking what percentage 10 is of zero would require calculating 10 ÷ 0, which is not mathematically defined.
If a value increases from zero to a positive number, report the absolute increase rather than claiming a conventional percentage increase.
Common Percentage Mistakes
Using the wrong denominator is the most frequent error. The denominator should be the total, original, or reference value relevant to the question.
Another common mistake is forgetting to multiply a decimal result by 100 when expressing it as a percentage. The decimal 0.35 represents 35%, not 0.35%.
The opposite mistake occurs in spreadsheets when a formula multiplies by 100 and the result cell is also formatted as Percentage. This can turn 50% into 5,000%.
A percentage should be converted into a decimal before multiplication. Twenty percent is 0.20, not 20.
Percentage change normally uses the original value as the denominator, not the new value. Successive discounts should be applied one after another rather than added. Percentage points should not be confused with relative percentage change, and markup should not be confused with margin.
A discounted value cannot usually be reversed by simply adding the same percentage. If a price was reduced by 20%, divide the final price by 0.80 to recover the original amount.
Avoid rounding intermediate values too early, and always identify what the percentage refers to. A statement such as "40%" is incomplete without specifying 40% of what.
How to Check a Percentage Answer
Estimate before accepting the final result. If you need to find 18% of 250, you know that 20% of 250 is 50, so the correct result should be slightly below 50. The exact calculation gives 45, which is reasonable.
For part-of-total questions, a part smaller than the whole normally produces a percentage below 100%. A part equal to the whole produces 100%. A part larger than the whole produces more than 100%.
For increases and decreases, compare the calculated amount with the original value and ask whether the size of the change seems realistic.
Worked Percentage Examples
To find 12% of 400, multiply 0.12 by 400. The answer is 48.
To find what percentage 24 is of 80, divide 24 by 80 and multiply by 100. The answer is 30%.
If 36 is 45% of an unknown number, divide 36 by 0.45. The whole is 80.
To increase 500 by 8%, multiply 500 by 1.08. The result is 540.
To reduce 500 by 8%, multiply 500 by 0.92. The result is 460.
If a value increases from 75 to 90, the increase is 15. Divide 15 by 75 and multiply by 100. The percentage increase is 20%.
If a value decreases from 90 to 72, the reduction is 18. Divide 18 by 90 and multiply by 100. The percentage decrease is 20%.
If an item costs $84 after a 30% discount, 70% of the original price remains. Divide 84 by 0.70. The original price was $120.
Frequently Asked Questions About Percentages
To calculate a percentage, divide the part by the whole and multiply by 100. To find a percentage of a number, convert the percentage into a decimal and multiply by the number. To recover an original whole, divide the known part by the percentage written as a decimal.
Twenty percent of 80 is 16. Twenty-five percent of 200 is 50. Fifteen percent of 300 is 45.
Thirty out of 50 is 60%, while 45 out of 60 is 75%.
Percentage increase is calculated by subtracting the original value from the new value, dividing by the original value, and multiplying by 100. Percentage decrease uses the reduction divided by the original value.
Percentage change compares a new value with an original value. Percentage difference compares two values without treating either one as the starting point.
Percentage points show the direct difference between percentages. A rise from 20% to 30% is 10 percentage points but a 50% relative increase.
A discount amount is found by multiplying the original price by the discount rate. The sale price is found by multiplying the original amount by the percentage that remains.
Two discounts should be applied in sequence. A 20% reduction followed by a 10% reduction produces an overall discount of 28%.
To add a percentage, multiply by one plus the decimal rate. To subtract a percentage, multiply by one minus the decimal rate.
A grade percentage is calculated by dividing points earned by total possible points and multiplying by 100. A weighted grade is found by multiplying each score by its weight and adding the results.
Profit margin uses selling price as the denominator, while markup uses cost.
In Excel or Google Sheets, divide the part cell by the total cell and format the result as a percentage. Do not multiply by 100 if percentage formatting is already applied.
Percentages can be greater than 100% and can also be negative. A conventional percentage change is undefined when the original value is zero.
Mental percentage calculations become easier when you know common benchmarks such as 1%, 5%, 10%, 12.5%, 25%, 50%, and 75%.
Final Thoughts
Most percentage problems can be solved with three core relationships. To find what percentage one number is of another, divide the part by the whole and multiply by 100. To find a percentage of a number, convert the percentage into a decimal and multiply. To find an original whole, divide the known part by the percentage written as a decimal.
For percentage change, always compare the difference with the original value. For discounts and reductions, multiply by the percentage that remains. For reverse percentages, divide by the final multiplier rather than simply adding the percentage back.
Before calculating, identify the part, the whole, the original value, and the new value. Decide whether the question asks for a percentage, an amount, a change, a difference, or an original total. Estimate the likely answer, complete the calculation, and check whether the result makes sense.
Percentages are not difficult once the correct reference amount is clear.