Math calculator

Free ratio calculator

Simplify and scale ratios — enter a ratio to see it in lowest terms, as a fraction, and scaled to any target value, updated live, as you type.

InputsLive
A
B
Result
Simplified ratio
2:3
4:6 simplifies to 2:3
Simplified A:B2:3
Decimal (a÷b)0.666667
Percentage66.6667%
Original A:B4:6

Ratio simplified by GCF. Decimal = a / b.

Results are estimates. Consult a professional.

How it's calculated

How the ratio calculator works

A ratio compares two or more quantities of the same kind. Writing a:b (read 'a to b') means for every a units of the first quantity there are b units of the second. Ratios can be scaled up or down by multiplying or dividing both parts by the same non-zero number.

Ratio: a : b = a/b
Equivalent ratio: a : b = (a×k) : (b×k) for any k ≠ 0
Proportion: a : b = c : d → ad = bc (cross-multiplication)
Weisstein, E. W. Ratio. MathWorld.
Example

Worked example: scaling a recipe ratio 3:2

Example: flour-to-sugar ratio 3:2 scaled from 5 cups to 10 cups

A recipe uses a flour-to-sugar ratio of 3:2, giving 3 cups flour and 2 cups sugar for 5 total cups. To double the recipe to 10 cups, multiply both parts of the ratio by 2.

Original: 3 : 2 (total parts = 5)
Scale factor: 10 ÷ 5 = 2
Scaled: (3×2) : (2×2) = 6 : 4
Flour = 6 cups, Sugar = 4 cups
6 : 4
Double the batch uses 6 cups of flour and 4 cups of sugar, keeping the same 3:2 ratio.
Quick reference

Common ratios in everyday use

Ratios appear constantly in cooking, mixing, and everyday measurement. The table below shows familiar examples along with their decimal equivalents.

ContextRatioDecimal equivalent
Baking (flour:water)2 : 12.0
Concrete mix (cement:sand:gravel)1 : 2 : 3
Paint tint (base:tint)4 : 14.0
Bleach solution (water:bleach)9 : 19.0
Map scale (1 cm = 50 km)1 : 5,000,000
Screen aspect ratio (widescreen)16 : 91.78

Source: common industry standards and everyday conventions.

Practical tips

Tips for working with ratios

Keep these habits in mind to avoid the most common ratio mistakes.

  • Simplify first — always reduce a ratio to its lowest terms by dividing both sides by their GCD (e.g. 8:6 → 4:3) before scaling.
  • Keep units consistent — both quantities must be in the same unit before forming a ratio; convert cm to cm or kg to kg.
  • Use cross-multiplication for proportions — if a:b = c:d, then ad = bc; solve for the unknown by isolating it on one side.
  • Find the unit ratio — divide both sides so one side equals 1 (e.g. 3:2 → 1.5:1) for easy mental scaling.
  • Watch the order — ratio order matters; flour:sugar 3:2 is different from sugar:flour 2:3.
Accuracy & limits

Accuracy and limitations

Ratio calculations are exact when inputs are integers or simple fractions. Decimal inputs may introduce floating-point rounding at the 15th significant digit. Ratios describe relative quantities only — they do not convey the actual size of either quantity without additional information. For three-way or multi-part ratios (a:b:c), the total-parts approach still applies but requires care when converting to individual fractions of a whole.

Glossary

Key terms

A comparison of two quantities written as a:b or a/b, showing how many times one value contains the other.
A statement that two ratios are equal: a:b = c:d.
A ratio obtained by multiplying or dividing both terms by the same non-zero number.
The largest integer that divides both terms of a ratio, used to simplify it to lowest terms.
The rule that if a/b = c/d then ad = bc, used to solve for an unknown in a proportion.
A ratio expressed with one term equal to 1 (e.g. 1:2.5), useful for direct comparison.
About

About this calculator

Part of our math calculators suite — explore all calculators.

Questions

Frequently asked questions about the free ratio calculator

A ratio calculator is a free online tool that helps you simplify any ratio to lowest integer terms, with decimal and percentage equivalents. A ratio compares two quantities. Simplifying it means dividing both numerator and denominator by their greatest common factor (GCF) — the same operation as reducing a fraction to lowest terms. It runs entirely in your browser with instant results and no sign-up.
Numerically, yes. A:B as a fraction is A/B. The semantic difference is contextual: ratios usually compare two quantities of the same type (mix 2:1 sand:water), while fractions usually represent a part of a whole (1/2 of a pie). The math is identical.
Yes. The calculator scales decimal inputs up to integers (1.5:3 becomes 15:30) before finding the GCF. The final simplified ratio is always in integer terms.
'4 to 3' or 'four to three'. The colon ':' is read as 'to'. In contexts like map scales (1:25000), it's the same: 'one to twenty-five thousand'.

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