Pick a mode with the five radio buttons under Choose Calculation Mode; the word between the two boxes changes to show how the numbers are read, and both boxes are cleared. Learn more about the modes
Type the two numbers in the order the row shows, percentage then amount, original then new, part then whole, or numerator then denominator; hover the ? for a hint. Learn more about the two numbers
Click Calculate; the answer appears after the equals sign with two decimals, with a percent sign in the three percentage modes; Reset returns to the first mode with empty boxes. Learn more about the result
The calculator opens under the heading Choose Calculation Mode with five radio buttons: Calculate Percentage of a Number, Calculate Percentage Change, Calculate Percentage Ratio, Add/Subtract Percentage and Fraction to Percentage. The first is selected when the page loads. Clicking another mode changes the word between the two boxes, which tells you how the numbers are read: "% of", "changed to", "is what % of", a small drop-down with "% added to" and "% subtracted from", or "/" for a fraction. The explanation box under the buttons changes with the mode too.
Switching mode empties both boxes and the result, so pick the mode first and type afterwards. Each mode is one formula: a percentage of a number, the percentage change from an old value to a new one, the percentage one number is of another, a number increased or decreased by a percentage, and a fraction written as a percentage. The five formulas are compared in The Five Percentage Calculations.
Entering the Two Numbers
DemoThree modes with their two numbers
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Every mode takes two numbers, typed in the two boxes on the calculator row. The word between them says how they are read, and the small ? before each box shows a hint on hover: in Calculate Percentage of a Number the first box is the percentage and the second the whole amount, so 20 and 150 means 20% of 150; in Calculate Percentage Change the first box is the original value and the second the new value; in Calculate Percentage Ratio the first is the part and the second the whole, so 30 and 120 asks what percent 30 is of 120; in Add/Subtract Percentage the first is the percentage and the second the base number; in Fraction to Percentage they are the numerator and the denominator, so 3 and 8 is 83.
The boxes accept decimals and negative numbers; the percent sign is never typed, the calculator supplies it. Nothing is computed until you click Calculate, so you can correct a number before asking for the answer. Which number goes first matters in every mode except the fraction, where swapping gives the reciprocal: the formulas are set out in The Five Percentage Calculations.
Calculating, Reading the Result and Resetting
DemoA change, an error, a subtraction, Reset
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Click Calculate and the answer appears after the equals sign at the end of the row, rounded to two decimals. In three modes it carries a percent sign: the percentage change, the percentage ratio and the fraction to percentage, so 80 changed to 100 reads 25.00%, 30 is what % of 120 reads 25.00% and 3/8 reads 37.50%. In the other two the answer is an amount: 20% of 150 reads 30.00, and 15% subtracted from 200 reads 170.00. A decrease shows as a negative change, 100 changed to 80 gives −20.00%.
If a box is empty or holds something that is not a number, the row reads "Error: Invalid input"; type both numbers and click Calculate again. A percentage change from an original value of 0 has no answer, and the row says "Error: The original value cannot be 0"; a whole or a denominator of 0 is refused the same way. Typing in either box clears the old answer. Reset returns the calculator to its opening state: the first mode, both boxes empty, the drop-down back on "% added to". The result of a mode change is also a cleared row, since the two boxes are emptied. How each answer is formed is explained in The Five Percentage Calculations.
The Explanation Box
DemoThe box for two modes and the subtract option
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The box under the Calculate and Reset buttons explains the selected mode in a few sentences: what the calculation finds and where it is used, such as discounts and tips for a percentage of a number, or price rises and population growth for a percentage change. It ends with a link to the section of this page that explains the formula, and it changes the moment you click another mode, before any number is typed.
In Add/Subtract Percentage the box follows the drop-down as well, so "% added to" and "% subtracted from" each have their own note, one for a mark-up or tax, one for a discount. The box does not react to the numbers you type; it describes the formula, while the row above shows the result. Read the two together: the row gives the answer, the box tells you what the answer means. The formulas themselves are in The Five Percentage Calculations, starting with Percentage of a Number.
One example runs through all five: 20% of 150 is 30; going from 150 to 180 is a 20% change; 30 is 20% of 150; 150 plus 20% is 180 and minus 20% is 120; and 15030 is 20%. The common mistake across all of them is to forget the factor 100, or to apply it twice. The percent sign and its meaning are listed in the arithmetic symbols reference.
Percentage of a Number
To take p% of a number N, turn the percentage into a fraction of one hundred and multiply: N⋅100p. For 20% of 150: 150⋅0.20=30. The calculator's first mode does exactly this, with the percentage in the first box and the amount in the second, so 20 and 150 give 30.00.
This is the calculation behind tips, discounts and shares of a total: a 15% tip on 60 is 9, a 30% discount on 80 is 24. Two shortcuts help with mental arithmetic: 10% is a shift of the decimal point, and p% of N equals N% of p, so 8% of 25 is 25% of 8, which is 2. The common mistake is to divide by the percentage instead of by 100, or to read the answer as the new price when the question asked for the discount alone; for the new price use Adding and Subtracting a Percentage.
Percentage Change
The percentage change from an old value to a new one is the difference divided by the old value, times 100: oldnew−old⋅100. From 80 to 100 the change is 8020⋅100=25%; from 100 back to 80 it is 100−20⋅100=−20%, not −25%, because the base has changed. The calculator's second mode takes the original value first and the new value second and marks a decrease with a minus sign.
The base is always the starting value, which is the usual mistake: dividing by the new value, or by the difference. A change from 0 has no percentage, since nothing can be divided by the starting value; the calculator answers "The original value cannot be 0" in that case. Percentage points are a different measure: a rate moving from 4% to 5% rises by one point but by 25% in relative terms.
What Percent One Number Is of Another
To express a part as a percentage of a whole, divide and multiply by 100: wholepart⋅100. 30 out of 120 is 12030⋅100=25%; 45 out of 60 is 75%. The calculator's third mode, labelled Calculate Percentage Ratio, takes the part first and the whole second and adds the percent sign to the answer.
This is the reverse of taking a percentage of a number, which is why the answer can be checked by going back: 25% of 120 is 30. The part may exceed the whole, giving more than 100%: 150 out of 120 is 125%. The common mistake is to swap the two numbers, which gives the reciprocal percentage, 400% instead of 25% in the example; the hints on the two boxes name the part and the whole to prevent it.
Adding and Subtracting a Percentage
Increasing or decreasing a number by a percentage is one multiplication: N⋅(1+100p) to add, N⋅(1−100p) to subtract. The calculator's fourth mode offers the two directions in a drop-down between the boxes, "% added to" and "% subtracted from", with the percentage in the first box and the base number in the second. The two cases have their own sections: Adding a Percentage for mark-ups, taxes and growth, and Subtracting a Percentage for discounts and losses.
With p=15 and N=200 the two answers are 230 and 170. The shared rule is that the percentage is taken of the base number, never of the result: adding 15% and then subtracting 15% does not return to the start, since the second 15% is taken of 230 and gives 195.50.
Adding a Percentage
Adding p% to a number N gives N+N⋅100p=N⋅(1+100p). For 15% added to 200: 200⋅1.15=230; the calculator shows 230.00 when the drop-down reads "% added to". A sales tax of 8% on 50 gives 54, and a 3% raise on 2,000 gives 2,060.
The factor form is the one to remember: a 15% increase is multiplication by 1.15, so two such increases multiply by 1.152=1.3225, a rise of 32.25% rather than 30%. The common mistake is to add percentage points to the number itself, 200+15=215, forgetting that 15% is a share of 200, not a count.
Subtracting a Percentage
Subtracting p% from a number N gives N−N⋅100p=N⋅(1−100p). For 15% subtracted from 200: 200⋅0.85=170; the calculator shows 170.00 when the drop-down reads "% subtracted from". A 30% discount on 80 leaves 56; a stock that falls 10% from 120 is worth 108.
A discount followed by the same percentage increase does not restore the price: 170⋅1.15=195.50, not 200, because the second percentage is taken of the smaller base. The common mistake is the reverse of the adding case, taking the number of points off the amount, 200−15=185. Subtracting more than 100% gives a negative result, which the calculator reports as such.
Fraction to Percentage
A fraction becomes a percentage by dividing the numerator by the denominator and multiplying by 100: ba⋅100%. For 83: 3÷8=0.375, so 37.5%; the calculator's fifth mode, with the numerator in the first box and the denominator in the second, shows 37.50%. Common fractions worth knowing: 41=25%, 31≈33.33%, 52=40%, 45=125%.
The idea is an equivalent fraction with denominator 100: 83=10037.5. The common mistake is to divide the other way round, 8÷3, which gives 266.67%; the numerator is the part on top. The parts of a fraction are named in Numerator and denominator, the equivalent-fraction view in Creating equivalent fractions, and the division route in Decimal conversion method.