Proportion Solver (Direct / Inverse)
WebEverything runs locally in your browser — nothing is uploaded
Type a proportion such as `2:3 = 4:x`, with `x` or `?` for the unknown, and it is solved at once, together with both ratios reduced to their simplest integers and the cross-multiplication check (`2 × 6 = 3 × 4 = 12`) so you can verify it. The key is the mode: direct proportions cross multiply (`a×d = b×c`), while inverse proportions multiply on the same side (`a×c = b×d`) — so `1:2 = 4:x` gives 8 in direct mode but 2 in inverse. Solving is done in exact fractions, so `1:3 = 1:x` gives precisely `3` rather than a floating-point approximation; a 0 in the ratio is reported as meaningless instead of producing a division-by-zero that looks like a number. One proportion per line, and a batch can be solved together. Everything runs locally in your browser.
Features
- Direct uses cross multiplication, inverse multiplies on the same side
- The unknown can sit in any of the four positions
- Solves the unknown, with a decimal approximation when it is not an integer
- Reduces both ratios to simplest integers, so equivalence is obvious
- Shows the cross-multiplication check for verification
- Exact fraction arithmetic, free of floating-point drift
- A 0 in the ratio (including a solved 0) is reported as meaningless, never a division by zero
- Accepts integers, decimals and simple fractions like `3/4`
- One proportion per line, so a batch is solved together
- A bad line only affects its own block, not the others
How to use
- Write one proportion per line, with `x` or `?` for the unknown
- Choose Direct or Inverse mode
- The solution, the simplified ratios and the check appear at once
- Use the row copy button to take a single result
FAQ
- How do I tell direct from inverse proportions?
- Look at how the two quantities move: if one grows as the other grows (same direction) it is direct; if one grows as the other shrinks (opposite directions) it is inverse. Accordingly `a:b = c:d` means `a×d = b×c` (cross multiply) when direct, and `a×c = b×d` (same-side multiply) when inverse. Picking the wrong mode changes the answer completely — `1:2 = 4:x` is 8 direct and 2 inverse.
- Does `x` have to be on the right?
- No. The unknown can be any of the four positions: `x:3 = 4:6`, `2:x = 4:6` and `2:3 = x:6` all solve. The tool applies the formula for wherever the unknown sits, so you do not have to rearrange it.
- Why is a ratio with a 0 called meaningless?
- A ratio with 0 as a term is not a ratio any more (`2:0` is meaningless). Forcing the formula would divide by zero and yield `Infinity` or `NaN` — which looks like a number but is wrong. So the tool reports it as meaningless rather than handing back a fake result.
- Can the answer be a fraction?
- Yes. `2:3 = 1:x` gives `x = 3/2`, and the tool also shows the decimal approximation `1.5`. All arithmetic is exact fractions internally, so the simplest integer ratio never drifts into `2:3.0000001`.
Related tools
Unit Converter
ConvertConvert between 26 categories of units — length, weight, temperature, energy, pressure, flow, force, density and more. All in your browser.
Fraction Calculator
ConvertSimplify fractions, find the greatest common divisor and least common multiple, convert decimals to fractions and do fraction arithmetic.
Number Base Converter
ConvertConvert numbers between binary, octal, decimal, hex, base 36 and base 64, with long IDs converted digit for digit. Runs in your browser.
URL Parser
WebParse a URL into scheme, host, port, path, query parameters and fragment, with each parameter shown raw and decoded. Runs entirely in your browser.
User-Agent Parser
WebParse a user agent into browser, version, OS, device type and engine, and see which rules matched. Pattern matching only. Runs entirely in your browser.
HTTP Status Codes
WebLook up an HTTP status code for its meaning, 1xx–5xx class, typical uses and common traps. Runs entirely in your browser.