Choose the mode that matches the wording of the question, try a quick example, and then read the substituted formula under the result. Percentage change needs an original baseline, while percentage difference treats both values symmetrically.
How to use the Percentage Calculator
Choose the calculation mode that matches the wording of your question, then enter no more than two values plus a direction where needed. Results update immediately, and each mode shows the substituted formula so you can check which value became the denominator.
Use a quick example to load a complete scenario, then replace those values with your own.
- Use Percent of for tips, taxes, allocations, and portions.
- Use What percent for part-to-whole ratios.
- Use Percentage change for an old-to-new comparison.
- Use Percentage difference when neither value is the baseline.
- Use Reverse percentage to recover a value before a discount or markup.
Percentage formulas for all six modes
Every mode uses a per-hundred relationship, but the baseline changes. In the formulas below, P is the percentage, Y is a value, and A and B are the two compared values.
- P% of Y: Y × (P ÷ 100)
- A is what percent of B: (A ÷ B) × 100
- Percentage change: (New − Original) ÷ |Original| × 100
- Increase or decrease: Starting value × (1 ± P ÷ 100)
- Percentage difference: |A − B| ÷ [(|A| + |B|) ÷ 2] × 100
- Reverse percentage: Final value ÷ (1 ± P ÷ 100)
Percentage change is not percentage difference
Percentage change divides the change by the original value, so reversing old and new can produce a different answer. The direction also matters: growth is positive and decline is negative.
Percentage difference uses the average magnitude of both values as the comparison base. It is symmetric, so switching the two entered values does not change the result.
Reverse a discount or markup correctly
A final price after a 20% discount equals 80% of the original price. Recover the original by dividing by 0.80, not by adding 20% to the discounted amount.
A 100% decrease leaves a final value of zero for every possible starting value, so the original cannot be recovered from the final value alone.
Common percentage examples
Percentages appear in shopping, taxes, tips, budgeting, salary changes, and investment comparisons. Match the calculation to the question before interpreting the result.
- Shopping: calculate the discount amount, then compare final unit prices.
- Tax and tips: calculate a percentage of the chosen subtotal.
- Salary: use percentage change only when an original salary is known.
- Investing: distinguish a return from the percentage difference between two unrelated values.
How this estimate is calculated
Percent of = Y × P/100 · What percent = Part/Whole × 100 · Change = (New − Original)/|Original| × 100 · Difference = |A − B|/[(|A| + |B|)/2] × 100Increase or decrease multiplies the starting value by 1 ± P/100. Reverse percentage divides the final value by 1 ± P/100. A zero denominator is undefined rather than silently converted to 0%.
Example: reverse a 20% discount
$80 after a 20% discount represents 80% of the original price. Divide 80 by 0.80 to recover the $100 original price. Adding 20% directly to $80 would produce $96 and would not reverse the discount.
Sources behind this calculation
These primary sources support the formula and help you verify rules or terms that may change.
NIST — The percent symbol represents one part in one hundred↗NIST Dataplot — Percent difference↗