Percentage Calculator
This professional percentage calculator handles the four core tasks: compute X% of Y, find what percent one number is of another, increase or decrease a value by a percentage, and calculate percentage change. Built for students, analysts, and professionals who need fast, accurate, and accessible results.
Interactive percentage calculator
Results
Data Source and Methodology
Authoritative reference: Wolfram MathWorld — Percentage. MathWorld—A Wolfram Web Resource. Last updated 2018. Direct link: https://mathworld.wolfram.com/Percentage.html.
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
Calculations implement the standard definitions of percentage, percentage points, multiplicative change, and relative change using IEEE 754 double precision. Rounding for presentation is configurable and defaults to up to 6 decimal places as needed.
The Formulas Explained
1) Percentage of a number: \( \text{Result} = \frac{p}{100}\times Y \)
2) What percent is X of Y: \( \text{Percent} = \frac{X}{Y}\times 100\% \), with \( Y \neq 0 \)
3) Increase/Decrease by rate r%: \( \text{New} = \text{Original}\times\left(1 \pm \frac{r}{100}\right) \)
4) Percentage change from A to B: \( \%\Delta = \frac{B - A}{\lvert A \rvert}\times 100\% \), defined for \( A \neq 0 \)
Glossary of Variables
| Symbol / Field | Meaning |
|---|---|
| p (Percentage %) | Rate expressed in percent (e.g., 15 means 15%) |
| X (Part) | Observed value compared to a whole |
| Y (Base / Whole) | Reference value; must not be zero when in denominator |
| Original | Starting amount before applying a percentage change |
| r (Rate %) | Percentage rate applied as an increase or decrease |
| A (Old), B (New) | Values used to compute percentage change from A to B |
| Result / New / Change | Computed outputs: main value, new value after change, and the difference |
How It Works: A Step-by-Step Example
Scenario: Increase 250 by 12%
- Select “Increase/Decrease by %”.
- Enter Original amount A = 250 and Rate r = 12.
- Choose “Increase”.
- Apply the formula: \( \text{New} = A \times \left(1 + \frac{r}{100}\right) = 250 \times (1 + 0.12) = 250 \times 1.12 = 280 \).
The change amount is \( 280 - 250 = 30 \) and the relative change is \( \frac{30}{250}\times 100\% = 12\% \).
Additional quick checks
- \(15\%\) of \(80\): \( \frac{15}{100}\times 80 = 12 \)
- What percent is \(30\) of \(120\): \( \frac{30}{120}\times 100\% = 25\% \)
- Percentage change from \(400\) to \(350\): \( \frac{350-400}{|400|}\times 100\% = -12.5\% \)
Frequently Asked Questions (FAQ)
How do I calculate X% of Y?
Multiply Y by X/100. Example: 7.5% of 200 = 200 × 0.075 = 15.
What percent is A of B?
Divide A by B and multiply by 100. Ensure B ≠ 0. Example: 45 of 90 is 50%.
What is the difference between percentage and percentage points?
Percentage points measure absolute differences between percentages. For example, moving from 10% to 12% is a 2 percentage point increase, which is a 20% relative increase.
How is percentage change defined when the old value is zero?
If old value is 0 and new value is nonzero, relative percentage change is undefined (would require division by zero). The tool reports this and shows the absolute change instead.
Can I enter negative values?
Yes. For example, negative revenues or temperatures are supported. Interpret the results in your context.
How many decimal places are used?
The calculator computes with full precision and formats results adaptively up to 6 decimal places. Round further as required by your use case.
Is this tool accessible?
Yes. It complies with WCAG 2.1 AA: keyboard operable, focus visible, high contrast, labels and inline validation, and ARIA live updates for results.