Solve the missing value in A:B = C:D, or enlarge and shrink both parts of a
ratio by the same factor. Use the missing-value mode for a proportion, or
the scaling mode when you already know both parts of a ratio.
How to use this calculator
In Solve ratio, enter exactly three values in A:B = C:D and clear the
unknown field. The example starts with A = 3, B = 4, C = 600, and D blank;
if you want to solve another field, clear it and fill D instead. Leaving all
four fields filled produces an error rather than a consistency check.
In Scale ratio, enter both parts, choose Enlarge or Shrink, and use a positive scale factor. Scaling does not automatically reduce a ratio to its lowest whole-number terms. Dividing 250:280 by 2.5 gives 100:112, even though that ratio can also be simplified to 25:28.
Keep corresponding quantities in compatible units and preserve their order. For a recipe ratio of flour to water, put flour first in both ratios.
Examples
Solve 3:4 = 600:D
D = 4 × 600 / 3 = 800, so the completed ratio is 3:4 = 600:800.
Shrink 250:280 by 2.5
Dividing both terms by 2.5 produces 100:112.
Scale a flour-to-water recipe
A recipe uses 300 g flour and 200 g water. To use 450 g flour, enter
300:200 = 450:D; D = 200 × 450 / 300 = 300. Use 300 g water to
preserve the original proportion.
Formula
Equivalent ratios satisfy A / B = C / D, so cross multiplication gives
A × D = B × C. Scaling uses (A × k):(B × k) when enlarging and
(A / k):(B / k) when shrinking.
Ratio limits
Ratios compare quantities only after their units are made compatible. Simplifying preserves proportion but can hide the original sample size, and rounding a scaled result can prevent the displayed parts from adding exactly to a requested total. A ratio with a zero second term cannot be treated as an ordinary finite division.