Percentage Tool
Explore eight percentage calculations including amounts, proportions, percentage changes, increases, decreases, reverse percentages, percentage differences, compound growth and percentage-point changes. Review calculated values, formula explanations, breakdown tables and dynamic charts, with downloadable CSV, JSON and chart images.
Find a percentage of a number.
Table of Contents
Highlights
- Eight calculation modes for common percentage problems
- Instant formula and detailed results breakdown
- Interactive proportion, comparison and compound growth charts
- Adjustable decimal places for displayed values
- Export results to CSV or JSON, and charts to PNG
How Percentage Tool Works?
A percentage describes a value relative to one hundred. The appropriate formula depends on whether you want an amount, a proportion, a comparison or repeated growth. The available calculations cover eight distinct cases.
| Calculation | Rule |
|---|---|
| Percentage of a number | Multiply the number by the percentage and divide by 100. |
| One number as a percentage of another | Divide the part by the total, then multiply by 100. |
| Percentage change | Divide new minus original by the absolute original value, then multiply by 100. |
| Increase or decrease | Multiply the starting value by one plus or minus the percentage divided by 100. |
| Reverse percentage | Divide the final value by one plus or minus the percentage divided by 100. |
| Percentage difference | Divide the absolute difference by the average of the two absolute values, then multiply by 100. |
| Compound growth or decline | Multiply the starting value by the growth factor raised to the number of periods. |
| Percentage-point change | Subtract the first percentage from the second. |
For example, 25% of 100 is:
To calculate the percentage change from 80 to 100, use:
Repeated changes compound rather than simply add. With a starting value of 1,000, a 5% rate per period and 10 periods:
Percentage points and relative changes are not interchangeable: moving from 20% to 25% is an increase of 5 percentage points but a 25% relative increase. The results include a breakdown table, with a filled percentage bar for suitable part-to-whole values, comparison bars for other calculations and a progression line for compound changes.
Practical Use Cases
Shoppers: Work out the reduction from a listed price, or reverse an advertised percentage increase or decrease to estimate the original figure.
Retailers: Apply a planned percentage increase or decrease to a starting price and inspect the adjustment amount alongside the new price.
Students: Find what percentage a score represents of the maximum possible score, or calculate a specified percentage of a number.
Business analysts: Compare current and previous metrics using percentage change, or use percentage difference when neither figure is naturally the baseline.
Marketers: Measure the percentage-point shift between two conversion rates and distinguish it from the relative percentage change.
Financial planners: Illustrate how a fixed positive or negative percentage rate affects a starting amount across a selected number of periods.
Accuracy and Limitations
Calculations use JavaScript floating-point arithmetic, so very large values and some decimal fractions can exhibit small rounding effects; the displayed decimal precision is configurable. Percentage change is undefined when the original value is zero, a part-to-whole percentage is undefined when the whole is zero, and percentage difference is undefined when both values are zero. Reverse calculations reject a zero adjustment factor. Compound calculations require a whole-number period count from 0 to 10,000 and a rate no lower than −100%; extremely large results may exceed the supported numeric range. The compound chart samples longer series rather than showing every period, and percentage fill bars only apply to values between 0% and 100%.
