SolveMathAI

Percentage calculator

Three questions, one answer each, with the working shown.

Enter to solve · Shift+Enter for a new line

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  • Every step shown
  • Arithmetic to calculus

A percentage is just a fraction with 100 on the bottom: 15% means 15 out of 100, or 0.15. Almost every percentage question is one of three shapes, and the calculator above does all three instantly. The solver below handles the wordier ones, like discounts, tips, tax and percentage error.

The three shapes

Nearly every percentage question is one of these. Name the shape first and the arithmetic is easy.

  1. A percent of a number

    Turn the percent into a decimal and multiply. 15% of 240 is 0.15 × 240 = 36.

  2. One number as a percent of another

    Divide the part by the whole, then multiply by 100. 45 out of 180 is 45 ÷ 180 = 0.25 = 25%.

  3. Percentage change

    Subtract, divide by the original, multiply by 100. From 80 to 92 is 12 ÷ 80 = 0.15 = a 15% increase. The original always goes on the bottom.

Worked examples

Each one is solved the way the solver solves it: the rule first, then the line.

What is 15% of 240?

15% of 24015\%\ \text{of}\ 240
  1. Percent to decimal
    15%=15100=0.1515\% = \frac{15}{100} = 0.15
  2. Multiply by the whole
    0.15×240=360.15 \times 240 = 36
Answer
3636

45 is what percent of 180?

45180×100\frac{45}{180} \times 100
  1. Part over whole
    45180=0.25\frac{45}{180} = 0.25
  2. Decimal to percent
    0.25×100=25%0.25 \times 100 = 25\%
Answer
25%25\%

What is the percentage change from 80 to 92?

92−8080×100\frac{92 - 80}{80} \times 100
  1. Find the change
    92−80=1292 - 80 = 12
  2. Divide by the original
    1280=0.15\frac{12}{80} = 0.15
  3. Decimal to percent
    0.15×100=15%0.15 \times 100 = 15\%
Answer
a 15% increase\text{a }15\%\text{ increase}

Going back the other way is not −15%: 12 ÷ 92 ≈ 13%. The starting value decides the answer.

A jacket costs $64 and is 20% off. What is the sale price?

64−20% of 6464 - 20\%\ \text{of}\ 64
  1. Find the discount
    0.20×64=12.800.20 \times 64 = 12.80
  2. Subtract from the price
    64−12.80=51.2064 - 12.80 = 51.20
  3. Or in one step
    64×0.80=51.2064 \times 0.80 = 51.20
Answer
$51.20\$51.20

Solved problems

Asked here and worked through in full. Open one for every step.

  1. What is 15% of 240?
    Answer 3636

Where marks get lost

Adding percentages of different wholes

A 10% rise then a 10% fall does not return you to the start: 100 → 110 → 99. Each percentage is taken of whatever the number is at that moment.

Percent versus percentage point

Moving from 4% to 6% is a rise of 2 percentage points, but a 50% increase. Headlines mix these two constantly.

Putting the new value on the bottom

Percentage change always divides by the original value, not the new one.

Questions

How do I find a percentage of a number?

Turn the percentage into a decimal and multiply. 15% becomes 0.15, so 15% of 240 is 0.15 × 240 = 36. The word “of” is always multiplication.

How do I work out what percentage one number is of another?

Divide the part by the whole, then multiply by 100. 45 out of 180 is 45 ÷ 180 = 0.25, which is 25%. The number after “of” goes on the bottom.

How do I calculate a percentage increase or decrease?

Take the change, divide by the original, multiply by 100. From 80 to 92 the change is 12, and 12 ÷ 80 = 0.15, a 15% increase. A negative result is a decrease.

What is the difference between percentage change and percentage difference?

Percentage change compares against the starting value, so it has a direction. Percentage difference compares against the average of the two values and has no direction, which is why the two rarely agree.

How do I reverse a percentage?

If $60 is the price after 20% off, that $60 is 80% of the original, so the original is 60 ÷ 0.8 = $75. Divide, never add the percentage back on.

How do I work out a percentage in my head?

10% is the decimal point moved one place left, and everything else is built from it. 15% of 240 = 24 (10%) + 12 (half of that) = 36. 20% is double the 10%; 5% is half of it.

What is the difference between a percentage increase and percentage points?

Percentage points are the plain difference between two percentages. A move from 4% to 6% is 2 percentage points and a 50% increase, both correct and very different.

Does it show the steps?

Yes. The calculator shows the arithmetic it used, and the solver below writes out the full method for word problems like tips, tax, markup and percentage error.