Ratio Calculator

This calculator handles the common ratio tasks: reducing a ratio to its simplest form, finding a missing term, scaling a ratio to a total amount, and splitting an amount across several proportional weights. Results update as you type and keep exact decimal precision.

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Simplified ratio

2 : 3

Original ratio: 16 : 24
A ÷ B as a decimal: 0.66666667

How to use this tool

1 Choose Simplify, Missing value, Scale, or Proportional split at the top of the workspace.
2 For simplification and scaling, enter the two ratio terms. Decimals such as 1.5 and 2.25 are accepted.
3 For a missing value, enter A, B and C, then choose whether the unknown is the fourth or the third term.
4 For a proportional split, enter the total and a weight for each item, then add or remove rows as needed.

Formula and calculation logic

Simplifying a ratio

A : B = (A ÷ g) : (B ÷ g), where g is the greatest common divisor

Both terms are scaled to integers and divided by their greatest common divisor. Decimal ratios are converted exactly first, so 1.5 : 2 becomes 3 : 4.

Missing value

A : B = C : X → X = B × C ÷ A; A : B = X : D → X = A × D ÷ B

Cross-multiplication solves the proportion. The first or second term must be non-zero, and the calculator reports a clear error instead of dividing by zero.

Scaling to a total

Part A = Total × A ÷ (A + B); Part B = Total × B ÷ (A + B)

The total is distributed in proportion to the two terms. The percentages sum to 100% and show the relative weight of each part.

Proportional split

Share i = Total × weight i ÷ sum of weights

Every item receives a share proportional to its weight. The shares add up to the total, and each percentage shows the item’s fraction of the whole.

Worked example

Simplify 16 : 24

A recipe uses 16 parts of one ingredient and 24 of another.

Greatest common divisor of 16 and 24 is 8
16 ÷ 8 = 2 and 24 ÷ 8 = 3
Simplified ratio: 2 : 3

The ratio 16 : 24 simplifies to 2 : 3, which is 0.66666667 as a decimal.

Find the missing value in 2 : 3 = 8 : X

A scale drawing uses the same ratio as a real object.

X = B × C ÷ A
X = 3 × 8 ÷ 2
X = 12

The missing term is 12, so the full proportion is 2 : 3 = 8 : 12.

Split 100 in the ratio 1 : 2 : 3

Three partners share profits in proportion to their contributions.

Sum of weights: 1 + 2 + 3 = 6
Shares: 100 × 1 ÷ 6 = 16.666667, 100 × 2 ÷ 6 = 33.333333, 100 × 3 ÷ 6 = 50
Percentages: 16.67%, 33.33%, 50%

The shares are 16.67, 33.33 and 50, and the percentages add up to 100%.

Edge cases and accuracy

Decimal ratios

Decimals are converted to a common integer scale before simplification, so 0.75 : 1.5 becomes 1 : 2 without floating-point rounding errors.

Zero and negative terms

A ratio with both terms zero has no meaning and is rejected. Negative terms are not supported in this calculator; use positive quantities.

Rounding a split

Each share is displayed with up to eight decimal places and rounded for display only. Adding the rounded shares may differ from the total by a tiny fraction.

Missing term position

The unknown can be the fourth term (A : B = C : X) or the third term (A : B = X : C). The formula and the copied equation change accordingly.

Frequently asked questions

How do I simplify a ratio? +

Divide both terms by their greatest common divisor. The calculator converts decimals to integers first, so the result is always a whole-number ratio.

What is cross-multiplication? +

In A : B = C : X, the products A × X and B × C are equal. Solving for X gives X = B × C ÷ A. The calculator applies this directly and avoids floating-point shortcuts.

Why does the calculator reject zero? +

A ratio with both terms zero is undefined, and a missing-value calculation cannot divide by a zero term. The tool reports the problem instead of returning infinity.

How does proportional splitting work? +

Each item’s share is the total multiplied by its weight and divided by the sum of all weights. Percentages are the same calculation expressed out of 100.

Can I split among more than two items? +

Yes. The proportional split mode accepts 2 to 10 items, each with its own weight. Add or remove rows without reloading the page.

Does the ratio calculator handle decimals? +

Yes. Terms such as 1.5 or 0.75 are accepted, converted to a common scale and simplified exactly. No exchange rates or unit conversions are applied.