# Percentage & Ratio Calculator

> X% of Y, % change, reverse %, percentage points, ratios and aspect ratios, with formulas. Answers every everyday percentage question (X% of Y, X is what percent of Y, percentage change, increase or decrease by a percentage, reverse percentage, percentage points versus percent) and every ratio task (simplify, scale, split an amount, aspect ratios). Each answer shows the formula and the steps.

Part of usefulweb.site (https://usefulweb.site/). Results are deterministic calculations from the inputs and the listed assumptions; the API returns exactly what the web page shows.

## Use it
- Human interface: https://percentageratiocalculator.usefulweb.site/ (interactive tool at https://percentageratiocalculator.usefulweb.site/tool)
- JSON API: POST https://percentageratiocalculator.usefulweb.site/api/v1/calculate with a JSON object of inputs (schema: https://percentageratiocalculator.usefulweb.site/api/v1/tool)
- OpenAPI: https://percentageratiocalculator.usefulweb.site/openapi.json
- MCP (Streamable HTTP): https://percentageratiocalculator.usefulweb.site/mcp - tool `percentage_ratio_calculator`

## Inputs
- mode (select): Question
- x (number): Value X - Percentage modes: the percentage or the start value (see the question). Aspect ratio: width.
- y (number): Value Y - Percentage modes: the base, end or final value. Aspect ratio: height.
- ratio (text): Ratio - For the ratio modes: 2 to 10 positive terms separated by ":" (e.g. 16:9, 2:3:5, 1.5:2).
- amount (number): Amount - Split: the total to share out. Scale: the value the chosen term should become.
- scaleTerm (integer): Term to scale - Scale mode: which ratio term (1 = first) should equal the amount.
- newWidth (number): New width - Aspect ratio: optional; the matching height is calculated.
- newHeight (number): New height - Aspect ratio: optional; the matching width is calculated.
- decimals (integer): Decimal places - Rounding of the displayed answer and of split amounts (2 = cents).

## Method
- X% of Y = X ÷ 100 × Y. X as a percent of Y = X ÷ Y × 100.
- Percentage change from X to Y = (Y − X) ÷ |X| × 100; positive is an increase.
- Increase Y by X% = Y × (1 + X/100); decrease Y by X% = Y × (1 − X/100).
- Reverse percentage: if Y is the value after a change of X%, the original is Y ÷ (1 + X/100) (use a negative X for a decrease, e.g. −20 for 20% off).
- Percentage points measure the plain difference between two percentages (3% − 2% = 1 percentage point); percent measures the relative change ((3 − 2) ÷ 2 = 50%).
- Ratios are simplified exactly: decimal terms are first multiplied by a power of 10 to make whole numbers, then divided by their greatest common divisor.
- Splitting an amount by a ratio uses the largest-remainder method at the chosen decimal places, so the parts always add up to exactly the amount.
- Aspect ratios: width:height simplified by the GCD, the decimal width ÷ height, and the nearest well-known ratio within 1%. Resizing keeps the ratio: new height = new width × height ÷ width.