Percentage Calculator

Every percentage question, answered in one place. Pick a mode — percent of a number, what percent one number is of another, percentage change, add or subtract a percent, reverse percentage, percentage difference, or finding the whole from a part — and see the result with the working shown, step by step.

What Is a Percentage?

Per cent means “per hundred”: a percentage is a fraction with 100 on the bottom. 25% is 25 out of every 100, which is the same as the fraction 25/100 and the decimal 0.25. That single fact explains every calculation on this page — converting between the forms takes one step each way: divide by 100 to turn a percent into a decimal, multiply by 100 to come back. Shifting the decimal point two places is the same operation done by eye.

The idea is old — Roman tax collectors worked in hundredths, and the % sign evolved from a slanted fraction bar — but its modern power is that it makes unlike quantities comparable. A 5% pay rise, a 5% exam improvement, and a 5% price cut are all the same kind of statement: five parts in every hundred, whatever the base. The catch is that the base matters enormously, which is where most percentage confusion begins.

How to Use This Percentage Calculator, Step by Step

Start with the question you are trying to answer, then pick the mode that matches its wording. The calculator shows the answer in large type and the working underneath, so you can check the method as well as the result. Change either input and the result updates at once, which makes it easy to test a second price, a second score, or a second pay figure without starting again.

1. Choose a mode from the drop-down menu at the top of the calculator.
2. Read the two labels that appear, and enter the first value in the first box.
3. Enter the second value in the second box, using plain numbers with no percent sign in the number boxes.
4. Read the large answer, then read the working line underneath it to see the formula that was used.
5. Try a nearby value to sense-check the answer: if the percent goes up, a percent-of answer should go up too.

Finding a Percent of a Number

Choose “What is X% of Y?”, enter the percent first and the number second. For 20% of 150, the calculator turns 20% into 0.20, then multiplies: 0.20 × 150 = 30. Use this mode for a share of a total, a portion of a bill, or a part of a quantity, such as 12% of 250, which is 0.12 × 250 = 30.

Finding What Percent One Number Is of Another

Choose “X is what % of Y?”, enter the part first and the whole second. For 30 out of 120, the working is (30 ÷ 120) × 100 = 25%. The same method answers 18 out of 60, which is (18 ÷ 60) × 100 = 30%. The second number is always the base, so swapping the two numbers changes the answer.

Finding a Percentage Increase or Decrease

Choose “Percentage change”, enter the old value first and the new value second. A move from 60 to 75 is (75 − 60) ÷ 60 × 100 = 25%, an increase. A move from 90 to 72 is (72 − 90) ÷ 90 × 100 = −20%, a decrease. The minus sign matters: it tells you the direction, and the old value is always the base.

Adding or Subtracting a Percent

Choose “Add or subtract X% from a number”, enter the number first and the percent second, then pick Increase or Decrease. Raising 80 by 15% gives 80 × 1.15 = 92, while cutting 80 by 15% gives 80 × 0.85 = 68. The multiplier carries the whole job: 1.15 means the original plus 15%, and 0.85 means the original minus 15%.

Finding the Original Value With Reverse Percentage

Choose “Reverse percentage”, enter the final value first and the percent second, then say whether the final value was reached by an increase or a decrease. If you paid 90 after a 10% discount, the original was 90 ÷ 0.90 = 100. If a value reached 138 after a 15% increase, the original was 138 ÷ 1.15 = 120, because 120 × 1.15 = 138.

Comparing Two Numbers With Percentage Difference

Choose “Percentage difference”, enter the two values in either order. For 70 and 90, the difference is 20, the average is 80, and the percentage difference is (20 ÷ 80) × 100 = 25%. The answer has no direction: it says how far apart the values are, not which one came first.

Finding the Whole From a Part

Choose “X is P% of what number?”, enter the part first and the percent second. If 36 is 40% of the whole, the whole is 36 ÷ 0.40 = 90. If 75 is 25% of the whole, the whole is 75 ÷ 0.25 = 300. This mode is the reverse of the first mode, and multiplying the answer back by the percent should return the part you started with.

The Seven Calculations, Explained

Two shortcuts are worth knowing. First, “of” is commutative: 15% of 240 equals 240% of 15, and the second is easier — 2.4 × 15 = 36. Awkward percentages often become easy when flipped, which is why 8% of 25 is best read as 25% of 8 = 2. Second, 10% of anything is just the number with the decimal point moved one place, and every other percentage can be built from 10%, 5%, and 1% chunks: 35% of 80 is 8 + 8 + 8 + 4 = 28.

Percentage Points vs Percent — The Trap

A rate moving from 5% to 7% rises by 2 percentage points, but the relative increase is 40% (2 ÷ 5 × 100). News reports and politicians mix these up constantly, and the difference is huge: a “2% rise” in a rate and a “2 percentage point rise” are completely different statements. Whenever you see a percentage applied to another percentage — interest rates, tax rates, exam pass rates — ask which one is meant. The Khan Academy percent lessons walk through this distinction with worked examples, and Wolfram MathWorld gives the formal definitions.

Common Percentage Mistakes

• Sequential changes do not add. A 20% discount followed by 10% off is 28% off overall, not 30%, because the second discount applies to the reduced price. The discount calculator shows this stacked math directly.
• Up then down does not cancel. Raise 100 by 20% to 120, then cut 20%: you land on 96, not 100. The undoing percentage is always different, because the second move is measured from a bigger base.
• A stock that halves must double to recover. A 50% fall needs a 100% rise to break even — the asymmetry table below makes this vivid.
• Rounding too early. Round only the final answer; rounding intermediate percentages compounds the error.

Everyday Uses

Shopping is the obvious one — discounts, tax, and tips all run on percentages — but the same maths powers finance (interest and returns, see the compound interest calculator), work (raises and deductions, see the salary calculator and tax calculator), and school (marks and grades). A percentage is only as honest as its base, so always check: percent of what? That one question prevents most percentage errors.

Worked Examples: Four Problems, Solved Step by Step

Example 1 — Sale price. A jacket costs $120 and is reduced by 30%. The discount is 30% of 120, which is 0.30 × 120 = $36, so you pay 120 − 36 = $84. The shortcut is to multiply by what remains: 120 × 0.70 = $84. Both routes agree, and the second is faster when the discount is a round number.

Example 2 — Exam score. You scored 42 out of 56. As a percentage that is (42 ÷ 56) × 100 = 75%. Notice the method: the “what percent” mode divides the part by the whole, then multiplies by 100. If the paper had been out of 60 instead, the same 42 marks would be 70% — the same performance, a different percentage, because the base changed.

Example 3 — A pay rise. A salary of $3,000 a month rises by 8%. The rise is 0.08 × 3,000 = $240, so the new salary is $3,240. Worked the other way, 3,000 × 1.08 = $3,240 directly, because multiplying by 1.08 adds the 8% in one step. The salary calculator turns this kind of raise into hourly, weekly, and annual figures.

Example 4 — Reverse percentage. You paid $170 for shoes after a 15% discount. The original price is not 170 × 1.15, which would give $195.50 and is wrong. Because $170 is 85% of the original, the original is 170 ÷ 0.85 = $200. Check: 15% of $200 is $30, and $200 − $30 = $170. Reverse problems always divide by what remains, never multiply by what was taken off.

Percentages and Money: Raises, Tax and Returns

Money is where percentages earn their keep. Interest on savings is a percentage of the balance: $5,000 growing by 12% in a year becomes $5,600, and the percentage change from $5,000 to $5,600 is (600 ÷ 5,000) × 100 = 12%. The same 12% applied for several years compounds, which is why the compound interest calculator exists — repeated percentage growth behaves very differently from a single year. A loan works in reverse: the interest rate is a percentage of what you owe, so a small rate difference changes the monthly payment.

Tax is another percentage story. If 20% of a $4,000 monthly income goes in tax, that is $800, leaving $3,200. But tax systems rarely use one flat percentage — they use bands, where different slices of income are taxed at different rates, which is why a marginal rate and an effective rate are different numbers. The tax calculator walks through that band structure. The habit that ties all of this together is always naming the base: 12% of what, 20% of what, a rise from what. Once the base is clear, every percentage problem on this page is one of the seven calculations above.

One more habit protects you from misleading percentages in headlines. When a report says “cases doubled”, that is a 100% increase, not a 200% one — doubling means the new value is 200% of the old, but the increase itself is 100%. Likewise, a fall “by 200%” is impossible for any positive quantity, since a 100% fall already reaches zero. Headlines that ignore the base are usually trying to impress rather than inform, and the seven calculations above let you check any of them in seconds.

Percentage Formulas in Plain Words

Every formula on this page is the same idea in different clothing: a percent is a part divided by a base, multiplied by 100. When you want a part, you multiply the base by the percent as a decimal. When you want the percent, you divide the part by the base. When you want the base, you divide the part by the percent as a decimal. The only hard part is naming the base correctly. In a change calculation the base is the starting value, in a difference calculation the base is the average of the two values, and in a discount the base is the price before the discount.

Zero needs care in two places. A percent of zero is zero, which is fine. But a percentage change from zero is undefined, because dividing by zero has no answer: a move from 0 to 50 cannot be expressed as a percent increase. The calculator says so rather than inventing a number, and the same applies when the whole is zero in a “what percent” question.

Percent, Fraction and Decimal: One Value, Three Forms

Percentages, fractions, and decimals are three ways of writing the same value. Learning a few common conversions by heart makes mental percentage work much faster, and the fraction calculator can convert the awkward cases for you.

1. Percent to decimal: divide by 100, or move the decimal point two places left. 45% becomes 0.45.
2. Decimal to percent: multiply by 100, or move the decimal point two places right. 0.45 becomes 45%.
3. Percent to fraction: write the percent over 100 and simplify. 60% becomes 60/100, which simplifies to 3/5.
4. Fraction to percent: divide the top number by the bottom number, then multiply by 100. 3/8 is 0.375, which is 37.5%.

Worked Examples: Percent of a Number

The table below gives eight clean results to check your method against. Each one follows the same two steps: turn the percent into a decimal, then multiply. If your answer differs, the error is usually in the first step, most often a decimal point in the wrong place.

For an awkward percent, build it from easy chunks. To find 17% of 300, take 10% (30), add 5% (15), and add 1% twice (3 plus 3, which is 6): 30 + 15 + 6 = 51. The chunk method also guards against decimal slips, because each chunk is easy to check on its own.

Worked Examples: Percentage Increase and Decrease

Percentage change always asks two questions: how much did the value move, and what was it moving from? The move is the new value minus the old value, and the base is the old value. The table below shows the pattern: the same move means a different percent when the starting value differs.

Two landmarks are worth fixing in memory. Doubling a value is a 100% increase: 50 becomes 100. Halving a value is a 50% decrease: 100 becomes 50. Tripling is a 200% increase, because the value grows by twice itself: 50 becomes 150. Saying a value “increased by 200%” and saying it “is 200% of the old value” are different claims, and the second one means only doubling.

Discounts, Tax and Tips

Shops, restaurants, and bills all use the same three calculations, and the table below works each one in full so the method is visible. The discount calculator handles sale prices in more detail, including stacked discounts.

Discounts in Shops

A 30% discount on a 240 coat means a saving of 0.30 × 240 = 72, so you pay 240 − 72 = 168. The faster route is to multiply by what remains: 240 × 0.70 = 168. Stacked discounts multiply rather than add: a 20% discount followed by 10% off turns 100 into 80, then into 72, which is 28% off in total, not 30%.

• Check the price the percent applies to: the full price, or a price already reduced.
• Check whether tax is added before or after the discount, since that changes the final total.
• Compare a percent discount with a cash discount on the same item: 25% off 80 is 20 off, the same as a 20 cash saving.
• Use reverse percentage to recover the original price from the price you paid.
• Work out the price per item when a deal covers several items, so two offers can be compared fairly.

Tax and Tips

Tax is usually added to a price, while a tip is added to a bill, but the arithmetic is identical: multiply by one plus the percent as a decimal. When tax is charged on the discounted price, a 100 item reduced by 20% and then taxed at 10% costs 80 × 1.10 = 88. A 15% tip is easy to build from 10% plus half of 10%: on a 60 bill, that is 6 plus 3, which is 9.

Grades, Marks and Test Scores

Marks become percentages by the “what percent” method: divide the marks earned by the total marks, then multiply by 100. The table below shows common results, and the same method works for any total, from a 20-mark quiz to a 200-mark exam.

Averaging percentages needs care when the tests have different totals. Scoring 85% on a 20-mark test and 70% on a 100-mark test does not give an overall 77.5%. The marks are 17 plus 70, which is 87 out of 120, or 72.5%. Always add the marks and add the totals, then convert once. The average calculator can average the raw scores first, which keeps the weighting honest.

Percentage Points vs Percent Change, Worked Out

When both values are already percentages, the difference between them has two names, and they answer different questions. The difference in percentage points is a simple subtraction. The percent change divides that difference by the starting percent. Both are correct; they simply measure different things, so a report should say which one it means.

• 4% to 6%: up 2 percentage points, and up 50% in relative terms, because 2 ÷ 4 = 0.50.
• 20% to 25%: up 5 percentage points, and up 25% in relative terms, because 5 ÷ 20 = 0.25.
• 80% to 72%: down 8 percentage points, and down 10% in relative terms, because 8 ÷ 80 = 0.10.
• 10% to 11%: up 1 percentage point, and up 10% in relative terms, because 1 ÷ 10 = 0.10.
• 50% to 55%: up 5 percentage points, and up 10% in relative terms, because 5 ÷ 50 = 0.10.

The small starting value in the first example is why the relative change looks so large. A move from 4% to 6% is a small absolute move and a large relative move at the same time, and neither description is wrong. The error comes only from using one description while the reader expects the other, which happens often with interest rates, pass rates, and survey results.

Reverse Percentage: Why Dividing Beats Adding Back

Reverse percentage problems tempt a wrong shortcut: adding the percent back on. If you paid 90 after a 10% discount, multiplying by 1.10 gives 99, which is wrong, because the 10% was taken from 100, not from 90. The correct route divides by what remains: 90 ÷ 0.90 = 100, and the check is 100 × 0.90 = 90. The same rule works for increases. A salary of 4,400 after a 10% rise came from 4,400 ÷ 1.10 = 4,000, because 4,000 × 1.10 = 4,400. A value of 132 after a 20% increase came from 132 ÷ 1.20 = 110, because 110 × 1.20 = 132.

The habit to build is simple: after an increase, divide by more than one; after a decrease, divide by less than one. Then run the check in the forward direction. If the forward check does not return the final value you started with, the original is wrong, however tidy it looks.

Percentage Difference vs Percentage Change

Percentage change has a direction and a starting point: it measures a move from an old value to a new one. Percentage difference has neither: it measures the gap between two values against their average, so swapping the values leaves the answer unchanged. For 50 and 75, the change from 50 to 75 is +50%, the change from 75 to 50 is −33.33%, and the percentage difference is 25 ÷ 62.5 × 100 = 40% in both directions.

• Use percentage change for before and after: prices over time, weight over time, scores across terms.
• Use percentage difference for two things measured side by side: two products, two readings, two estimates.
• Use percentage difference when neither value is clearly the base, so picking one would bias the answer.
• Use percentage change when the starting value is the natural base, such as last year or the original price.

The ratio calculator covers a related comparison: a ratio states how two quantities relate, while a percentage states one quantity as a share of a base. A ratio of 3 to 2, for example, means the first quantity is 150% of the second, and the second is 66.67% of the first.

Real-Life Uses Beyond Shopping

Percentages turn up wherever a part must be compared with a whole, or a new value with an old one. The list below shows how wide that range is, and why the same seven calculations keep reappearing in different clothes.

• Health: body fat is reported as a percent of body weight, so the body fat calculator and the BMI calculator both depend on percentage thinking, even though their headline results are not percents.
• Pay: raises, deductions, and overtime are usually stated as percents of pay, which the salary calculator and the tax calculator turn into cash amounts.
• Money growth: interest and investment returns are percents of a balance, and repeated percents compound, as the compound interest calculator shows year by year.
• Cooking and scaling: scaling a recipe to 150% means multiplying every ingredient by 1.50, and halving it means using 50% of each amount.
• Sport: a shooting or passing percent is successful attempts divided by total attempts, multiplied by 100, exactly like an exam score.
• Surveys and polls: results are reported as percents of the people asked, so the base is the sample size, not the whole population.
• Data and growth: a rise from 400 visitors to 500 is a 25% increase, and the same 100 extra visitors from a base of 2,000 would be only 5%.
• Household budgets: spending shares, such as housing as a percent of income, make budgets comparable even when incomes differ.

Mental Maths Shortcuts That Always Work

Shortcuts are safe when they are exact rearrangements of the formula, not guesses. The five below are all exact, and each one can be checked with the calculator on this page or with the basic calculator.

1. Find 10% by moving the decimal point one place left: 10% of 340 is 34.
2. Find 1% by moving the decimal point two places left: 1% of 340 is 3.40.
3. Build any percent from 10%, 5%, and 1% chunks: 35% of 60 is 6 + 6 + 6 + 3 = 21.
4. Flip an awkward percent: 16% of 25 equals 25% of 16, which is 4, because multiplication works in either order.
5. Halve for 50% and halve again for 25%: 25% of 48 is 12, because half of 48 is 24 and half of 24 is 12.

Estimation is the partner of every shortcut. Before trusting a precise answer, round the inputs and check the size: 19% of 510 should be close to 20% of 500, which is 100, so an answer near 96.90 is plausible and an answer near 9.69 has a decimal slip. The exact value is 0.19 × 510 = 96.90.

Common Mistakes and How to Check Your Answer

Most percentage errors are not arithmetic slips. They are base errors: the right percent applied to the wrong number, or two percents added when they should multiply. The checks below catch the common cases before they reach a decision.

• Name the base out loud before calculating: percent of what, change from what, discount off what.
• Never add sequential percents: apply the first, then apply the second to the new value.
• Never assume a rise and a fall of the same percent cancel: test the round trip with real numbers.
• Round only at the end: rounding a percent halfway through a chain of steps shifts the final answer.
• Check that a percent over 100% makes sense: it means more than the base, which is fine for growth but impossible for a share of a fixed total.
• Run the reverse check: multiply your answer back and confirm you return to a number you started with.

If an answer looks surprising, change one input at a time in the calculator and watch which direction the answer moves. A percent-of answer should rise when either input rises. A “what percent” answer should rise when the part rises and fall when the whole rises. If the answer moves the wrong way, the mode or the input order is usually the problem.

Which Mode Should You Choose?

Match the wording of your question to the mode, not to the numbers in front of you. The same two numbers can answer several different questions, and only the wording tells you which one you asked.

• “What is 20% of 90?” uses percent of a number: 18.
• “45 is what percent of 180?” uses what percent: 25%.
• “How much did it rise from 80 to 100?” uses percentage change: +25%.
• “Add 12% to 250” uses add or subtract: 280.
• “I paid 72 after 20% off; what was the original?” uses reverse percentage: 90.
• “How far apart are 60 and 80?” uses percentage difference: 28.57% (20 ÷ 70 × 100).
• “36 is 30% of what?” uses finding the whole: 120.

Verify each answer above: 20% of 90 is 18; 45 ÷ 180 × 100 = 25; (100 − 80) ÷ 80 × 100 = 25; 250 × 1.12 = 280; 72 ÷ 0.80 = 90; the average of 60 and 80 is 70, and 20 ÷ 70 × 100 = 28.57; 36 ÷ 0.30 = 120. If you need a different tool, the full set is linked from the PrimesDaily homepage.

Frequently Asked Questions

How do I calculate a percentage increase in a spreadsheet?

Use the formula (new − old) ÷ old, formatted as a percentage. If the old value is in cell A1 and the new value in B1, type =(B1−A1)/A1 and apply the % format. That is exactly the percentage-change mode on this page, and it handles decreases too — they simply come out negative.

What is a percent of a percent?

It is just multiplication of two fractions. 20% of 50% is 0.20 × 0.50 = 0.10, which is 10%. This comes up with stacked discounts and with rates applied to rates: a 10% fee charged on a price that already includes 20% tax is not a 30% addition, it is 1.10 × 1.20 = 1.32, a 32% total uplift.

What is the difference between percent and percentage points?

Percent is relative; percentage points are absolute differences between two percentages. 5% to 7% is +2 percentage points but +40% in relative terms.

How do I find the original price after a discount?

Use the reverse mode: divide the price you paid by (1 − discount ÷ 100). Paid $80 after 20% off means the original was 80 ÷ 0.80 = $100.

Why does a 20% rise followed by a 20% fall not return to the start?

Because the fall is measured from the higher value. 100 → 120 → 96. To undo a 20% rise you need a 16.67% fall.

How do I work out a tip quickly?

Find 10% by moving the decimal point one place, then scale: a 15% tip on $60 is $6 + $3 = $9. A 20% tip is just 10% doubled.

Can a percentage be over 100%?

Yes — it just means more than the whole base. 150% of 200 is 300. Growth of 200% means the value tripled (original + twice the original).

How do I calculate a percentage of a total?

Divide the part by the total and multiply by 100. If 45 out of 180 people chose an option, the share is (45 ÷ 180) × 100 = 25%. Going the other way, 25% of a total of 180 is 0.25 × 180 = 45. The total is always the base in this question, so it goes on the bottom of the division.

What does a 100 percent increase mean?

It means the value doubled. A move from 40 to 80 is a 100% increase, because the increase of 40 equals the starting value, and the new value is 200% of the old one. A 200% increase is different: it means the value tripled, because it grew by twice itself. A move from 40 to 120 is a 200% increase.

How do I add a percentage to a price?

Multiply the price by one plus the percent as a decimal. Adding 12% to 250 gives 250 × 1.12 = 280, which is the original 250 plus 30. Adding 5% to 80 gives 80 × 1.05 = 84. The multiplier method is faster than finding the percent and adding it separately, and it avoids adding the wrong amount.

How do I work out a percentage decrease in a price?

Subtract the new price from the old price, divide by the old price, and multiply by 100. A price falling from 150 to 120 dropped by 30, and 30 ÷ 150 × 100 = 20%, so it is a 20% decrease. The new price is 80% of the old price, which is the same statement from the other side: 120 ÷ 150 × 100 = 80%.

How do I convert a fraction to a percentage?

Divide the numerator by the denominator, then multiply by 100. The fraction 7/20 becomes 0.35, which is 35%. The fraction 3/4 becomes 0.75, which is 75%. The fraction calculator can simplify the fraction first, which often makes the division easier.

Disclaimer: This calculator is for general education and everyday arithmetic. For tax, loan, or investment decisions, use the dedicated calculators on this site or consult a professional.