Percentage Calculator

How to use the percentage calculator

1. Pick the question that matches the sentence you are trying to finish. “What is 35% of 90?” is the first type, “9 is what percent of 36?” is the second, and “36 is 75% of what number?” is the third.
2. Fill in the two numbers you know. The calculator hides the box for the number you are solving for, so you can’t enter it by mistake.
3. Read the answer and the sentence under it. The sentence restates the problem with the answer filled in. If it reads oddly, you probably chose the wrong question type.

Negative numbers and percentages above 100 are allowed. A value can be 150% of another, and a temperature or a balance can be negative. The results are rounded to six decimal places for display only.

One equation, three unknowns

Every basic percentage problem is the same equation with a different piece missing. The open textbook Prealgebra 2e from OpenStax writes it as “amount is percent of base”:

The examples in section 6.2 of that textbook make good checks, and the calculator reproduces each of them:

• What number is 35% of 90? 0.35 × 90 = 31.5 (Example 6.14).
• 125% of 28 is what number? 1.25 × 28 = 35. A percent over 100 gives an answer bigger than the base (Example 6.15).
• 36 is 75% of what number? 36 ÷ 0.75 = 48 (Example 6.16).
• 6.5% of what number is $1.17? 1.17 ÷ 0.065 = $18 (Example 6.17).
• What percent of 36 is 9? 9 ÷ 36 = 0.25 = 25% (Example 6.18).
• 144 is what percent of 96? 144 ÷ 96 = 1.5 = 150% (Example 6.19).

The trick is to translate the sentence word by word. “Of” means multiply, “is” means equals, and “what number” or “what percent” is the unknown. Once the sentence is an equation, the arithmetic is one multiplication or one division.

Percents, decimals and fractions

A percent is a ratio per hundred, so converting between forms is a matter of moving the decimal point two places or dividing by 100:

• Percent to decimal: divide by 100. 35% = 0.35, 6.5% = 0.065, 0.5% = 0.005, 125% = 1.25.
• Decimal to percent: multiply by 100. 0.875 = 87.5%, 2 = 200%.
• Fraction to percent: divide the top by the bottom, then multiply by 100. 1/8 = 0.125 = 12.5%; 2/3 = 66.67% after rounding.
• Percent to fraction: put it over 100 and simplify. 35% = 35/100 = 7/20.

The most common slip is with small percentages. Half a percent is 0.005, not 0.5; using 0.5 would make the answer one hundred times too large. The result panel shows the decimal the calculator used, so you can catch this.

Everyday examples

A restaurant tip. An 18% tip on a $68.50 bill is 0.18 × 68.50 = $12.33, which is OpenStax Example 6.20. Many people tip on the amount before tax; whatever you choose, enter that figure as the whole.

A test score. 42 correct answers out of 48 is 42 ÷ 48 = 0.875, or 87.5%. That is the “A is what percent of B” question, with the points you earned as A and the points possible as B.

Sales tax. A 7.25% tax on a $40 purchase adds 0.0725 × 40 = $2.90, so you pay $42.90. To find the price before tax from a receipt total, divide by 1.0725 rather than subtracting 7.25% of the total; the percentage increase calculator handles that reverse step.

A budget share. If rent is $1,350 of a $4,500 monthly budget, it takes 1,350 ÷ 4,500 = 30%.

Working back to the whole. A store says you saved $15, which was 20% off. The original price was 15 ÷ 0.20 = $75. This is the third question type, and it is the one people most often try to solve by multiplying instead of dividing.

Shortcuts for doing it in your head

• 10% is the number with the decimal point moved one place left: 10% of 68.50 is 6.85.
• 5% is half of that (3.43 after rounding), and 20% is double it (13.70). An 18% tip sits a little under 20%.
• 1% moves the decimal two places: 1% of 4,500 is 45, so 3% is 135.
• Swap the numbers when it helps. P% of B equals B% of P, because both are P × B ÷ 100. 8% of 50 is the same as 50% of 8, which is 4.
• 25%, 50% and 75% are quarters: divide by 4, by 2, or take three quarters.

Use the shortcut for a quick estimate and the calculator for the figure you will write down.

Mistakes that change the answer

Using the wrong base. “What percent of the class are girls?” and “girls are what percent more than boys?” have different bases. The first divides by the whole class; the second compares two groups and divides by the number of boys. Decide which number is “the whole” before you start.

Percent versus percentage points. If a rate moves from 4% to 5%, it rose by one percentage point, but by 25% of its old value (1 ÷ 4). News reports and survey results mix these up regularly.

Adding percentages of different wholes. 10% of one price plus 10% of another is not 20% of anything. Percentages only add when they share the same base.

Expecting a percent to stay under 100. A part can’t exceed its whole, but one number can easily be 150% or 300% of another when they are just two separate quantities being compared.

Rounding and reporting percentages

Percentages are usually rounded for reporting, and rounding can make a set of shares add to 99% or 101% instead of 100%. Three equal shares are each 33.33…%, which rounds to 33% three times for a total of 99%. That is not an error in the data, only in the display. If a table has to total exactly 100%, adjust the share with the largest rounding remainder, or show one more decimal place.

Pick a precision that matches the data. 7 out of 9 survey answers is 77.8%, but reporting it as 77.78% suggests a precision nine people can’t support. For money, compute with the full percentage and round the final amount to the cent, not the percentage.

When you compare two percentages, say whether you mean the difference in points or the percent change between them. The percentage increase calculator does the second.

Sources & assumptions

How this calculator gets its numbers. Full method: our methodology.

• Percent is written as a decimal before multiplying or dividing: P% = P ÷ 100.
• Part = percent × whole; percent = part ÷ whole × 100; whole = part ÷ percent.
• Negative values and percentages over 100 are allowed; the whole can’t be 0 when dividing by it.
• Results are rounded to six decimal places for display only.

Sources

1. OpenStax (Rice University), Prealgebra 2e, 6.2 Solve General Applications of Percent. “Amount is percent of base” and Examples 6.14–6.20 (35% of 90 = 31.5; 36 is 75% of 48; 6.5% of $18 = $1.17; 9 is 25% of 36; an 18% tip on $68.50), plus percent increase and decrease in Examples 6.23 ($26 to $36, 38.5%) and 6.24 ($3.71 to $3.64, 1.9%).
2. OpenStax (Rice University), Prealgebra 2e, 6.1 Understand Percent. Percent as a ratio per 100 and converting between percents, decimals and fractions.

Last reviewed November 2, 2026. The equation and examples follow the open Prealgebra 2e textbook; round to the precision your task asks for.