Percentage Calculator

Written by the Utiliby editorial team · Last updated October 17, 2026 · Rules and formulas reviewed October 2026

What this free percentage calculator does

Percentages are everywhere: discounts in a shop, interest on a loan, the tip at a restaurant, marks on an exam, a rise in prices, the share of a budget. Most people can do the easy cases in their head, but a hard case, such as working back to an original price, often leaves them reaching for a phone. A percentage calculator removes the doubt. You enter the numbers you have and get the answer, and this one also shows the working, so that you learn the method as well as the result.

The calculator covers the full set of everyday percentage problems on one page. The first tab answers the three classic questions at once: what is X% of Y, X is what percent of Y, and X is Y% of what. The second tab handles percent change, percent difference, increasing or decreasing a number by a percent and the reverse percentage, in which you find the original value. The third tab converts a percent into a decimal, a fraction and a ratio, and chains several percent changes to find the net result. A picture of a hundred squares and simple bars shows the answer, and a print option exports only the results. Everything runs in your browser.

How to use the percentage calculator

1. Pick the question. Use tab 1 for part, whole and percent questions, tab 2 for change over time, and tab 3 for conversions and chains.
2. Type your numbers. Boxes accept decimals and negative values. The answers change as you type.
3. Read the steps. The numbered working under each answer shows how it was found.
4. Check the picture. The grid shows what share of the whole the percent covers.
5. Save. Copy the results, download them as a CSV file or print a clean summary.

The three percentage formulas

A percent is a fraction of 100. The word comes from the Latin per centum, meaning by the hundred. Every basic percentage problem links three quantities: the part, the whole and the percent. If you know two, you can find the third.

The calculator uses exactly these formulas and prints each substitution, so you can follow the arithmetic line by line.

Percent change, increase and decrease

Percent change measures how much something moved relative to where it started. The formula is (new − old) ÷ old × 100. If rent rises from 800 to 860, the change is 60 ÷ 800 × 100 = 7.5%. If a stock falls from 50 to 40, the change is −10 ÷ 50 × 100 = −20%. A positive result is an increase and a negative result is a decrease.

The starting value is always the base. That is why a rise followed by an equal fall does not return you to the start. Gain 50% on 100 and you have 150. Lose 50% of 150 and you have 75, which is 25% below where you began. To get back from 150 to 100 you need a fall of one third, or 33.3%. Understanding this asymmetry helps with investments, price changes and pay.

Percent difference versus percent change

Sometimes there is no before and after, only two numbers to compare, such as the price of the same item in two shops or the heights of two people. Percent difference treats the two values equally by dividing their gap by their average: |a − b| ÷ ((a + b) ÷ 2) × 100. For 80 and 100, the gap is 20 and the average is 90, so the difference is 22.2%. By contrast, percent change from 80 to 100 is 25%, and from 100 to 80 is −20%. Choose percent change when one value came first and percent difference when neither did.

Reverse percentages: finding the original value

A common puzzle is to find the original value when you only know the final one and the percent that was applied. A jacket costs 84 in a sale after 30% off. What was the original price? The sale price is 70% of the original, so the original is 84 ÷ 0.70 = 120. In the same way, if a salary is 33,000 after a 10% rise, the earlier salary was 33,000 ÷ 1.10 = 30,000. The wrong approach, taking 30% of 84 and adding it back, gives 109.20, which is not the original. Use the reverse percentage box in tab 2 whenever the percent was applied to a value you no longer know.

Chaining percentages and percentage points

When several percent changes happen one after another, multiply the factors instead of adding the percents. A price that rises 10% in year one and 15% in year two has gone up by 1.10 × 1.15 − 1 = 26.5% overall, not 25%. A 20% discount followed by a further 10% off is 0.80 × 0.90 = 0.72, a total of 28% off, not 30%. The chain tool lists each step and the running value.

Percentage points are a different idea. They describe the gap between two percentages. If an interest rate goes from 4% to 5%, that is a rise of one percentage point but a 25% increase in the rate. News stories mix these up often, so check which one is meant. If a poll shows support moving from 40% to 44%, that is four percentage points, or a 10% relative increase.

Where percentage calculations are used

• Shopping. Sale prices, coupons, sales tax and unit comparisons. For stacked discounts and buy-one-get-one offers, see the discount calculator.
• Money. Interest, fees, tips, commission and investment returns.
• Work. Pay rises, bonus shares and growth targets. The pay raise calculator turns a percent into annual and hourly pay.
• School. Exam marks, weighted grades and error rates.
• Health. Body composition, nutrition labels and recovery rates.
• Business. Margins, markup, conversion rates and market share.
• Statistics. Percent error, relative change and proportions.

Common percentage mistakes and how to avoid them

• Using the wrong base. Percent change uses the old value, not the new one.
• Adding percents that should be multiplied. Two successive changes combine as factors.
• Confusing percent with percentage points. Say which you mean.
• Subtracting a percent from the final price. Use the reverse percentage instead.
• Forgetting to divide by 100. 15% is 0.15, not 15.
• Dividing by zero. Percent change from zero is undefined, because there is no base.

Quick mental-math tricks

• 10%. Move the decimal point one place left.
• 5%. Take half of 10%.
• 1%. Move the point two places left.
• 15%. Add 10% and 5%. For 240 that is 24 + 12 = 36.
• 20%. Double 10%.
• 25%. Divide by 4. 50%. Divide by 2. 75%. Take 25% off.
• Swap the numbers. 8% of 50 equals 50% of 8, which is 4. Pick the easier one.

Use the calculator to check these shortcuts until they become automatic.

Privacy, accuracy and responsible use

The calculator runs in your browser and stores nothing. It shows up to six decimal places, and floating-point arithmetic can leave tiny rounding differences in very long decimals, so round the final answer to the precision you need. The tool is a general maths aid. For tax, legal, investment or medical decisions, confirm figures with a qualified professional.

Related free calculators

Use these free online tools together with this one:

• Stack discounts, add sales tax and compare deals with the discount calculator.
• Find the mean, median and mode of a list with the average calculator.
• Turn a percent raise into new annual and hourly pay with the pay raise calculator.
• Add a tip and split a restaurant bill with the split bill calculator.
• Measure return on spend as a percentage with the marketing ROI calculator.

Frequently asked questions

Sources and further reading

• Khan Academy, Percentages.
• Merriam-Webster, Percent (definition and origin).
• National Council of Teachers of Mathematics, Teaching ratio and proportion.

Sources were consulted in October 2026. Standards and rules can change, so always check the official page for your situation.