How do I calculate a percentage of a number?

To find X% of Y, multiply Y by X and divide by 100. The formula is: result = Y × (X / 100). For example, 20% of 150 = 150 × 0.20 = 30. This works for any numbers — discounts, tips, tax calculations, and more. You can also move the decimal point two places left in the percentage and then multiply.

How do I calculate percentage change between two numbers?

Percentage change = ((New value − Old value) / |Old value|) × 100. A positive result means an increase, negative means a decrease. For example, if a price went from $80 to $100: ((100 − 80) / 80) × 100 = 25% increase. Note that percentage change uses the original value as the reference, not the new value.

How do I find what percentage one number is of another?

Divide the part by the whole and multiply by 100. Formula: percentage = (part / whole) × 100. For example, 25 out of 200 = (25 / 200) × 100 = 12.5%. This is useful for calculating test scores, market share, completion rates, and proportions of any kind.

How do I add a percentage to a number?

Multiply the number by (1 + percentage/100). For example, to add 15% to 100: 100 × 1.15 = 115. This is equivalent to calculating the percentage amount (100 × 0.15 = 15) and then adding it to the original (100 + 15 = 115). This method is commonly used for calculating prices with tax or tips.

How do I calculate a discount percentage?

Discount % = ((Original price − Sale price) / Original price) × 100. For example, an $80 item on sale for $60: ((80 − 60) / 80) × 100 = 25% off. To find the sale price from a known discount: Sale price = Original × (1 − Discount/100). So $80 with 25% off = 80 × 0.75 = $60.

How do I find the original price before a discount?

Divide the sale price by (1 − Discount/100). Formula: Original = Sale price / (1 − Discount%). For example, if you paid $60 after a 25% discount: $60 / (1 − 0.25) = $60 / 0.75 = $80. This reverse calculation is useful when you see a final price but want to know the original price before the reduction was applied.

What is the difference between percentage change and percentage difference?

Percentage change compares a new value to an old value using the old value as the reference: ((new − old) / old) × 100. Percentage difference compares any two values using their mean as the reference: |A − B| / ((A + B) / 2) × 100. Use percentage change when there is a clear "before and after" relationship. Use percentage difference when comparing two independent values with no inherent direction.

What are percentage points and how are they different from percentages?

A percentage point is the arithmetic difference between two percentages, while a percentage is the relative change. If an interest rate goes from 5% to 7%, that is a 2 percentage point increase, but a 40% relative increase ((7−5)/5 × 100). This distinction matters in finance, statistics, and elections. Confusing the two leads to major misinterpretations of data.

How do I calculate successive or compound percentages?

Sequential percentages are NOT additive. To apply −20% then −10%, multiply the factors: 0.80 × 0.90 = 0.72, which is a 28% total decrease — not 30%. For increases, the same applies: +20% then +10% = 1.20 × 1.10 = 1.32, a 32% total increase — not 30%. Always multiply the percentage factors together and subtract 1 to find the net change.

How do I convert a fraction to a percentage?

Divide the numerator by the denominator and multiply by 100. Formula: percentage = (numerator / denominator) × 100. For example, 3/8 = (3 ÷ 8) × 100 = 37.5%. Common fractions: 1/2 = 50%, 1/3 ≈ 33.33%, 1/4 = 25%, 1/5 = 20%, 3/4 = 75%, 2/3 ≈ 66.67%.

How do I convert a percentage to a fraction?

Write the percentage over 100 and simplify by finding the greatest common divisor (GCD). For example, 75% = 75/100 = 3/4 (divide both by 25). For decimals like 37.5%, first remove the decimal: 375/1000, then simplify: 375/1000 = 3/8. If the percentage has repeating decimals like 33.33%, the fraction is 1/3.

What is percentage error and when is it used?

Percentage error measures how far an observed (measured) value deviates from an expected (true) value. Formula: % error = |observed − expected| / |expected| × 100. It is widely used in science, engineering, and manufacturing for quality control. For example, if you measured 105 grams but the true weight is 100 grams, the percentage error is 5%.

How do I calculate a price increase percentage?

Increase % = ((New price − Old price) / Old price) × 100. If the price went from $10 to $12: ((12 − 10) / 10) × 100 = 20% increase. This formula is identical to the general percentage change formula and works for any type of increase — rent, salary, stock prices, or costs.

How do I calculate sales tax on a purchase?

Total with tax = Price × (1 + Tax rate/100). For 8% tax on a $100 item: $100 × 1.08 = $108. The tax amount alone = $100 × 0.08 = $8. To find the pre-tax price from a total: Pre-tax = Total / (1 + Tax/100). For $108 with 8% tax: $108 / 1.08 = $100.

Why does A% of B equal B% of A?

This is the commutativity property of percentages. Mathematically, A% of B = (A/100) × B = (A × B) / 100. And B% of A = (B/100) × A = (B × A) / 100. Since multiplication is commutative (A × B = B × A), both expressions are equal. For example, 8% of 25 = 25% of 8 = 2. This shortcut can make mental math much easier.

How to calculate percentage in Excel or Google Sheets?

For X% of Y: =Y*X/100 or =Y*X% (Excel treats "%" as /100). For percentage of total: =A1/B1 then format as percentage. For percentage change: =(B1-A1)/A1 and format as percentage. For adding percentage: =A1*(1+B1/100). Tip: format cells as "Percentage" (Ctrl+Shift+5) so 0.25 displays as 25%.

What is the rule of three for percentages?

The rule of three sets up a proportion to find an unknown. If 100% corresponds to a total value, then X% corresponds to what value? Formula: result = (total × X) / 100. Example: if 100% = 80 students, what is 35%? Answer: (80 × 35) / 100 = 28 students. It also works in reverse: if 28 students is 35%, the total is (28 × 100) / 35 = 80.

How do I reverse-calculate a percentage to find the whole?

If you know that a value X is Y% of some unknown number, the whole = X / (Y / 100). For example, if 30 is 25% of some number: 30 / 0.25 = 120. This inverse percentage calculation is useful when you know the part and the percentage but need to find the original total.

How do I calculate percentage of weight loss?

Weight loss % = ((Starting weight − Current weight) / Starting weight) × 100. For example, going from 200 lbs to 180 lbs: ((200 − 180) / 200) × 100 = 10% weight loss. This same formula works for any reduction — inventory shrinkage, population decline, or budget cuts.

How do I calculate salary raise percentage?

Raise % = ((New salary − Old salary) / Old salary) × 100. If your salary went from $50,000 to $55,000: (($55,000 − $50,000) / $50,000) × 100 = 10% raise. To find what salary a specific raise gives: New salary = Old salary × (1 + Raise%/100). A 10% raise on $50,000 = $50,000 × 1.10 = $55,000.

What is per mille (‰) and what are basis points?

Per mille (‰) means "per thousand" — 1‰ = 0.1% = 0.001. It is used in blood alcohol content, birth rates, and some tax calculations. Basis points (bps) are used in finance — 1 basis point = 0.01% = 1/10,000. So 50 basis points = 0.50%. Central bank rate changes are often expressed in basis points for precision.

How do I correctly average percentages?

You cannot simply average percentages if the group sizes differ. Instead, use a weighted average: multiply each percentage by its group size, sum the products, then divide by the total size. For example, 80% of 50 students and 60% of 100 students: (0.80×50 + 0.60×100) / (50+100) = (40+60)/150 = 66.7%, not the simple average of 70%.

Percentage Calculator: 10 Free Tools

Calculate percentages instantly. 10 modes with step-by-step solutions and visual charts. For shopping deals, also try our discount calculator (stacked discounts, BOGO, and more). For tax-inclusive pricing, use the VAT calculator or the margin calculator for profit margins.

Basic

Advanced

Percentage

Value

How Percentages Work

A percentage is a way of expressing a number as a fraction of 100. The word "percent" comes from Latin "per centum" meaning "by the hundred". Here are the formulas used in this calculator:

X% of Y = Y × (X ÷ 100)
What % is X of Y = (X ÷ Y) × 100
Percentage change = ((New − Old) ÷ |Old|) × 100
Add X% to Y = Y × (1 + X ÷ 100)
Before increase = Final ÷ (1 + X ÷ 100)
Before discount = Final ÷ (1 − X ÷ 100)
Percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100
Inverse percentage = Value ÷ (Percentage ÷ 100)
Fraction to % = (Numerator ÷ Denominator) × 100
Percentage error = |Observed − Expected| ÷ |Expected| × 100

Example Calculations

Store discount

$80 item with 25% off: 80 × (1 − 0.25) = $60

Restaurant tip

18% tip on $45 bill: 45 × 0.18 = $8.10

Test score

42 correct out of 50: (42 ÷ 50) × 100 = 84%

Original price

$60 after 25% off: 60 ÷ 0.75 = $80

Salary raise

$50,000 salary with 8% raise: 50,000 × 1.08 = $54,000

Stock change

Stock went from $120 to $150: ((150−120)/120) × 100 = +25%

Population growth

City grew from 80,000 to 92,000: ((92,000−80,000)/80,000) × 100 = +15%

Loan interest

4.5% annual interest on $10,000: 10,000 × 0.045 = $450/year

Percentage Points vs Percentages

A common source of confusion is the difference between percentage points and percentages. If an interest rate goes from 5% to 7%, the increase is 2 percentage points but a 40% relative increase. Media headlines often mix these up, leading to misinterpretation. In elections, polls, and financial reporting, always check whether the change is in percentage points (absolute) or percent (relative).

Common Percentage Mistakes

The most frequent mistake is treating sequential percentages as additive. A 20% discount followed by a 10% discount is NOT 30% off — it is 28% off (0.80 × 0.90 = 0.72). Similarly, a 50% increase followed by a 50% decrease does NOT return to the original — it results in a 25% loss (1.50 × 0.50 = 0.75). Always multiply the percentage factors, never add them.

The Commutativity Trick

A useful shortcut: A% of B always equals B% of A. This is because (A/100) × B = (B/100) × A. For example, 8% of 25 = 25% of 8 = 2. When faced with a hard mental calculation like 16% of 50, flip it to 50% of 16 = 8 — much easier!

FAQ

How do I calculate a percentage of a number?: To find X% of Y, multiply Y by X and divide by 100. The formula is: result = Y × (X / 100). For example, 20% of 150 = 150 × 0.20 = 30. This works for any numbers — discounts, tips, tax calculations, and more. You can also move the decimal point two places left in the percentage and then multiply.
How do I calculate percentage change between two numbers?: Percentage change = ((New value − Old value) / |Old value|) × 100. A positive result means an increase, negative means a decrease. For example, if a price went from $80 to $100: ((100 − 80) / 80) × 100 = 25% increase. Note that percentage change uses the original value as the reference, not the new value.
How do I find what percentage one number is of another?: Divide the part by the whole and multiply by 100. Formula: percentage = (part / whole) × 100. For example, 25 out of 200 = (25 / 200) × 100 = 12.5%. This is useful for calculating test scores, market share, completion rates, and proportions of any kind.
How do I add a percentage to a number?: Multiply the number by (1 + percentage/100). For example, to add 15% to 100: 100 × 1.15 = 115. This is equivalent to calculating the percentage amount (100 × 0.15 = 15) and then adding it to the original (100 + 15 = 115). This method is commonly used for calculating prices with tax or tips.
How do I calculate a discount percentage?: Discount % = ((Original price − Sale price) / Original price) × 100. For example, an $80 item on sale for $60: ((80 − 60) / 80) × 100 = 25% off. To find the sale price from a known discount: Sale price = Original × (1 − Discount/100). So $80 with 25% off = 80 × 0.75 = $60.
How do I find the original price before a discount?: Divide the sale price by (1 − Discount/100). Formula: Original = Sale price / (1 − Discount%). For example, if you paid $60 after a 25% discount: $60 / (1 − 0.25) = $60 / 0.75 = $80. This reverse calculation is useful when you see a final price but want to know the original price before the reduction was applied.
What is the difference between percentage change and percentage difference?: Percentage change compares a new value to an old value using the old value as the reference: ((new − old) / old) × 100. Percentage difference compares any two values using their mean as the reference: |A − B| / ((A + B) / 2) × 100. Use percentage change when there is a clear "before and after" relationship. Use percentage difference when comparing two independent values with no inherent direction.
What are percentage points and how are they different from percentages?: A percentage point is the arithmetic difference between two percentages, while a percentage is the relative change. If an interest rate goes from 5% to 7%, that is a 2 percentage point increase, but a 40% relative increase ((7−5)/5 × 100). This distinction matters in finance, statistics, and elections. Confusing the two leads to major misinterpretations of data.
How do I calculate successive or compound percentages?: Sequential percentages are NOT additive. To apply −20% then −10%, multiply the factors: 0.80 × 0.90 = 0.72, which is a 28% total decrease — not 30%. For increases, the same applies: +20% then +10% = 1.20 × 1.10 = 1.32, a 32% total increase — not 30%. Always multiply the percentage factors together and subtract 1 to find the net change.
How do I convert a fraction to a percentage?: Divide the numerator by the denominator and multiply by 100. Formula: percentage = (numerator / denominator) × 100. For example, 3/8 = (3 ÷ 8) × 100 = 37.5%. Common fractions: 1/2 = 50%, 1/3 ≈ 33.33%, 1/4 = 25%, 1/5 = 20%, 3/4 = 75%, 2/3 ≈ 66.67%.
How do I convert a percentage to a fraction?: Write the percentage over 100 and simplify by finding the greatest common divisor (GCD). For example, 75% = 75/100 = 3/4 (divide both by 25). For decimals like 37.5%, first remove the decimal: 375/1000, then simplify: 375/1000 = 3/8. If the percentage has repeating decimals like 33.33%, the fraction is 1/3.
What is percentage error and when is it used?: Percentage error measures how far an observed (measured) value deviates from an expected (true) value. Formula: % error = |observed − expected| / |expected| × 100. It is widely used in science, engineering, and manufacturing for quality control. For example, if you measured 105 grams but the true weight is 100 grams, the percentage error is 5%.
How do I calculate a price increase percentage?: Increase % = ((New price − Old price) / Old price) × 100. If the price went from $10 to $12: ((12 − 10) / 10) × 100 = 20% increase. This formula is identical to the general percentage change formula and works for any type of increase — rent, salary, stock prices, or costs.
How do I calculate sales tax on a purchase?: Total with tax = Price × (1 + Tax rate/100). For 8% tax on a $100 item: $100 × 1.08 = $108. The tax amount alone = $100 × 0.08 = $8. To find the pre-tax price from a total: Pre-tax = Total / (1 + Tax/100). For $108 with 8% tax: $108 / 1.08 = $100.
Why does A% of B equal B% of A?: This is the commutativity property of percentages. Mathematically, A% of B = (A/100) × B = (A × B) / 100. And B% of A = (B/100) × A = (B × A) / 100. Since multiplication is commutative (A × B = B × A), both expressions are equal. For example, 8% of 25 = 25% of 8 = 2. This shortcut can make mental math much easier.
How to calculate percentage in Excel or Google Sheets?: For X% of Y: =Y*X/100 or =Y*X% (Excel treats "%" as /100). For percentage of total: =A1/B1 then format as percentage. For percentage change: =(B1-A1)/A1 and format as percentage. For adding percentage: =A1*(1+B1/100). Tip: format cells as "Percentage" (Ctrl+Shift+5) so 0.25 displays as 25%.
What is the rule of three for percentages?: The rule of three sets up a proportion to find an unknown. If 100% corresponds to a total value, then X% corresponds to what value? Formula: result = (total × X) / 100. Example: if 100% = 80 students, what is 35%? Answer: (80 × 35) / 100 = 28 students. It also works in reverse: if 28 students is 35%, the total is (28 × 100) / 35 = 80.
How do I reverse-calculate a percentage to find the whole?: If you know that a value X is Y% of some unknown number, the whole = X / (Y / 100). For example, if 30 is 25% of some number: 30 / 0.25 = 120. This inverse percentage calculation is useful when you know the part and the percentage but need to find the original total.
How do I calculate percentage of weight loss?: Weight loss % = ((Starting weight − Current weight) / Starting weight) × 100. For example, going from 200 lbs to 180 lbs: ((200 − 180) / 200) × 100 = 10% weight loss. This same formula works for any reduction — inventory shrinkage, population decline, or budget cuts.
How do I calculate salary raise percentage?: Raise % = ((New salary − Old salary) / Old salary) × 100. If your salary went from $50,000 to $55,000: (($55,000 − $50,000) / $50,000) × 100 = 10% raise. To find what salary a specific raise gives: New salary = Old salary × (1 + Raise%/100). A 10% raise on $50,000 = $50,000 × 1.10 = $55,000.
What is per mille (‰) and what are basis points?: Per mille (‰) means "per thousand" — 1‰ = 0.1% = 0.001. It is used in blood alcohol content, birth rates, and some tax calculations. Basis points (bps) are used in finance — 1 basis point = 0.01% = 1/10,000. So 50 basis points = 0.50%. Central bank rate changes are often expressed in basis points for precision.
How do I correctly average percentages?: You cannot simply average percentages if the group sizes differ. Instead, use a weighted average: multiply each percentage by its group size, sum the products, then divide by the total size. For example, 80% of 50 students and 60% of 100 students: (0.80×50 + 0.60×100) / (50+100) = (40+60)/150 = 66.7%, not the simple average of 70%.