Percentage Calculator

How to Use the Percentage Calculator

1. Add Your Fraction Problem

   Use Calculator for keypad entry, Math Input for typed expressions, or Canvas to draw, handwrite, or upload a clear photo. Try entries such as “15% of 240,” “18 is what percent of 60,” or “add 10% to 85.”

2. Choose Your Output

   Step-by-step answers are the default. You can also select Explain Like I’m 10, Create Practice Test, Create Study Guide, Create Flashcards, or Find My Mistake if you want feedback on work you upload.

3. Choose a Language

   Use the language dropdown labeled “Default” to choose the language for the explanation.

4. Get the Result

   Select Solve to submit your percentage problem and receive the chosen explanation or learning output.

How to Calculate Percentages

Every percentage problem connects a part, a whole, and a percent. The trick is deciding which of those three values you already know.

Find a Percentage of a Number

Use this when you know the percent and the whole, such as finding a discount, tip amount, tax amount, test-score portion, or share of a total.

Percent means “per hundred,” so divide the percent by 100 before multiplying:

\[ \text{part}=\frac{p}{100}\times\text{whole} \]

For example, find \(15\%\) of \(80\):

\[ 0.15\times80=12 \]

So, \(15\%\) of \(80\) is \(12\). The word “of” tells you to multiply. You can think of \(15\%\) as \(15/100\), which is the decimal \(0.15\).

Find What Percent One Number Is of Another

Use this form when the question sounds like, “18 is what percent of 60?” Here, 18 is the part and 60 is the whole.

\[ \text{percent}=\frac{\text{part}}{\text{whole}}\times100\% \]

\[ \frac{18}{60}\times100\%=30\% \]

So, 18 is \(30\%\) of 60. Put the whole in the denominator, because you are comparing the part to the entire amount.

The whole cannot be zero here because division by zero is undefined. If you first reduce a part-to-whole fraction, you can simplify the part-to-whole fraction before converting it to a percent.

If you know the part and the percentage but need the whole, divide the part by the percentage written as a decimal:

\[ \text{whole}=\frac{\text{part}}{\text{percent as a decimal}} \]

For example, if 18 is \(30\%\) of a number:

\[ \text{whole}=\frac{18}{0.30}=60 \]

So, 18 is \(30\%\) of 60.

A percentage change is different from percentage points. Moving from \(20\%\) to \(25\%\) is a rise of 5 percentage points, but it is a \(25\%\) relative increase.

Add or Subtract a Percentage

Use these formulas when an amount increases or decreases by a percentage. The original amount must be clear, since it is the base of the calculation.

For an increase:

\[ \text{new value}=\text{original}\times\left(1+\frac{p}{100}\right) \]

For a decrease:

\[ \text{new value}=\text{original}\times\left(1-\frac{p}{100}\right) \]

For instance, increasing 75 by \(20\%\) gives:

\[ 75\times(1+0.20)=75\times1.20=90 \]

Adding \(20\%\) and then subtracting \(20\%\) does not usually return to the starting value. After a 20% increase, the decrease is based on the larger new amount, not the original amount.

Understanding Percentages

A percent is a comparison with 100. For example, \(45\%\) means 45 out of every 100 equal parts. That is why \(45\%=45/100=0.45\).

To calculate with a percent, turn it into a decimal by dividing by 100. Thus, \(25\%=0.25\). If decimal conversion is the step slowing you down, use these percentage-to-decimal conversion steps for extra practice.

“\(x\%\) of a number” starts with a known percent and asks for a part. “\(x\) is what percent of a number?” starts with two amounts and requires division to discover the percent.

For increases and decreases, the original amount is your base. If the base changes after one step, the next percentage must use that new amount.

Worked Example

A jacket costs \(80\) dollars. It is discounted by \(25\%\), then sales tax of \(8\%\) is added to the discounted price. What is the final price?

1. Find the discount amount:

\[ 25\%\text{ of }80=0.25\times80=20 \]

The discount is \(\$20\).

2. Subtract the discount from the original price:

\[ 80-20=60 \]

The jacket’s discounted price is \(\$60\).

3. Find \(8\%\) of the discounted price:

\[ 8\%\text{ of }60=0.08\times60=4.80 \]

At an \(8\%\) rate, the added amount is \(\$4.80\). Notice that this percentage uses 60 as its base, not the original 80.

4. Add the tax to the discounted price:

\[ 60+4.80=64.80 \]

The final price is:

\[ \boxed{\$64.80} \]

You can verify it by multiplying the original price by both change factors:

\[ 80\times0.75\times1.08=64.80 \]

When a problem begins as a part-to-whole relationship, it can also help to convert a fraction to a percent before calculating.

Common Mistakes

1. Dividing by the part instead of the whole

   Students may calculate \(60\div18\) for “18 is what percent of 60.” The whole belongs on the bottom, so use \(18\div60\), then multiply by \(100\%\).

2. Multiplying by the percent number instead of its decimal

   Writing \(25\times80\) for \(25\%\) of 80 treats 25 as a whole number. Divide by 100 first: \(25\%=0.25\), then multiply by 80.

3. Adding 20 instead of adding 20%

   Adding 20 to 100 is not the same as increasing 100 by \(20\%\). Find \(20\%\) of the original amount, or multiply by \(1.20\).

4. Using the old base for a second percentage

   After a discount, students sometimes calculate the next percentage from the original price. Each new percentage uses the amount present at that step unless the question says otherwise.

5. Assuming opposite percentages cancel

   A 20% increase followed by a 20% decrease uses two different bases. For example, \(100\times1.20\times0.80=96\), not 100.

Percentage Calculator in Excel

To find a percentage of a whole in Excel, use a formula such as:

\[ =A2*B2 \]

If \(B2\) contains \(15\%\), Excel stores it as \(0.15\), so the formula finds 15% of the value in \(A2\).

To find what percent one value is of another, use:

\[ =\frac{A2}{B2} \]

Then format the result cell as Percentage. To increase or decrease a value, use:

\[ =A2*(1+B2) \]

or:

\[ =A2*(1-B2) \]

Excel’s Percentage format changes how a decimal appears; it does not change the underlying calculation. For example, 0.15 displays as 15% when formatted as a percentage.