Percentage Calculator

Three questions, three different formulas

Nearly every percentage problem people bring to a calculator is one of three questions, and each one rearranges the same two numbers differently. This page keeps all three on screen at once so you do not have to decide which formula you need before you can start typing. The first block answers "what is X% of Y", which is the shape of a discount, a tip, a commission or a GST amount. The second answers "X is what percent of Y", which is the shape of a test mark, a deposit measured against a purchase price, or one line item as a share of a total. The third answers "what changed between X and Y", which is the shape of a rent rise, a price increase or a fall in monthly sales.

Situations these three blocks cover

• Adding the 10% GST to a quoted price before you write the invoice.
• Checking that a 30% off tag on a $189 jacket really takes $56.70 off.
• Turning a mark of 47 out of 60 into a percentage for a report card or a moderation spreadsheet.
• Seeing what share of a $12,400 project budget a single $1,850 subcontractor invoice represents.
• Measuring a rent increase from $540 to $575 a week so you can compare it against CPI figures.
• Comparing this quarter's revenue against last quarter's in a board report or a BAS summary.
• Working out how much of a home deposit target you have reached so far.

What the page does with the numbers you type

Each block recalculates on every keystroke, so there is no button to press and no page reload. Block one multiplies the second field by the first and divides by 100. Block two divides the first field by the second and multiplies by 100. Block three subtracts the starting value from the ending value, divides that difference by the starting value, then multiplies by 100, which is the step most people get wrong by dividing by the finishing number instead. Under every answer sits a line of working that shows the actual arithmetic with your figures substituted in, so you can copy the method into a spreadsheet or explain it to someone else.

Results are rounded to ten significant figures and then displayed with up to six decimal places, using your device's number formatting for thousands separators. Every field accepts decimals and negative numbers. Two guards exist: block two refuses to divide by zero and says so, and block three tells you that percent change is undefined when the starting value is zero, because there is nothing to compare the change against. In block three an increase is shown in cyan and a decrease in red, with the direction written out in words so a minus sign cannot be missed at a glance.

A worked example

The page loads with real defaults you can edit rather than blank boxes. Block one starts at 15 and 200 and reports that 15% of 200 = 30, with the working line "Because 200 x 15 / 100 = 30". Block two starts at 30 and 200 and reports that 30 is 15% of 200. Block three starts at 200 and 250 and reports a 25% increase, because 50 divided by 200 is 0.25. Change the finishing value to 150 and the same block flips to a 25% decrease. Notice that going up 25% and then down 25% does not return you to where you started, because the second percentage is taken from a larger base.

Limits and things it will not do

This is a straight arithmetic calculator, not a finance model. It does not compound anything over time, does not apply interest schedules, does not handle percentage points as distinct from percentages, and does not remove tax from a tax-inclusive figure in one step. To strip 10% GST from a total you divide by 11, which is a different operation to taking 10% off. Very large or very small inputs will round at the ten significant figure mark, and the display caps at six decimals, so results that need more precision should be checked in a spreadsheet. Nothing is saved between visits, so refreshing the page returns the default numbers.

When another calculator suits better

For interest that builds on itself year after year, use the Compound Interest Calculator. For repayments on a borrowed amount, use the Loan Calculator. If you are converting between units rather than proportions, try the Unit Converter, and for days between two dates use the Date Difference Calculator. If the percentage you are working out is GST for a client bill, the Invoice Generator will lay the whole document out for you, and our guide on invoicing basics for Australian sole traders explains where that 10% belongs on the page.

Everything happens in your browser and nothing is uploaded to a server. There is no signup, no limit on how many sums you run, and no record kept of the figures you enter.

Questions people ask

How do I calculate a percentage of a number?

Multiply the number by the percentage and divide by 100. For example, 15% of 200 is 200 x 15 / 100 = 30. The first block does this as you type.

How do I express one number as a percentage of another?

Divide the first number by the second, then multiply by 100. A mark of 47 out of 60 is 47 / 60 x 100 = 78.333333%.

Why does the percent change block ask for the original value first?

Because percent change is always measured against where you started. The difference is divided by the original value, not the new one, so 200 to 250 is a 25% increase while 250 to 200 is a 20% decrease.

Can I enter negative numbers or decimals?

Yes. Every field accepts decimals and negative values. The only two blocked cases are dividing by zero in the second block and a starting value of zero in the third, where percent change has no meaning.

How do I take 10% GST out of a price that already includes it?

Divide the total by 11 rather than taking 10% off. A $220 tax-inclusive price contains $20 of GST, whereas 10% of $220 is $22, which is why the two methods disagree.