Online Percentage Calculator – Fast & Free
Percentage calculations are easy to get wrong. Whether you're working out a discount, checking how much something has changed, or comparing two values, manual maths invites errors, and most people aren't sure they've got it right.
The percentage calculator covers percentage change, percentage difference, increase and decrease, all in one place. Type your numbers and the result appears instantly. No formulas, no sign-up, works on any device.
Percentage Calculator
Please provide any two values below and click the "Calculate" button to get the third value.
Percentage Calculator in Common Phrases
Select a phrase below and fill in the values to calculate.
Percent Calculator
Convert values between Percent, Fraction, and Decimal formats instantly.
Answers are rounded to 7 decimal places.
Percentage Change Calculator (Add/Subtract)
Calculate percentage increase or decrease. Useful for tips, sales price, percent off, discounted price, and more.
Answers are rounded to 7 decimal places.
Percentage Difference Calculator
Calculates the percentage difference between two values and the percentage change from Value 1 to Value 2.
Percent Error Calculator
Calculate the percentage error between an experimental (measured) value and a theoretical (known) value.
Answers are rounded to 7 decimal places.
More Calculations
Quick tools for specific percentage needs
What the Calculator Can Do
Percentage questions tend to fall into one of six recognisable patterns. Choose whichever matches your situation, fill in the values you’ve already got, and the remaining one works itself out.
| Mode | What it solves | Example |
|---|---|---|
| What is X% of Y? | Find the part when you know the percentage and the whole | What is 20% of 150? → 30 |
| X is what % of Y? | Find the percentage when you know the part and the whole | 45 is what % of 180? → 25% |
| % increase/decrease from X to Y? | Find how much a value has changed relative to the original | From 80 to 100 → 25% increase |
| X increased/decreased by Y% equals? | Apply a percentage change to a starting value | $200 minus 15% → $170 |
| % difference between X and Y? | Compare two values symmetrically, no fixed starting point | Between 60 and 90 → 40% |
| X is Y% of what? | Find the whole when you know the part and its percentage | 30 is 20% of what? → 150 |
How to Use Our Percentage Calculator
Getting started takes seconds. Follow these quick steps to choose a mode, enter values, and read the result.
- Choose the mode that matches your question.
- Enter the two numbers you know and leave the value you want to find empty.
- Read the result as it updates instantly while you type.
- Use Tab and Shift + Tab to move between fields faster.
- Click Clear to reset the current calculator mode and start again.
Scientific Notation in the Percentage Calculator
You might notice that results occasionally appear in scientific notation rather than as a full number. That happens automatically when the result is too large or too small to display usefully otherwise, a compact way of writing numbers using powers of 10 rather than stringing out every digit.
- 0.000027 = 2.7 × 10⁻⁵
- 270,000 = 2.7 × 10⁵
What Is a Percentage?
A percentage is a fraction where the denominator is always 100, that’s the whole idea. Fifty out of 100 is 50%. One in 10 is also 10%, because 1/10 and 10/100 are the same proportion just written differently. The word comes from the Italian per cento, meaning “for a hundred,” and the % symbol is thought to have emerged from scribes shortening cento repeatedly in handwritten ledgers over centuries, until the abbreviation took on a life of its own.
Understanding the Concept
Most people have been using percentages their whole lives without thinking much about the underlying maths. They’re on price tags, in interest rates, in weather forecasts, on exam results, on nutrition labels, woven into almost every quantitative statement we encounter. Stripped back, one percent is just one-hundredth: 5% and 0.05 are the same number, the same number, whichever way you write it.
A Simple Way to Visualise Percentages
A visualisation that tends to make the idea click: picture a chest of drawers divided into exactly 100 equal compartments, each one standing for 1% of whatever you’re counting. Load it with 400 cookies spread evenly and each section holds 4. Ask for 15% and you’re pulling out the contents of 15 compartments, 15 × 4 = 60. The maths scales up or down with the drawer size, but the proportional logic is always the same.
Core Percentage Calculator Formulas
Behind any percentage calculation, there are three numbers in play. Provide any two of them and the calculator works out the third automatically, every time:
- Percentage: P = 100 × (part ÷ whole)
- Part: part = whole × (P ÷ 100)
- Whole: whole = 100 × (part ÷ P)
Reverse Percentage, Finding the Original Value
Use reverse percentage when you know the final value and the percentage change, but need the original value.
Original price before a discount
Sale price ÷ (1 − discount as decimal) = original price.
A jacket on sale for $85 was marked down 15%. Working backwards: 1 minus 0.15 is 0.85, and $85 divided by 0.85 is $100. That’s what it cost before.
Original value before a percentage increase
Final value ÷ (1 + increase as decimal) = original value.
A salary of $52,000 followed a 4% raise. Divide by 1.04 and the pre-raise figure is $50,000.
Tip: Divide the final value by (1 ± the decimal) to get back to the starting value.
“X% More Than” and “X% Less Than”
For “X% more than Y” or “X% less than Y,” use the base value first, then add or subtract the percentage amount.
| Question | Base value | Percentage | Answer |
|---|---|---|---|
| 15% more than 200 | 200 | +15% | 230 |
| 20% less than 150 | 150 | −20% | 120 |
| 50% more than 60 | 60 | +50% | 90 |
| 10% less than 500 | 500 | −10% | 450 |
Converting Between Fractions, Decimals, and Percentages
A fraction, a decimal, and a percentage can all represent the same underlying value, different formats, same number. Converting between them is straightforward once the pattern is clear.
Fraction to percentage
Divide top by bottom, multiply by 100.
- 3/4 → 3 ÷ 4 = 0.75 → 75%
- 7/20 → 7 ÷ 20 = 0.35 → 35%
Decimal to percentage
Multiply by 100. Equivalently, move the decimal point two places right.
0.65 → 65% {'|'} 0.08 → 8% {'|'} 1.20 → 120%
Percentage to decimal
Divide by 100, or nudge the decimal point two places to the left.
45% → 0.45 {'|'} 7.5% → 0.075 {'|'} 120% → 1.20
Percentage to fraction
Write it over 100, then cancel down by dividing both sides by their common factor.
- 75% → 75/100 → ÷ 25 → 3/4
- 40% → 40/100 → ÷ 20 → 2/5
Quick reference: 1/2 = 0.5 = 50% {'|'} 1/4 = 0.25 = 25% {'|'} 3/4 = 0.75 = 75% {'|'} 1/5 = 0.20 = 20% {'|'} 1/10 = 0.10 = 10%
Percentage Calculator: Change and Difference
Use this section when your question compares two values instead of finding a part of a whole. Choose the formula based on whether you have a clear starting value.
Percentage Difference
Use this when you’ve got two values and neither one is the original, you’re comparing them on equal terms, not measuring a change. The formula averages the two values and uses that as the reference point, which gives both equal weight, and it’s why the formula treats both sides equally.
|V1 − V2| ÷ ((V1 + V2) ÷ 2) × 100
Between 10 and 6: absolute difference is 4, average is 8, so 4 ÷ 8 × 100 = 50% difference.
Percentage Change (Increase and Decrease)
When there’s a clear before and a clear after, this is the formula: ((New − Old) ÷ Old) × 100.
Positive result means an increase; negative means a decrease. The sign tells you the direction, the magnitude tells you how significant it was.
Increase by a percentage
New value = base + base × (% ÷ 100).
A $100 price goes up by 20%: add 100 × 0.20 = $20, giving $120 in total.
Decrease by a percentage
New value = base − base × (% ÷ 100).
A $200 item with a 50% discount: subtract 200 × 0.50 = $100, leaving $100.
Why increase and decrease percentages are not equal
This catches people off guard more often than you’d expect. A 25% increase followed by a 25% decrease doesn’t return you to where you started, because the second calculation runs on a bigger base than the first.
| Start | Change | Result | |
|---|---|---|---|
| Increase by 25% | $80 | +25% | $100 |
| Decrease by 25% | $100 | −25% | $75 |
$80 grows by 25% to $100. Take 25% off $100 and you’re at $75, five dollars short of the start. To exactly reverse a 25% increase, you’d need a 20% decrease, not a matching 25%.
Edge Cases and Common Errors
When the original value is zero
If the starting value is zero, the formula would divide by zero, so there is no valid percentage result. Report the movement as an absolute number instead, for example $0 to $500 is a $500 increase.
Negative percentage results
A negative result simply means the new value is lower than the old one. From 200 to 150, the result is −25%, a straightforward 25% decline.
Percentages above 100%
Nothing unusual about a result above 100%, it just means the value more than doubled. Revenue climbing from $50,000 to $130,000 gives a 160% increase. Large number, perfectly valid calculation.
Percent Error in the Percentage Calculator
Percent error puts a precise number on the gap between what was measured and what the expected value was. It’s the standard accuracy metric in lab science, research, and quality assurance work, which is why the tool includes a dedicated percent error mode.
|Experimental − Theoretical| ÷ |Theoretical| × 100
- Subtract the theoretical value from the experimental one
- Take the absolute value of that result
- Divide by the absolute value of the theoretical figure
- Multiply by 100
Advanced Percentage Calculator Concepts
Percentage Points vs Relative Change
These two generate persistent confusion, including among people who work with data for a living. They sound nearly identical. They’re measuring entirely different things, and mixing them up produces a very different picture of the same situation.
- Percentage points: the arithmetic difference between two percentage figures. A rating climbing from 30% to 50% is a 20 percentage point rise. Just subtraction.
- Relative change: how much the original percentage shifted proportionally. That same 30% to 50% move is a 66.7% relative increase, because 50 is two-thirds larger than 30.
A clear illustration from politics: a candidate’s poll rating drops from 40% to 35%. In percentage point terms that’s a 5 pp fall. As relative change, it’s a 12.5% drop from the original support base. Both are accurate, but they answer different questions.
Per Mille and Basis Points
In some fields, a single percentage point is too large a unit to be useful. Financial markets are the main example, rate movements that matter happen below the one-percent threshold. Two specialised notations fill that gap.
- Per mille (‰): one thousandth (0.001). Ten times more precise than a percent. Used in blood alcohol measurement, some statistical contexts, and wherever percentage points are too coarse. A budget of $2,400 at 1‰ is $2.40.
- Basis point (‱): one ten-thousandth (0.0001). The working unit of interest rate movements. “The central bank raised rates by 50 basis points” translates to a 0.50% increase. Divide by 100 to convert basis points to a percentage.
Compounding and Averaging Percentages
Two calculation mistakes crop up when people apply the arithmetic of ordinary numbers to percentages. Both produce answers that look reasonable but are quietly wrong.
- Compounding: $100,000 at 2% annual interest for five years looks like a straightforward 10% gain, $110,000 at the end. The actual balance is $110,408. That extra $408 builds up because each year’s interest earns interest in the years that follow. Small amounts individually, but they accumulate.
- Averaging: Four annual returns of 5%, 6%, 10%, and then −10% average out to 2.75% by simple arithmetic. But that’s not what actually happened to the money. The geometric mean, roughly 2.45% per year, accounts correctly for the compounding effect and gives you the real growth rate. It’s worth keeping in mind for investment or financial analysis.
Percentage of a Percentage
Multiply the two percentages together and divide by 100. That’s the whole operation.
- (A% × B%) ÷ 100 = result %
- 10% of 20% = (10 × 20) ÷ 100 = 2%, not 30%
Where this matters in practice: a business with a 20% profit margin, taxed at 5% on those profits, has a tax burden of 1% of total revenue, not 5% of it. The maths: 5 × 20 ÷ 100 = 1. It consistently produces a smaller number than people expect.
Real-World Percentage Calculator Applications
It’s genuinely difficult to go a few hours without running into a percentage somewhere. Here’s where the tool gets used most:
- Shopping: Two questions dominate: how much am I actually saving, and what did it cost before the reduction? Both answered instantly.
- Tax and tips: Adding VAT, stripping it back out of an already-taxed price, or working out what tip to leave, everyday calculations that come up constantly.
- Personal finance: Loan repayments, APR comparisons, investment returns, most of the numbers that matter in personal finance are percentages once you look at them closely.
- Business decisions: Revenue growth, margin analysis, and headcount comparisons turn up in business at every level, from pricing to hiring.
- Science and research: Experimental accuracy, survey margins, population comparisons all get expressed as percentages, and percent error is a standard part of any measurement discipline.
- Weather and daily forecasts: Chance of rain, UV index, humidity, more percentage-based figures than most people realise.
- Comparing financial products: There’s no good way to evaluate a savings account, credit card, or mortgage offer without checking the numbers side by side.
Percentage Calculator: Frequently Asked Questions
How do I find the original price before a discount?
Divide the sale price by (1 minus the discount as a decimal). A jacket now selling for $85 after a 15% markdown: $85 ÷ 0.85 = $100. That’s what it cost before.
What is 15% more than 200?
Work out 15% of 200, that’s 30, and add it to 200. You get 230. For “X% less than Y,” the same idea applies but you subtract instead: find X% of Y, take it away. Both directions work the same way.
How do you calculate profit percentage?
Apply the standard formula: ((Selling Price − Cost Price) ÷ Cost Price) × 100
- Subtract the cost price from the selling price
- Divide that result by the cost price
- Multiply by 100
How do you calculate percent change?
Use the increase/decrease mode when you have an old value and a new value. The calculator applies the formula and labels the result as an increase or decrease automatically.
What is scientific notation in the Percentage Calculator?
When a result is very large or very small, the result is written in scientific notation automatically rather than showing every digit. 270,000 becomes 2.7 × 10⁵; 0.000027 becomes 2.7 × 10⁻⁵. Same numbers, just expressed more compactly. You don’t need to configure anything, it switches over on its own.