How to use the Percentage calculator
- Pick the question you have. Each row answers one type of percentage question, such as percent of a number or percent change.
- Type your numbers into the row. Enter the values in the boxes inside the sentence.
- Read the answer and steps. The result and the formula with your numbers appear instantly under the row.
Percentage formulas
X is what % of Y? → X ÷ Y × 100
X is Y% of what? → X ÷ (Y ÷ 100)
% change from X to Y → (Y − X) ÷ |X| × 100
% difference of X and Y → |X − Y| ÷ ((|X| + |Y|) ÷ 2) × 100
Add X% to Y → Y × (1 + X ÷ 100) · Subtract X% from Y → Y × (1 − X ÷ 100)
X% as a decimal → X ÷ 100 · decimal as % → decimal × 100
Sale price → Price × (1 − off ÷ 100) · Original before X% added → Final ÷ (1 + X ÷ 100)
Share of total → value ÷ sum × 100 · Grade → score ÷ total × 100
Markup → (price − cost) ÷ cost × 100 · Margin → (price − cost) ÷ price × 100
Successive changes → [(1 + a)(1 + b) − 1] × 100 · Percent error → |measured − expected| ÷ |expected| × 100
Worked examples
- Percent of: 15% of 80 = 0.15 × 80 = 12.
- What percent: 30 is 30 ÷ 120 × 100 = 25% of 120.
- Find the whole: if 45 is 30% of a number, the number is 45 ÷ 0.30 = 150.
- Percent change: from 80 to 100 is (100 − 80) ÷ 80 = 25% increase; from 100 back to 80 is a 20% decrease.
- Percentage difference: 40 and 50 differ by 10 ÷ 45 × 100 ≈ 22.22%.
- Add / subtract: $250 plus 8% is $270; $80 minus 25% is $60.
- Discount: $80 with 25% off is $60, a $20 saving.
- Reverse percentage: $108.25 including 8.25% tax was $100.00 before tax.
- Breakdown: a $2,000 budget of 1,200 / 450 / 300 / 50 splits into 60% / 22.5% / 15% / 2.5%.
- Grade: 43 out of 50 is 86% (B) on a standard 10-point scale.
- Markup vs margin: cost $60, price $100 → 66.67% markup but 40% margin.
- Successive changes: +10% then −10% is a net −1%, not zero.
- Percent error: measuring 9.6 when 9.81 is expected is a 2.14% error.
- Conversions: 37.5% = 0.375 = 3/8; 0.0625 = 6.25%.
Percent change vs. percentage difference
Use percent change when there’s a clear before and after (a price, a salary, a population). It divides by the starting value, so the direction matters. Use percentage difference when comparing two values with no natural starting point (two stores’ prices, two measurements). It divides by their average, so it gives the same answer either way.
Markup vs. margin
Markup and margin use the same profit but different bases. Markup divides profit by cost; margin divides it by selling price, so margin is always the smaller number. A 50% markup is only a 33.3% margin. Retailers usually set prices by markup and report profitability by margin.
Percentage points vs. percent
When a rate moves from 4% to 5%, it rose by 1 percentage point, which is a 25% relative increase. News stories about interest rates, polls and unemployment often mix these up, so the last row shows both. For discounts with sales tax, try the sales tax calculator; for restaurant bills, the tip calculator.
What your results mean
Every row shows its formula with your numbers plugged in, so you can check the math or show your work. Results are rounded to six decimal places.
Tips
- Percent change divides by the starting value; percentage difference divides by the average of the two.
- To undo a percentage increase, divide by (1 + rate) rather than subtracting the same percentage.
- Commas, $ and % signs are ignored when you type, so you can paste numbers directly.
Frequently asked questions
How do you calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number: 15% of 80 = 0.15 × 80 = 12.
How do you calculate percentage increase?
(New − Old) ÷ Old × 100. From 80 to 100 is a 25% increase.
How do you calculate the percentage difference between two numbers?
Divide the absolute difference by the average of the two numbers and multiply by 100: 40 and 50 → 10 ÷ 45 × 100 ≈ 22.2%.
What is the difference between percent and percentage points?
Going from 4% to 5% is a 1 percentage point rise but a 25% increase.
What is the difference between markup and margin?
Markup is profit ÷ cost; margin is profit ÷ selling price. Cost $60 and price $100 is a 66.7% markup but a 40% margin.
Why does +10% then −10% not return to the start?
The second change applies to a bigger number. 100 → 110 → 99, a net change of −1%. Multiply the factors: 1.10 × 0.90 = 0.99.
How do you calculate percent error?
|Measured − Expected| ÷ |Expected| × 100. Measuring 9.6 when 9.81 is expected gives about a 2.14% error.
How do I calculate my grade percentage?
Divide your score by the total possible and multiply by 100: 43/50 = 86%. On a common 10-point scale that is a B, but schools set their own cutoffs.
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