mathematics calculator

Ratio Calculator

Simplify ratios, solve proportions, compare equivalent ratios, split totals, and calculate unit rates with exact decimal parsing.

Result

Enter a ratio and choose Calculate.

Formula version 1.0.0 · Decimal inputs are converted to exact integer ratios.

Exact proportions

Ratio formulas and worked examples

A ratio compares quantities. Equivalent ratios multiply or divide every term by the same nonzero factor.

Simplify

Divide both terms by their greatest common divisor.

Example: 18:24 = 3:4.

Solve a proportion

a/b = c/d exactly when ad = bc.

Example: x/8 = 15/12 gives x = 10.

Split a total

For a:b and total T, shares are Ta/(a+b) and Tb/(a+b).

Example: split 70 in 2:5 to get 20 and 50.

Percent and unit rate

For 2:3, the shares are 40% and 60%. The unit rate of a:b is a/b per one unit.

How to use this calculator

Choose a task in Calculation type, such as Simplify a ratio, Solve a proportion, or Split a total by ratio.
Enter the requested First term (a), Second term (b), and any additional labeled values.
For Solve a proportion, leave exactly one of First term (a), Second term (b), Third term (c), or Fourth term (d) blank.
Select Calculate and read the Result plus the normalized Simplified ratio.
Open Show calculation steps to inspect exact scaling or cross-multiplication; select Reset before a new task.

Symbols and units

Symbol	Meaning	Unit or domain
`a:b`	A ratio comparing first term a with second term b	Finite base-10 integers or decimals; invalid zero combinations are rejected
`c:d`	A second ratio used in a proportion	Finite base-10 integers or decimals
`k`	Scale factor applied to both terms of an equivalent ratio	Finite nonzero decimal accepted by the selected mode
`T`	Total divided into shares according to a:b	Finite decimal; interpretation depends on the user's unit
`ad = bc`	Cross-product condition for equivalent ratios	Both divisor positions must form a determinate proportion
`a/b`	Unit rate: amount of a per one unit of b	b must not be zero

Checked examples

Solve a missing proportion term

Inputs: Calculation type: Solve a proportion; First term (a): blank; Second term (b): 8; Third term (c): 15; Fourth term (d): 12.

Calculation: Set x/8 = 15/12. Cross-multiply: 12x = 8 × 15 = 120. Divide by 12: x = 10.

Result: 10; simplified ratio 5:4.

The missing first term is 10 because 10:8 and 15:12 are equivalent.

Check: tests/ratio-general.test.ts — solves every missing proportion position

Split a total in a two-to-five ratio

Inputs: Calculation type: Split a total by ratio; First term (a): 2; Second term (b): 5; Total: 70.

Calculation: Add ratio parts: 2 + 5 = 7. First share: 70 × 2/7 = 20. Second share: 70 × 5/7 = 50.

Result: 20 and 50; simplified ratio 2:5.

The two shares add back to 70 and preserve the requested 2:5 relationship.

Check: tests/ratio-general.test.ts — splits a total and converts shares to percentages

Assumptions, rounding, and limits

Inputs are finite base-10 integers or decimals; decimal places are scaled to integers so simplification is exact.
Equivalent ratios divide all integer terms by their greatest common divisor and use a normalized sign.
Solve a proportion requires exactly one blank. Indeterminate or zero-divisor combinations return an error instead of a partial answer.
A split total preserves the entered total apart from unavoidable displayed decimal formatting; the unit or currency is supplied by the user.
Percentage shares are computed from a/(a+b) and b/(a+b); a+b must not be zero.
Displayed decimals do not create additional real-world precision and should be interpreted in the context of the entered quantities.

Frequently asked questions

Are 1.5:2.5 and 3:5 the same ratio?

Yes. The calculator scales the decimals to exact integers and reduces 15:25 by their greatest common divisor to 3:5.

Why must exactly one proportion field be blank?

One unknown can be solved from the other three terms. Two or more unknowns do not provide enough information for a unique result.

What does a unit rate mean?

It expresses the first quantity per one unit of the second quantity, using a/b. The two quantities may have different units, such as distance per hour.

Sources and review

OpenStax: Ratios and Proportions — Accessed 2026-10-25

Formula version: ratio.general@1.0.0
Formula review: Formula review: Equatara formula review
Editorial review: Editorial review: Equatara editorial review
Last verified: 2026-10-25
Applicability: Global, locale-independent ratio and proportion arithmetic. Decimal inputs are converted to exact integer ratios before calculation.
Next review: On material formula/source change, or by 2028-10-25.

Found a problem?

Report a formula, result, example, source, or accessibility issue through the calculator correction process. Do not include sensitive input values.

Calculate ratios and proportions