Ratio and Proportion Calculator: Scales, Splits and Concrete Mixes

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How to use this tool

Choose the task, fill in the boxes, and the labels adjust to match. Simplify reduces a ratio to lowest whole number terms, proportion solves a colon b equals c colon x, divide splits a quantity in a given ratio, and scale converts between drawn and real lengths at a 1 to N scale.

Decimals are fine in the simplify mode. The tool scales them to whole numbers first, so 2.5 to 5 correctly reduces to 1 to 2 rather than producing a decimal ratio.

What a ratio actually is

A ratio is a comparison stripped of units, which is exactly why it survives unit changes. A concrete mix of 1 to 2 to 4 works in shovels, buckets or wheelbarrows, because only the proportions are specified. The moment you fix the total, the ratio turns into real quantities: 700 kg of mix at 1 to 2 to 4 is 100 of cement, 200 of sand and 400 of aggregate, each part being the total times its share over the sum of parts, which is 7.

A proportion is a statement that two ratios are equal, and solving one is a single cross multiplication. If 3 tonnes needs 4 loads, then 9 tonnes needs x where 3 to 4 equals 9 to x, and x is 9 times 4 over 3, which is 12.

Drawing and map scales are ratios doing real work

A 1 to 50 drawing means one unit on paper is fifty of the same unit in reality, so 35 mm scaled off the sheet is 1750 mm built. Going the other way, divide. A 2.4 m wall on a 1 to 1250 map occupies 1.92 mm, which is also a useful reminder of how little detail survives at map scales.

The standard construction set runs 1 to 5, 10, 20, 50, 100 and 200, and the common UK map scales are 1 to 1250, 2500 and 10000. The number to hold onto is that the denominator is a pure multiplier, nothing more.

A worked check you can repeat on paper

Split a 1000 dollar cost in the ratio 2 to 3. The parts sum to 5, so the shares are 1000 times 2 over 5 and 1000 times 3 over 5, which is 400 and 600. They add back to the total, which is the check worth doing every time.

For the scale mode, measure 35 mm on a 1 to 50 drawing. Real length is 35 times 50, which is 1750 mm or 1.75 m. If your answer ever looks absurd, the commonest cause is scaling a photocopied drawing that was not printed at true size.

Mistakes that catch people out

Scaling from a print that is not at true scale. Photocopiers and fit to page printing quietly resize drawings. Fix: check the printed scale bar against a ruler before measuring anything.

Splitting by the parts instead of the sum. Dividing 700 in 1 to 2 to 4 means dividing by 7, not by 3 parts or by 4. Fix: sum the parts first, every time.

Simplifying across different units. A ratio of 500 g to 2 kg is 1 to 4, not 500 to 2. Fix: convert to the same unit before comparing.

Inverting the scale direction. Multiplying when you should divide turns a 1.75 m wall into a 4.4 km one, which at least is obvious. The dangerous version is on scales near 1. Fix: drawn times N gives real, always.

How this was checked

The simplifier was verified on whole numbers, decimals and three part ratios: 12 to 18 reducing to 2 to 3, 2.5 to 5 reducing to 1 to 2, and 6 to 9 to 15 reducing to 2 to 3 to 5. The proportion solver was checked against 3 to 4 equals 9 to 12. The divider was checked with the concrete example, 700 in 1 to 2 to 4 returning exactly 100, 200 and 400, and the scale converter against 35 mm at 1 to 50 returning exactly 1750.

Related Calculators and Reference

Slope ratios like 1 in 40 are handled by the Grade to Degrees Converter. For real mix design beyond simple volume ratios, the Concrete Mix Calculator works in volumes, bags and cost. Percentages, which are ratios to 100, live in the Percentage Calculator, and map measurement connects to the Length and Distance Converter when old plans bring chains and links into it.