Ratio & Proportion Calculator
Solve a proportion for its missing value, or scale a whole list of quantities — like a recipe — from one known change.
Worked examples
Enlarging a photo print without warping it
A print shop wants to blow a 3 in by 4 in proof up to fit a 12-inch-tall frame while keeping the exact same width-to-height ratio.
- Original ratio
- 3 in : 4 in
- New height
- 12 in
New width ≈ 9 in keeps the same proportions
Stretching a pancake batter recipe for extra eggs
A base recipe calls for 2 cups flour, 3 eggs, and 250 g sugar — the cook wants to use up 5 eggs from an open carton instead of buying more.
- Flour
- 2 cups
- Eggs (base)
- 3
- Sugar
- 250 g
5 eggs → scale ×1.67 → 3.33 cups flour, 416.7 g sugar
How the math works
A proportion a/b = c/d states that two ratios describe the same relationship at different scales. Cross-multiplying clears both denominators at once — multiply each side by the product of the two denominators and the fractions cancel out, leaving a·d = b·c. Whichever of the four values is missing, the other three plug straight into a rearranged version of that same equation. Scaling a whole list works the same way at once: take the one item where you know both the original quantity and its new target value, divide new by original to get a single scale factor, then multiply every other item's original quantity by that same factor to rescale the entire list consistently.
scaled = original × (new ÷ original of the reference item)
Frequently asked questions
What's the difference between a ratio and a proportion?
A ratio is a single comparison between two quantities, like 3 cups of flour to 4 cups of water (written 3:4 or 3/4). A proportion is a statement that two ratios are equal, like 3/4 = 9/12 — it's the equation you solve when you know one full ratio and only part of a second one. This page's "Proportion" mode solves that equation for the missing piece; "Scale a list" applies the same idea across every item in a whole list at once.
Why do I need to leave exactly one box blank in Proportion mode?
With four values in a/b = c/d, three of them fully pin down the fourth through cross-multiplication (a·d = b·c) — there's nothing left to solve if all four are filled in, and not enough information if two or more are missing. Leaving exactly one blank tells the calculator which value you want it to compute; fill in a different box and it re-solves for whichever one is empty at that moment.
Can Scale mode be used for anything besides recipes?
Yes — the math is just "multiply every quantity by the same factor," which applies anywhere you're resizing a list proportionally: scaling a drawing or floor plan, adjusting a paint or cleaning-solution mix by batch size, resizing a print run's material list, or converting a small-batch shop formula to a larger production run. Recipes are just the easiest everyday example.
What if my scale factor comes out as a repeating decimal, like 1.6666...?
The calculator keeps the full decimal internally and only rounds for display, using whatever precision you pick in the Precision control (2 decimal places by default, up to 5, or Full for the unrounded value). A factor like 5/3 displays as 1.67 at 2 decimals but is never actually truncated to that rounded value mid-calculation, so every row's scaled quantity stays accurate.
Can the two sides of a proportion use different units, like inches on one side and centimeters on the other?
No — a/b = c/d only works correctly when a and b share the same unit as each other, and c and d share the same unit as each other (the two sides don't need to match one another, since it's a pure ratio). Mixing units within one side, like typing 3 in for a but 4 cm for b, will produce a number but not the ratio you actually meant. Convert to matching units first if your source values aren't already consistent.
Why did changing one item's new value update every other row in Scale mode?
Every row shares one scale factor — that's the whole point of scaling a list together instead of adjusting items one at a time. Typing a new value into any row derives the factor from that row (new value ÷ original quantity) and immediately reapplies it to every other row's original quantity. If you want to override just one item without disturbing the others, edit its original quantity instead — that only changes that row's own scaled output, not the shared factor.