math calculator

Percentage Calculator

Solve percentage changes, ratios, and differences.

Formula Verified by Dr. Elena Rostova, PhD

Quick actions: Save inputs, view saved runs, print, share, or export results

Saved Runs

Inputs

Mode

Percent%

Value

Starting value

Ending value

First value

Second value

Results

Percentage result

Percent used15%

Base value240

Bookmark this Percentage Calculator

Save this page to solve discounts, taxes, growth rates, and ratio comparisons without rebuilding the formulas each time.

Formula

Percentage formulas

Percent of = percent / 100 x value; Change = (new - old) / |old| x 100

The calculator supports percent of a value, percent change, and percent difference.

Step by step

How the calculation works

1Choose the percentage mode.
2Enter the values required by that mode.
3Apply the matching percentage formula.
4Review the supporting rows to see the base values.

Example

Example percentage calculation

15% of 240 is 36, and a change from 200 to 250 is a 25% increase.

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How to understand and use this calculator

Percentages as scaled fractions of 100

A percentage is a ratio expressed per hundred. The symbol % literally means “out of 100,” which makes percentages one of the most convenient ways to compare values of different sizes. In finance, business, medicine, and statistics, percentages convert raw quantities into comparable proportional statements.

If 15 out of 60 students pass an exam, the raw fraction is 15/60. When converted into a percentage, the result is 25%, which immediately communicates the scale of success. This normalization is the reason percentages are used in tax rates, profit margins, interest rates, concentration labels, voting results, and demographic reports.

Core percentage formulas

The calculator supports three primary mathematical families of percentage problems. Each has a different denominator and should not be confused with the others.

1. Percentage of a value:

$$\text{Part} = \frac{p}{100} \times \text{Whole}$$

2. Percentage change (when there is a true starting value):

$$\text{Percentage Change} = \frac{\text{New} - \text{Original}}{|\text{Original}|} \times 100$$

3. Percentage difference (when both values have equal status):

$$\text{Percentage Difference} = \frac{|A - B|}{(A + B)/2} \times 100$$

These formulas answer different questions. Percentage change tells you how much something increased or decreased relative to the original baseline. Percentage difference tells you how far apart two peer values are relative to their midpoint.

Worked examples and interpretation

Suppose a store raises a price from $80 to $92. The change is $12. Dividing by the original value gives 12/80 = 0.15, or a 15% increase. If the price instead falls from $80 to $68, the change is -12. Dividing by 80 yields -15%, indicating a 15% decrease.

Now compare two competing product prices: $80 and $92. Here there is no natural “original” value if the goal is just comparison. We therefore use percentage difference: the absolute difference is 12, the average is 86, and the result is 12/86 ≈ 13.95%. This is not the same as a 15% increase. Choosing the correct denominator is the central conceptual skill in percentage mathematics.

Common mistakes in percentage calculations

One common mistake is adding or subtracting percentage points as though they were multiplicative rates. For example, a 20% decrease followed by a 20% increase does not return you to the original value because the second percentage is applied to a smaller base. Another error is dividing by the wrong baseline when measuring change. Always ask: “Change relative to what?” before choosing the denominator.

Related concepts

Percentage points

The arithmetic difference between two percentages.

Relative change

A change measured relative to a starting baseline.

Ratio

A comparison of one quantity to another using division.

Frequently Asked Questions

What is a percentage?+

A percentage is a fraction or ratio expressed per hundred. 25% means 25 out of 100, or 0.25 in decimal form.

How do I calculate 15% of a number?+

Convert 15% to 0.15 and multiply by the base value. For example, 15% of 80 is 0.15 × 80 = 12.

What is the difference between percentage change and percentage difference?+

Percentage change uses an original starting value as the baseline. Percentage difference compares two peer values using their average as the baseline.

How do I convert a decimal to a percentage?+

Multiply the decimal by 100 and add the percent sign. For example, 0.375 becomes 37.5%.

How do I convert a percentage to a decimal?+

Divide the percentage by 100. For example, 8% becomes 0.08.

Why is a 50% decrease followed by a 50% increase not equal to zero change?+

Because the second change is applied to the reduced base. If 100 falls to 50, then a 50% increase on 50 only adds 25, giving 75.

What are percentage points?+

Percentage points describe the arithmetic difference between two percentages. Moving from 12% to 18% is a rise of 6 percentage points, not necessarily a 6% increase.

How do I calculate a discount percentage?+

Subtract sale price from original price, divide by the original price, and multiply by 100.

Can a percentage be greater than 100?+

Yes. Percentages above 100% indicate a quantity larger than the baseline, such as a 150% increase or 125% concentration relative to a reference value.

When should I use the absolute value in percentage change?+

When you want the magnitude of change without regard to direction, or when following the standard absolute-baseline convention for certain applied comparisons.

How to understand and use this calculator

Percentages as scaled fractions of 100

Core percentage formulas

The calculator supports three primary mathematical families of percentage problems. Each has a different denominator and should not be confused with the others.

1. Percentage of a value:

$$\text{Part} = \frac{p}{100} \times \text{Whole}$$

2. Percentage change (when there is a true starting value):

$$\text{Percentage Change} = \frac{\text{New} - \text{Original}}{|\text{Original}|} \times 100$$

3. Percentage difference (when both values have equal status):

$$\text{Percentage Difference} = \frac{|A - B|}{(A + B)/2} \times 100$$

Worked examples and interpretation

Common mistakes in percentage calculations

Related concepts

Percentage points

The arithmetic difference between two percentages.

Relative change

A change measured relative to a starting baseline.

Ratio

A comparison of one quantity to another using division.

Frequently Asked Questions

What is a percentage?+

A percentage is a fraction or ratio expressed per hundred. 25% means 25 out of 100, or 0.25 in decimal form.

How do I calculate 15% of a number?+

Convert 15% to 0.15 and multiply by the base value. For example, 15% of 80 is 0.15 × 80 = 12.

What is the difference between percentage change and percentage difference?+

Percentage change uses an original starting value as the baseline. Percentage difference compares two peer values using their average as the baseline.

How do I convert a decimal to a percentage?+

Multiply the decimal by 100 and add the percent sign. For example, 0.375 becomes 37.5%.

How do I convert a percentage to a decimal?+

Divide the percentage by 100. For example, 8% becomes 0.08.

Why is a 50% decrease followed by a 50% increase not equal to zero change?+

Because the second change is applied to the reduced base. If 100 falls to 50, then a 50% increase on 50 only adds 25, giving 75.

What are percentage points?+

Percentage points describe the arithmetic difference between two percentages. Moving from 12% to 18% is a rise of 6 percentage points, not necessarily a 6% increase.

How do I calculate a discount percentage?+

Subtract sale price from original price, divide by the original price, and multiply by 100.

Can a percentage be greater than 100?+

Yes. Percentages above 100% indicate a quantity larger than the baseline, such as a 150% increase or 125% concentration relative to a reference value.

When should I use the absolute value in percentage change?+

When you want the magnitude of change without regard to direction, or when following the standard absolute-baseline convention for certain applied comparisons.

Percentage Calculator

Inputs

Results

Bookmark this Percentage Calculator

Percentage formulas

How the calculation works

Example percentage calculation

Learn more about this calculation

Percentage Change Guide: Increase, Decrease, Difference

Ratio and Proportion Guide: Simplify, Solve, Split Totals

Bayes' Theorem Calculator

Fibonacci & Golden Ratio Calculator

Percentage Calculator

Inputs

Results

Bookmark this Percentage Calculator

Key output metrics

Proportion Analysis

Scale Comparison

How to understand and use this calculator

Percentages as scaled fractions of 100

Core percentage formulas

Worked examples and interpretation

Common mistakes in percentage calculations

Related concepts

Frequently Asked Questions

Percentage formulas

How the calculation works

Example percentage calculation

Learn more about this calculation

Percentage Change Guide: Increase, Decrease, Difference

Ratio and Proportion Guide: Simplify, Solve, Split Totals

Bayes' Theorem Calculator

Fibonacci & Golden Ratio Calculator

Key output metrics

Proportion Analysis

Scale Comparison

How to understand and use this calculator

Percentages as scaled fractions of 100

Core percentage formulas

Worked examples and interpretation

Common mistakes in percentage calculations

Related concepts

Frequently Asked Questions