Free Online Percentage Calculator

What the percentage calculator shows

This percentage calculator answers the five questions that come up every day: what a percent of an amount is, what percent one number is of another, how much a price or a salary has changed in percent, what you get after adding or taking off a percentage, and what the markup and margin are between a cost and a selling price. You choose the question, enter two numbers and the answer appears straight away.

Percentages are the language of almost every money decision. A sale price, a savings rate, a fund fee, a pay rise, inflation, a tax, an investment return: each is a percentage, and in each case what matters most is what the percentage is taken of. Most mistakes are not about hard arithmetic but about the wrong base: a percentage of the old price instead of the new one, of the selling price instead of the cost, a percent instead of a percentage point.

The calculator is useful when you want to check a discount quickly, compare two rates, see how much of your income goes on rent or set a price for something you sell. It is not tied to a currency: the numbers can be dollars, euros, units or points. The examples in this guide use dollars, but the calculator shows plain numbers. Everything runs in your browser, and nothing you enter is sent anywhere.

In this guide:

• How to pick a mode, fill in the fields and read the results
• The five formulas behind every calculation
• The difference between a percent and a percentage point, and between markup and margin
• Why +20% and −20% do not bring you back, and how to find a price before a discount
• Percentages in personal finance, and simple versus compound percentages
• Three worked examples, a formula table and common mistakes

If you are new to managing money, start with the basics article on what investing is and how to get started: nearly every idea in it is expressed as a percentage.

How to use the percentage calculator

At the top of the Your numbers panel is the Calculation row with five buttons: % of, What %, Change, +/− % and Margin. On a phone they take two rows, on a wide screen one. Below them the calculator spells out your question in words, such as "What is 15% of 2,400?", with a short hint on what the mode is good for. The fields of the chosen mode follow.

The Amount and Percent values are shared by the % of and +/− % modes: if you enter 2,400 and 15% in one, they are waiting for you in the other. Each mode keeps its own numbers until you press Reset.

All fields are number boxes, without sliders. Amounts accept anything from minus one trillion to one trillion, so negative numbers such as a loss work too. Percent accepts 0 to 1,000,000; you reduce an amount with the Take off button, not with a minus sign. Under the Percent field is a row of Common percentages: 5%, 10%, 15%, 20%, 25% and 50%. Decimals are fine, such as 12.5. A value outside a field's limits is pulled back to the limit when you leave the box. On phones each field has − and + buttons that step by 10 for amounts and by 1 for percentages.

Reading the results

The headline depends on the mode: a number in % of and +/− %, a percentage in What % and Change, and a margin or a selling price in Margin. The figures below it are:

• in % of, What is left, the amount minus the part you found, plus a bar split into Part and What is left;
• in What %, As a fraction, the same two numbers with a slash between them;
• in Change, the signed Difference and the Ratio, such as × 1.20;
• in +/− %, the Difference and To undo it, the percentage that takes the result back to the starting amount, plus a bar split into Starting amount and Added, or Result and Taken off;
• in Margin, the other two of price, markup and margin, plus Profit, with a bar split into Cost and Profit.

Numbers show up to two decimals. The bars appear only where a split makes sense: in % of, for example, only for a positive amount and a percentage of 100 or less.

Pin to compare keeps the current question and answer. When you change the numbers, the headline shows the difference, such as +3 pp vs pinned, and a caption sums it up: "Pinned scenario: Change from 25,000 to 28,000 = +12%". A difference between two percentages is given in percentage points (pp), a difference between two amounts as a number. Switching the mode or the I know the choice, or pressing Reset, clears the pin; the Add or take off switch keeps it. PDF saves the question, the fields and the results, Share shares a link without your numbers, and Reset restores the defaults. On phones and tablets the results sit in a bar at the bottom of the screen; Details opens the figures, notes and buttons.

Five percentage formulas

A percent is one hundredth. 15% means 15 out of 100, or 0.15. All five modes of the calculator are versions of one idea: the part equals the whole times the percent, divided by 100. The only difference is what you know and what you are looking for.

% of:      Part   = Amount × p ÷ 100
What %:    p      = Part ÷ Whole × 100
Change:    p      = (To − From) ÷ |From| × 100
+/− %:     Result = Amount × (1 ± p ÷ 100)
Margin:    Markup = (Price − Cost) ÷ Cost × 100
           Margin = (Price − Cost) ÷ Price × 100

• p is the percentage;
• |From| is the absolute value of the old number, that is the number without its minus sign;
• ± is plus for the Add button and minus for Take off.

The calculator does not round anything inside; it only shows the result with up to two decimals. So 16.666…% appears as 16.67%, and any further calculation you base on the rounded number can be a cent or two off.

Two derived formulas

The To undo it figure in +/− % works like this, and in the Margin mode the price can be found from a markup m or a margin g:

To undo it         = (Amount ÷ Result − 1) × 100
Price from markup  = Cost × (1 + m ÷ 100)
Price from margin  = Cost ÷ (1 − g ÷ 100)

The last formula works only for a margin below 100%. Enter 100 or more and the calculator explains that a margin is a share of the selling price and has to stay below 100%.

Percentage change and percentage points

Percentage change is always measured from the old value. A price that rose from $1,250 to $1,500 went up by $250, which is 20% of 1,250. If the price fell from $1,500 to $1,250, the difference is the same $250, but against 1,500 it is only 16.67%. A rise and a fall by the same amount have different percentages, and that is not an error.

The Ratio figure says the same thing in another way: × 1.20 means the new value is 1.2 times the old one, × 0.50 that it is half. Ratios are easy to chain: changes of × 1.10 and × 0.90 make × 0.99 together, which is −1%.

The ratio also clears up "times" versus "percent". A 100% increase is a doubling (× 2.00); a 200% increase is a tripling (× 3.00), not a doubling. If a price goes from $5,000 to $10,000, the Change mode shows +100% and × 2.00. Falling "by half" is −50% and × 0.50, not −200%: a positive quantity cannot fall by more than 100%.

When the old value is negative, the calculator divides by its absolute value. A loss that shrinks from −200 to −100 therefore shows as +50%: things got better. Without the absolute value the formula would give −50% and mislead you. The Ratio reads the same way: × 1.50, that is 1 + 50%, not −100 ÷ −200 = × 0.50, which would point the other way. From zero there is no percentage change, and the calculator tells you so.

Percent or percentage point

When the thing that changes is itself a percentage, such as a savings rate, a central bank rate, inflation or a fee, there are two ways to describe the change. Percentage points (pp) are the plain difference: a rate of 4% that becomes 3% has fallen by 1 pp. Percent is the relative change: 1 out of 4 is 25%, so the rate has fallen by 25%.

The calculator uses both. The Change mode gives the relative change, and when you pin one percentage and compare it with another, the difference next to the headline is in percentage points.

Adding and subtracting percentages

Adding a percentage means taking an amount plus a share of it: $1,000 plus 20% is 1,000 + 200 = $1,200, or in one step 1,000 × 1.2. Taking a percentage off removes that share: $1,000 minus 20% is 1,000 × 0.8 = $800. The +/− % mode does exactly this: choose Add or Take off, enter the amount and the percent, and Result shows the new amount while Difference shows the part added or removed, with its sign.

The interesting figure is To undo it. It answers the question: which percentage takes the result back to where it started? After +20% it is −16.67%; after −20% it is +25%. The percentage that undoes a change is always taken of the new number, and that number is different. When the two percentages differ, the calculator explains it in a note: "To get from 1,200 back to 1,000 you need −16.67%, not −20%: the second percentage is taken of a different amount."

The pattern is clear: the bigger the percentage, the further the step there and the step back drift apart. At 5% the gap is barely visible; at 50% it is dramatic. Lose half, and you have to double what is left just to get back.

Discounts, price rises and reversing a percentage

A discount is a percentage taken off a price. A $240 jacket with 15% off costs 240 × 0.85 = $204, and the discount is $36. The calculator shows this in two ways: in % of, 15% of 240 is 36, and What is left, 204, is the sale price; in +/− % with Take off, Result shows 204 directly.

A price rise works the same way with Add. If an annual gym membership cost $1,250 last year and is now 20% dearer, the new price is $1,500. If you know both prices, the Change mode tells you how much the price rose in percent.

How to find the price before a discount

The harder task is the reverse: the tag says $204 and "15% off". What did the item cost before? The usual mistake is to add 15% to $204, which gives $234.60, not $240. The discount was taken from the old, larger price, so the way back is by division:

Price before discount = Sale price ÷ (1 − discount ÷ 100)
204 ÷ (1 − 0.15) = 204 ÷ 0.85 = 240

In the calculator, the Margin mode does this division. A margin, like a discount, is a share of the larger price, so the formula is the same.

The same idea gives you a gross amount from a net one when you know the total percentage deducted. Taxes that follow more complicated rules need a dedicated tool, though. VAT is charged on the price before tax, so in a price that includes 20% VAT the tax is not 20% of the total but one sixth of it, 16.67%. The VAT calculator adds or removes VAT at any rate and has the standard rates of several European countries built in, such as 19% in Germany, 20% in France, 21% in Spain and 22% in Italy.

Markup vs margin

Markup and margin describe the same profit measured against different amounts. Markup is the profit as a share of the cost; margin is the profit as a share of the selling price. An item that cost $800 and sells for $1,000 makes $200 of profit. Against the cost that is 25%, the markup; against the price it is 20%, the margin.

That gives the main rule: with a positive profit, the margin is always smaller than the markup. A margin cannot reach 100%, because the profit cannot exceed the whole price while the cost is positive. A markup has no upper limit: an item that cost $100 and sells for $400 has a markup of 300% but a margin of only 75%.

In the Margin mode the I know the switch sets where you start: Price, Markup or Margin. The Cost field is always there, and the second field changes. When you know the price, the headline is Margin and the figures are Markup, Selling price and Profit. When you know the markup or the margin, the headline is Selling price and the figures are Markup, Margin and Profit. Markup can go down to −100%, and margin from −1,000% to anything below 100%: negative values mean selling at a loss.

Confusing markup with margin is expensive. A seller who wants a 30% margin but adds a 30% markup gets only a 23.08% margin: a cost of $800, a price of $1,040 and a profit of $240 instead of $342.86. If taxes, rent and wages take 25% of revenue, that mistake turns a planned profit into a loss.

Percentages in personal finance

Percentages turn up most often where your own money is involved. Here are a few questions the calculator answers in seconds.

• What share of your income goes on housing? What % mode: $2,300 of rent out of a $5,600 monthly income is 41.07%. To split your income into needs, wants and savings, try the 50/30/20 budget planner.
• What is your savings rate? $600 set aside out of $4,000 is 15% of income. Your savings rate shapes how fast your wealth grows more than any return does.
• How much did your pay really rise? The Change mode gives the nominal rise. If prices rose 10% over the same period, $1,000 now buys only what $909.09 bought before. That is the same effect as the To undo it figure after +10%: −9.09%. The article on inflation explains why money loses value.
• What does a fund fee cost? A 1% yearly fee on $100,000 is $1,000 every year. The gap between fees of 0.2% and 1% is only 0.8 pp, but the Change mode shows the second is 400% higher, five times as much. The guide on how to read an ETF covers fund costs.
• What does a deposit really pay after tax? A percent of the interest shows how much the tax takes. More in the article on whether a bank deposit is worth it.

Loan rates per month, per year and per day

Loan terms come in different units: 2% a month, 24% a year, 0.01% a day. To compare them, convert everything to a year. The simple conversion multiplies: 2% a month × 12 = 24% a year. But when interest is charged on interest, the year costs more: 1.02 to the twelfth power is 1.2682, or 26.82% a year. On top of that, fees, insurance and other required payments push the real cost of a loan above its nominal rate.

You can walk through a few months step by step with the +/− % mode, but for the full cost of a loan with every payment included, the APR calculator is the better fit: it works out the yearly rate from the payment schedule and the extra costs.

Investment returns and the averaging trap

$10,000 that first gains 50% and then loses 50% does not return to $10,000. After the gain it is $15,000; after the loss, $7,500. The simple average of the two years is zero, but in fact you lost 25%. The Change mode from 10,000 to 7,500 shows exactly −25%.

That is why returns over several years are not averaged but compounded: for this example the yearly rate is about −13.4%. The annualized return calculator works it out for your own investments. Why swings in value are the price of a higher expected return is the subject of the article on risk and return.

Simple vs compound percentages over time

The percentage calculator works out one step: one change, one addition, one share. Money over time grows step after step, and that is where simple and compound percentages part ways.

Simple interest is paid each year on the starting amount only. $10,000 at 10% a year earns $1,000 a year, so after ten years you have $20,000. Compound interest is paid on the amount plus the interest already earned: $11,000 after the first year, $12,100 after the second and $25,937.42 after ten. The $5,937.42 difference is interest on interest.

Simple:    Amount × (1 + p ÷ 100 × n)
Compound:  Amount × (1 + p ÷ 100)ⁿ

Here n is the number of years. You can apply the +/− % mode year by year: enter 10,000, add 10%, then enter the result, 11,000, and add 10% again. For two or three steps that is a good illustration; for ten or thirty years the compound interest calculator is easier, since it lays out the growth year by year and draws a chart.

The more years and the higher the rate, the further simple and compound percentages drift apart. The article on compound interest and the time value of money explains why time is an investor's most valuable resource.

Percentage formulas at a glance

This table brings everything together: the question, how to work it out by hand and which mode of the calculator answers it.

Worked examples

Each example shows what the calculator returns. The amounts are in dollars, although the calculator shows them as plain numbers.

Common mistakes

• The wrong base. Change is measured from the old value, a discount from the price before it, a margin from the selling price. A different base gives a different answer.
• Adding percentages in a row. +10% and another +10% is +21%, not +20%; +20% and −20% is −4%, not zero. Changes in a row multiply.
• Percent instead of percentage points. A rate rising from 10% to 12% is +2 pp, or +20%. Both numbers are correct, but they answer different questions.
• Reversing a discount by adding. The price before a 15% discount is the sale price divided by 0.85, not multiplied by 1.15.
• Markup instead of margin. A 30% markup gives only a 23.08% margin. Plan prices from the measure your accounts actually use.
• Taking VAT out by subtracting the rate. The tax in a price with 20% VAT is 16.67% of the total, not 20%.
• An average instead of a compound return. +50% and −50% average zero but are really −25%.
• Rounding in the middle. The calculator shows two decimals; if you carry on from a rounded number, the final answer can be a cent or two off.

Limitations and next steps

The percentage calculator is simple on purpose: one step, two numbers, one answer. Here is what it does not do:

• No time. There are no years, no compounding and no charts. For growth over time, use the compound interest calculator.
• No currencies or taxes. Numbers are just numbers. For VAT there is the VAT calculator, for loan costs the APR calculator.
• No history. You can pin only one result, and it is cleared when you switch the mode, press Reset or reload.
• No price breakdown. The Margin mode knows only the cost and the price, without taxes, shipping or marketplace fees. Add those to the cost yourself.
• Rounding on screen only. Inside, the calculator works with full precision, but it shows at most two decimals.

The results are arithmetic, not financial advice. When a percentage feeds an important decision, such as a loan, a tax or a price for your business, check the terms in the source document: the contract, the law or the accounts.

Next steps: see how your savings rate turns into wealth in the compound interest calculator, split your income with the 50/30/20 budget planner, or check the real return on your investments with the annualized return calculator.