Percentage Calculator

Solve the three core percentage problems (percent of a number, percent increase or decrease, and percent difference) with the formula shown for each result.

Last updated:

Was this calculator helpful?

★ ★ ★ ★ ★
5.0/5 (1 votes)
Embed this calculator

Calculation Examples

Calculation Case Result
What is 15% of 200? 200 × 0.15 = 30
50 is what percent of 250? (50 ÷ 250) × 100 = 20%
Percent increase from 80 to 100 (100 − 80) ÷ 80 × 100 = 25%
Percent difference between 90 and 110 |110 − 90| ÷ ((90 + 110) ÷ 2) × 100 = 20 ÷ 100 × 100 = 20%
Mihail Doncenco
Mihail Doncenco Site Creator & Calculator Expert

Founder and developer of CalcMate. Builds and maintains every calculator on this site, focusing on formula accuracy and clear, practical results.

How to Use the Percentage Calculator

Select your problem type and enter the values. All percentage problems rest on one ratio: \[ \text{Percentage} = \left( \dfrac{\text{Part}}{\text{Whole}} \right) \times 100 \] The calculator rearranges it for whichever quantity is unknown (the part, the whole or the percentage) and shows the formula it used next to the result. Percentage difference formula: absolute difference between V1 and V2 divided by the average of V1 and V2, multiplied by 100

The Three Core Types of Percentage Problems

Most everyday percentage questions fall into three types:

1. Percent of a Number: finding a share of a value. Formula: \(\text{Part} = \text{Whole} \times \dfrac{\%}{100}\). Example: 15% of 200 is \(200 \times 0.15 = 30\). Use it for sales tax, tips, discounts and commissions.

2. Percent Change (Increase or Decrease): the relative change from an original to a new value. Formula: \(\%\text{ Change} = \dfrac{V_{new} - V_{old}}{V_{old}} \times 100\). A positive result is an increase, a negative one a decrease. The original value is always the denominator. Example: a price rising from $80 to $100 is \(\dfrac{100 - 80}{80} \times 100 = 25\%\) up. Percent change is undefined when \(V_{old} = 0\), and it is not symmetric: a 20% rise followed by a 20% fall leaves you at 96% of the start (\(1.2 \times 0.8 = 0.96\)).

3. Percent Difference: a comparison of two values when neither is the "original". Formula: \(\dfrac{|V_2 - V_1|}{\frac{V_1 + V_2}{2}} \times 100\). The denominator is the average of the two values, so swapping them gives the same result. It suits two measurements of equal standing, such as readings from two instruments. Some fields define percent difference differently, for example by dividing by the larger value, so check which definition you need.

Percent of a number formula: Part = Whole × Percentage / 100

Useful Tips 💡

  • For percent change, always divide by the original (starting) value, not by the new value and not by the average. Using the wrong base is the most common error.
  • Percent change and percent difference answer different questions. Use percent change when one value is clearly the starting point. Use percent difference to compare two peer measurements with no before and after.
  • To convert a percentage to a decimal, move the decimal point two places left: 15% becomes 0.15, and 4.5% becomes 0.045.

📋Steps to Calculate

  1. Select the calculation type: Percent of a Number, Percent Change or Percent Difference.

  2. Enter the values for your problem type.

  3. Click "Calculate" to see the result and the formula applied.

Mistakes to Avoid ⚠️

  1. Mixing up percent change and percent difference. Sales growing from 800 to 1,000 is a 25% change (base 800), while the percent difference between 800 and 1,000 is 22.2% (base 900).
  2. Dividing by the new value in a percent change. For 80 to 100 the correct base is 80, giving 20 ÷ 80 × 100 = 25%. Using 100 gives 20%.
  3. Using a percentage as a whole number. 15% of 200 is 0.15 × 200 = 30, not 15 × 200. The calculator accepts both formats to avoid this.
  4. Treating percentage points and percent change as the same thing. Rates rising from 3% to 5% are up 2 percentage points but up 66.7% in percent change.

Practical Applications📊

  1. Work out discounts and sales tax. A $120 item with 20% off and 8% sales tax costs 120 × 0.80 × 1.08 = $103.68. Percentages multiply, they do not add: treating it as -20% + 8% = -12% gives $105.60, which is $1.92 too high.

  2. Check a raise against inflation. A move from $65,000 to $68,000 is a 4.6% raise. With 4% inflation, your real gain is about 0.6 percentage points.

  3. Compare two independent measurements. Use percent difference, not percent change, when neither value is the "true" one, for example two instruments measuring the same quantity.

  4. Work backward from a discounted price. If an item costs $96 after 20% off, the original was 96 ÷ 0.80 = $120.

Questions and Answers

How do I calculate percent increase or decrease?

Subtract the original value from the new one, divide by the original value and multiply by 100: \(\%\text{ Change} = \dfrac{V_{new} - V_{old}}{V_{old}} \times 100\). A positive result is an increase, a negative one a decrease. A price rising from $100 to $120 gives \(\dfrac{120 - 100}{100} \times 100 = 20\%\), and falling from $100 to $80 gives \(\dfrac{80 - 100}{100} \times 100 = -20\%\). Dividing by the new value instead of the original gives a wrong result. The formula is undefined if the original is 0.

How do I calculate the percent of a number?

Multiply the number by the percentage divided by 100: \(\text{Result} = Y \times \dfrac{X}{100}\) for X% of Y. For 20% of 50: \(50 \times 0.20 = 10\). The same step gives sales tax (price × tax rate), discounts (price × discount rate) and commissions (revenue × commission rate).

What formulas does the percentage calculator use?

The calculator uses three formulas. Percent of a number: \(\text{Part} = \text{Whole} \times \dfrac{\%}{100}\), rearranged to find the whole or the percentage when the other two are known. Percent change: \(\dfrac{V_{new} - V_{old}}{V_{old}} \times 100\), with the original value as the denominator. Percent difference: \(\dfrac{|V_2 - V_1|}{\frac{V_1 + V_2}{2}} \times 100\), with the average of the two values as the denominator.

What is a percentage and how is it defined mathematically?

A percentage is a ratio expressed as a fraction of 100, and it has no unit. The word comes from the Latin "per centum", meaning per hundred. Formally \(\% = \dfrac{\text{Part}}{\text{Whole}} \times 100\), so 25% equals 25/100 = 0.25. Percentages put ratios of different sizes on one scale: a 25% increase on $100 and a 25% increase on $1,000,000 are the same relative change, although the amounts differ by a factor of 10,000.

What is a percentage calculator and what problem types does it solve?

A percentage calculator solves problems in which one of three quantities is unknown: the part, the whole or the percentage. The base formula \(\text{Part} = \text{Whole} \times \dfrac{\%}{100}\) can be rearranged to find the whole from the part and the percentage, or the percentage from the part and the whole. Two specialized formulas cover percent change (original and new value) and percent difference (two values compared with their average).

What is percentage difference and when is it used?

Percentage difference is the size of the gap between two values relative to their mean. It ignores direction (it uses the absolute value) and does not treat either value as the original: \(\dfrac{|V_2 - V_1|}{\frac{V_1 + V_2}{2}} \times 100\). Scientists and engineers use it to compare two independent measurements of the same quantity, such as two lab instruments or two test methods. It is symmetric: swapping \(V_1\) and \(V_2\) gives the same result. Other fields use other definitions, for example dividing by the larger value.

What is the difference between percent change and percent difference?

Percent change divides by a specific starting value, and percent difference divides by the average of two values. Percent change: \(\dfrac{V_{new} - V_{old}}{V_{old}} \times 100\). Percent difference: \(\dfrac{|V_2 - V_1|}{(V_1 + V_2)/2} \times 100\). For 90 and 110, percent change (with 90 as the original) is 22.2%, while percent difference is \(\dfrac{20}{100} \times 100 = 20\%\). Use percent change for before and after comparisons and percent difference for two independent measurements.
Disclaimer: This calculator is designed to provide helpful estimates for informational purposes. While we strive for accuracy, financial (or medical) results can vary based on local laws and individual circumstances. We recommend consulting with a professional advisor for critical decisions.