Percentage Calculator
Four calculators in one, covering every common percentage question — with the working shown so you can check the answer makes sense.
Result
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About the Percentage Calculator
Percentages are the arithmetic people most often get slightly wrong, usually because the question is ambiguous rather than because the maths is hard. “What is 20% of 80” and “20 is what percent of 80” are different questions with different answers, and they are phrased almost identically. Adding 20% and then removing 20% does not return you to where you started, which surprises a lot of people and costs some of them money.
This calculator separates the four distinct questions into their own modes. The first finds a part from a whole: 20% of 80 is 16. The second finds a rate from two numbers: 20 is 25% of 80. The third finds the change between two values: from 80 to 100 is a 25% increase. The fourth applies a change to a number: 80 increased by 20% is 96 — and 96 decreased by 20% is 76.8, not 80, which is exactly the asymmetry that catches people out.
Each mode shows the formula it used and the numbers substituted into it. That is deliberate: a result you can verify is worth considerably more than one you have to trust, particularly when you are checking a discount, a tax figure or a change in a metric that somebody is going to ask you about.
How to use it
- Pick the question you are askingPercent of, is-what-percent, percentage change, or add and subtract a percentage.
- Enter your two numbersBoth fields update the result immediately — there is no calculate button.
- Read the answer and the workingThe formula and the substituted values are displayed alongside the result.
- Try the reverseSwitch modes to sanity-check from the other direction, which catches most input mistakes.
- Copy the resultTake the number, or the full working, to wherever you need it.
Features
- Four separate modesEach of the common percentage questions handled explicitly rather than through one ambiguous form.
- Working shownThe formula and substituted values displayed with every answer.
- Percentage changeIncrease and decrease between two values, with the direction stated in words.
- Add and subtractApply a percentage uplift or reduction, which is what discount and tax calculations need.
- Live resultsAnswers update as you type, so exploring different numbers is fast.
- Sensible roundingResults rounded to a readable number of decimal places, with the full value available.
Who uses this tool
- ShoppingWork out a sale price, compare two discounts, or find the original price from a discounted one.
- Business reportingCalculate month-on-month growth or decline and state it correctly in a report.
- StudentsConvert a mark into a percentage, or find what score is needed to reach a target grade.
- Finance and taxAdd VAT or sales tax to a net figure, or work backwards from a gross amount.
Tips worth knowing
- A 20% increase followed by a 20% decrease leaves you 4% below where you started — percentage changes are not symmetrical.
- To reverse a discount, divide rather than multiply: a price of 80 after 20% off means the original was 80 ÷ 0.8 = 100.
- Distinguish percentage points from percent. Moving from 10% to 12% is a rise of 2 percentage points, but a 20% increase.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For 20% of 80: 80 × 20 ÷ 100 = 16. The first mode of this calculator does exactly that and shows the substitution.
How do I work out percentage increase or decrease?
Subtract the old value from the new one, divide by the old value, and multiply by 100. From 80 to 100: (100 − 80) ÷ 80 × 100 = 25% increase. Always divide by the original value, not the new one — that is the most common mistake.
How do I find the original price before a discount?
Divide by one minus the discount as a decimal. If an item costs 80 after 20% off: 80 ÷ 0.8 = 100. People often add 20% back instead, which gives 96 and is wrong.
What is the difference between percent and percentage points?
Percentage points measure the absolute gap between two percentages; percent measures the relative change. A rise from 10% to 12% is 2 percentage points, and also a 20% increase. Financial and political reporting depends on the distinction.
Why doesn't adding then subtracting the same percentage return the original?
Because each step is applied to a different base. Adding 20% to 100 gives 120; subtracting 20% from 120 removes 24, not 20, leaving 96. The second percentage operates on the larger number.
How do I calculate a percentage change from zero?
You cannot — dividing by zero is undefined, so percentage change from a starting value of zero has no meaning. Report the absolute change instead, or describe it as new rather than as a percentage rise.