On This Page
- How to use this calculator
- How to calculate percentage
- Percentage increase and decrease
- Percentage change vs percentage difference
- Percentage off: discount calculations
- How to calculate percentage in Excel
- Worked examples
- Frequently asked questions
How to Use This Calculator
Choose the calculation type from the dropdown at the top of the calculator. Enter two values and the result appears immediately, along with a breakdown and step-by-step working. Each mode solves a different percentage problem.
What is X% of Y?
The default mode. Enter a percentage and a number to find what that percentage of the number equals. Useful for tips, tax, test scores, discounts, or any "find X percent of Y" situation. The result grid also shows the number increased and decreased by that percentage.
X is what % of Y?
Enter a part and a whole to find the percentage. Use this when you know both values and need to express their relationship as a percentage. For example: 45 out of 60 is 75%.
Percentage change from X to Y
Enter an original value and a new value. The calculator shows the percentage increase or decrease between them, with the direction clearly labeled. Use this for price changes, salary adjustments, revenue growth, or any before-and-after comparison.
Percentage difference between X and Y
This mode compares two values without a defined direction. Unlike percentage change (which has a clear starting point), percentage difference treats both values equally, using their average as the reference. Use it when neither value is the "original."
Percentage off (discount)
Enter a discount percentage and the original price. The calculator shows the sale price and the exact amount saved. Useful for shopping, retail pricing checks, and negotiating.
How to Calculate Percentage
Every percentage problem comes down to one formula. The word "percent" means "out of one hundred." So any percentage is just a fraction with 100 as the denominator, expressed as a single number followed by a % sign.
The trick is identifying the "part" and the "whole" in whatever problem you're looking at. Once you have those two numbers, the arithmetic is straightforward.
Finding X% of a Number
This is the most common type of percentage calculation. You know the percentage and the total, and you want the amount. Rearrange the formula:
What is 15% of 80? (15 ÷ 100) × 80 = 0.15 × 80 = 12. What is 8.5% tax on a $240 purchase? 0.085 × 240 = $20.40. Same formula every time.
Finding the Percentage from Two Numbers
You scored 47 out of 60 on a test. What percentage is that? Divide the part by the whole, then multiply by 100: (47 ÷ 60) × 100 = 0.7833 × 100 = 78.3%. Same calculation works for any "X out of Y" problem.
Using the % Key on a Physical Calculator
Most handheld calculators handle the ÷ 100 step automatically with the % key. To find 15% of 80: press 8 0 × 1 5 %. The calculator converts 15% to 0.15 and multiplies. For percentage change, the logic varies by calculator model, so the formula method is more reliable for those problems.
Mental Math Shortcut: The 10% Method
Ten percent of any number is that number divided by 10. From there, build quickly. 20% = 10% doubled. 5% = half of 10%. 15% = 10% + 5%. 25% = divide by 4. These shortcuts are fast enough to check a restaurant tip or a sale price in your head without reaching for a calculator.
Here's why that matters in practice: a 20% tip on a $47 bill. 10% = $4.70. Double it: $9.40. Done in under three seconds.
Percentage Increase and Decrease
These two calculations are among the most searched percentage problems online. They share the same formula structure, just framed from opposite directions.
Percentage Increase Formula
A product cost $80 in January and $96 in March. The increase is $16. As a percentage: (16 ÷ 80) × 100 = 20% increase. Notice you always divide by the original value. That's the base. Dividing by the new value gives a different answer and is a common mistake.
Percentage Decrease Formula
Revenue dropped from $200,000 to $170,000. The drop is $30,000. As a percentage: (30,000 ÷ 200,000) × 100 = 15% decrease. The calculator's percentage change mode handles both directions automatically and labels the result as increase or decrease.
Working Backwards: Finding the Original Value
You know the result after a percentage change, but want the original. Divide the current value by the multiplier: (1 + rate) for an increase, (1 − rate) for a decrease.
- After a 20% increase, a price is $96. Original: $96 ÷ 1.20 = $80
- After a 15% decrease, a price is $170. Original: $170 ÷ 0.85 = $200
This reverse calculation appears constantly in finance and retail, anywhere you're working from a post-change figure and need the starting point. The Markup Calculator and Profit Margin Calculator on this site both use this same logic for pricing.
Percentage Points vs Percentage Change
These two phrases are not interchangeable, though media outlets and reports confuse them constantly. Interest rates moved from 2% to 3%. That is a 1 percentage point increase, but a 50% increase in the rate itself. Both statements are mathematically correct. Percentage points describe the raw arithmetic difference. Percent change describes the proportional movement relative to the original.
This distinction matters most in economic reporting, where a 1 percentage point change in an unemployment rate sounds minor but represents a 25% relative change if the starting rate was 4%.
Percentage Change vs Percentage Difference
Both calculations compare two numbers, but they answer different questions. Picking the wrong one produces a result that's technically a number but practically misleading.
When to Use Percentage Change
Use percentage change when one value clearly came before the other. Sales last quarter versus this quarter. A stock price at open versus close. Your weight six months ago versus now. There's a defined baseline, and you're measuring movement away from it. The original value is the denominator.
When to Use Percentage Difference
Use percentage difference when two values exist side by side with no time order or causal relationship. Comparing prices at two competing stores. Measuring two readings from the same instrument. Testing two samples from the same batch. Neither value is the "original," so using one as the base would be an arbitrary choice. The formula removes that arbitrariness by using the average of the two values as the reference:
Store A charges $50 for a product. Store B charges $75. Absolute difference: $25. Average: $62.50. Percentage difference: (25 ÷ 62.50) × 100 = 40%.
Using percentage change gives two different answers depending on direction: $50 to $75 is a 50% increase, but $75 to $50 is a 33.3% decrease. Neither is wrong, but both are directional. When there's no natural direction, percentage difference's 40% is the honest answer.
Percentage Off: Discount Calculations
The percentage off calculation comes up every time there's a sale, a coupon code, or a negotiated reduction. The formula is straightforward:
A $120 jacket is 25% off. Sale price: $120 × (1 − 0.25) = $120 × 0.75 = $90. Savings: $30. The multiplier (0.75 in this case) is just 1 minus the decimal form of the discount.
Stacked Discounts: Why They Don't Add Up
When two discounts apply in sequence, they do not combine additively. A 20% off promotion followed by an additional 10% off is not 30% off. Here's the actual math:
Original: $100. After 20% off: $80. After 10% off the $80: $72. Total saving: $28, which equals a 28% total discount, not 30%. The second discount always applies to the reduced price, not the original. Stacked discounts always underperform the sum of their rates.
The combined rate formula: 1 − (1 − 0.20) × (1 − 0.10) = 1 − 0.80 × 0.90 = 1 − 0.72 = 28%.
Finding the Original Price Before a Discount
A sale price of $90 is labeled as 25% off. What was the original price? Divide the sale price by (1 − discount rate): $90 ÷ 0.75 = $120. This reverse calculation is useful for verifying whether a "was $X, now $Y" claim is consistent, or for working out original values in cost analysis.
How to Calculate Percentage in Excel
Excel handles every type of percentage calculation with simple cell formulas. No special functions needed for most scenarios.
X% of a Number
Percentage in A1 (e.g., 15), number in B1 (e.g., 80): =(A1/100)*B1 returns 12. If A1 is already formatted as a percentage cell (storing 0.15 internally), use =A1*B1 directly.
What Percentage Is A of B?
Part in A1, whole in B1: =(A1/B1)*100 returns the percentage as a plain number. To display a % sign automatically, format the result cell as Percentage and use =A1/B1. Excel's percentage format multiplies by 100 during display.
Percentage Change
Old value in A1, new value in B1: =(B1-A1)/ABS(A1)*100. For a column tracking change against a fixed baseline, lock the reference: =(B2-$B$1)/$B$1*100 and drag down. The dollar signs keep the base cell anchored as you copy the formula.
Percentage Increase and Decrease in Excel
To apply a 15% increase to A1: =A1*1.15. To make the rate adjustable, put the percentage in B1 and use =A1*(1+B1/100). For a decrease: =A1*(1-B1/100). Using =A1*(1+$B$1/100) with an absolute reference lets you change the rate in one cell and instantly update an entire column.
Percentage Difference in Excel
Values in A1 and B1: =ABS(A1-B1)/((A1+B1)/2)*100. The ABS function ensures the result is always positive regardless of which value is larger. This is equivalent to the percentage difference formula and works correctly for scientific and quality-control comparisons.
For percentage change in Excel specifically: =(B1-A1)/A1 with the result cell formatted as Percentage is the shortest version. Format as Percentage handles the multiplication by 100 automatically.
Worked Examples
Example 1: Test Score
A student answers 42 questions correctly out of 56. What percentage did they score?
- Part = 42, whole = 56
- (42 ÷ 56) × 100 = 0.75 × 100 = 75%
Use the "X is what % of Y?" mode: enter 42 as the part and 56 as the whole.
Example 2: Salary Increase
An employee earns $52,000 a year and receives a 7% raise. What is the new salary?
- Raise amount: (7 ÷ 100) × 52,000 = $3,640
- New salary: $52,000 + $3,640 = $55,640
- Shortcut: $52,000 × 1.07 = $55,640
Use the "What is X% of Y?" mode: enter 7 as the percentage and 52000 as the number to find the raise amount directly. Related: the Work Hours Calculator lets you track hourly pay and overtime alongside this type of rate adjustment.
Example 3: Revenue Drop
Monthly revenue fell from $85,000 to $71,400. What is the percentage decrease?
- Change: $85,000 − $71,400 = $13,600
- % decrease: (13,600 ÷ 85,000) × 100 = 16%
Use the "% change from X to Y" mode: enter 85000 as the original and 71400 as the new value. The calculator labels the result as a decrease automatically.
Example 4: Discount Price
A $280 laptop bag is reduced by 35%. What is the final price?
- Discount amount: 35% × $280 = $98.00
- Sale price: $280 − $98 = $182.00
- Shortcut: $280 × 0.65 = $182.00
Use the "% off (discount)" mode: enter 35 as the discount percentage and 280 as the original price.
Example 5: Comparing Two Lab Measurements
Two instruments measure the same sample and return 48.2 and 51.6. What is the percentage difference between the readings?
- Absolute difference: |48.2 − 51.6| = 3.4
- Average: (48.2 + 51.6) ÷ 2 = 49.9
- % difference: (3.4 ÷ 49.9) × 100 = 6.81%
Use the "% difference: X and Y" mode. Neither reading is the baseline, so percentage difference is the correct choice here rather than percentage change.
Frequently Asked Questions
How do you calculate a percentage of a number?
Divide the percentage by 100, then multiply by the number. 15% of 200: (15 ÷ 100) × 200 = 0.15 × 200 = 30. On a standard calculator, press 200 × 15 % and the % key handles the division automatically.
How do you calculate percentage increase?
Subtract the old value from the new value, divide by the old value, then multiply by 100. From 50 to 65: ((65 − 50) ÷ 50) × 100 = (15 ÷ 50) × 100 = 30% increase. The denominator is always the original, not the new value.
How do you calculate percentage decrease?
Subtract the new value from the old value, divide by the old value, then multiply by 100. From 80 to 60: ((80 − 60) ÷ 80) × 100 = (20 ÷ 80) × 100 = 25% decrease. The formula is identical to percentage increase; a negative result means a decrease.
How do you calculate percentage change between two numbers?
Formula: ((new − old) ÷ |old|) × 100. A positive result is an increase, a negative result is a decrease. Using the absolute value of the old number in the denominator handles negative starting values correctly. For example: old = −50, new = −40. Change: ((−40 − (−50)) ÷ 50) × 100 = (10 ÷ 50) × 100 = 20% increase.
How do you calculate percentage difference between two numbers?
Take the absolute difference of the two values, divide by their average, then multiply by 100. |A − B| ÷ ((A + B) ÷ 2) × 100. Unlike percentage change, this produces the same result regardless of which value is A and which is B. It's the right formula when no direction is implied, such as comparing prices, measurements, or any two quantities from the same category.
How do you calculate percentage off?
Multiply the original price by the decimal form of the discount. For 30% off $150: $150 × 0.30 = $45 savings. Sale price: $150 − $45 = $105. Shortcut: $150 × 0.70 = $105. The multiplier (0.70) is just 1 minus the discount rate (1 − 0.30).
How do you calculate percentage in Excel?
For X% of Y with values in A1 and B1: =(A1/100)*B1. For what percentage A is of B: =(A1/B1)*100, or format the cell as Percentage and use =A1/B1. For percentage change: =(B1-A1)/ABS(A1)*100. Excel's percentage format multiplies by 100 automatically during display, which catches people out when they expect a raw number and get a fraction instead.
What is the difference between percentage change and percentage points?
Percentage points are the arithmetic difference between two percentages. Percentage change is the proportional movement relative to the starting value. A tax rate rising from 20% to 25% is a 5 percentage point increase, but a 25% increase in the rate itself ((5 ÷ 20) × 100). Both are correct, but they describe different things. News reports and financial documents sometimes use one when they mean the other.
How do you calculate percentage error?
Percentage error compares a measured or estimated value to a known or theoretical value: ((|measured − actual|) ÷ actual) × 100. A measurement of 48 cm against a true value of 50 cm: ((|48 − 50|) ÷ 50) × 100 = (2 ÷ 50) × 100 = 4% error. This is common in science labs and quality control checks.
How do you calculate profit percentage?
Profit percentage is profit divided by cost (or revenue, depending on whether you want gross margin or markup), multiplied by 100. Profit as a percentage of cost: ((selling price − cost) ÷ cost) × 100. Buy for $40, sell for $50: ((50 − 40) ÷ 40) × 100 = 25% profit on cost. For margin as a percentage of revenue: ((50 − 40) ÷ 50) × 100 = 20% margin. The Profit Margin Calculator and ROI Calculator both build on this same percentage arithmetic.
How do you calculate grade percentage?
Divide total points earned by total points possible, then multiply by 100. Earned 347 points out of 400: (347 ÷ 400) × 100 = 86.75%. For weighted grades, multiply each score by its weight, sum the weighted scores, then divide by the sum of all weights. The GPA Calculator handles the credit-weighted version of this automatically for course grades.
References
- Khan Academy: Percent Word Problems: worked examples and practice for the core percentage formulas used in this calculator.
- Microsoft Support: Calculate percentages in Excel: official documentation for the Excel formulas referenced in the percentage-in-Excel section above.
- NIST: SI Units and Quantities: background on dimensionless quantities including percentage and how they are formally defined in measurement standards.