What is the difference between a ratio and a fraction?

Both express division, but a ratio compares quantities and may be written a:b, while a fraction is commonly treated as a number a/b. The same algebra can relate them.

Do the two quantities need the same units?

For a dimensionless ratio, yes. Convert units first—for example, compare 1 metre with 50 centimetres as 100 cm:50 cm = 2:1.

Why must A, B, and C all be positive?

This implementation models ratios of positive magnitudes. Rejecting zero and negative terms keeps reduction and proportional scaling within that stated domain.

Can a ratio contain decimals?

Yes. The reducer scales decimal terms to integers when safe, then divides by their greatest common divisor.

What question does Ratio calculator answer?

Use the Ratio calculator for fast, clear results with formulas and practical examples. The implemented relationship is x₁:x₂=x₃:R ⇒ R=x₂x₃/x₁; x₁=Ratio A; x₂=Ratio B; x₃=Ratio C.

Which inputs does Ratio calculator use?

It uses the visible fields Ratio A, Ratio B, Ratio C. No hidden value is substituted for an omitted required input.

What happens when Ratio calculator receives an invalid or extreme value?

The page rejects missing, ambiguous, out-of-range, or non-finite values and refuses to display a non-finite result.

Why can Ratio calculator differ from another result?

Different unit conventions, endpoint policies, fee or rate assumptions, formula domains, and premature rounding can produce a different answer.

Can I use Ratio calculator as professional advice?

No. It answers the displayed mathematical question and cannot account for omitted real-world facts.

How can I verify the Ratio calculator result?

Recalculate the two evaluated examples without rounding intermediate values and compare the declared formula or convention with Elementary ratio and proportion.

Ratio calculator

Result12

Simplified ratio2:3

Formula

Ratio calculator evaluates the registered expression “x₁:x₂=x₃:R ⇒ R=x₂x₃/x₁; x₁=Ratio A; x₂=Ratio B; x₃=Ratio C” with the validated inputs. Full calculation precision is retained until the result is formatted for display.

x₁:x₂=x₃:R ⇒ R=x₂x₃/x₁; x₁=Ratio A; x₂=Ratio B; x₃=Ratio CElementary ratio and proportion

What this calculator answers

Use this calculator when positive quantities are compared by division and the same relationship should be scaled to a third positive quantity. The quantities must use compatible units before forming the ratio.

Input definitions

Ratio A and Ratio B: The first comparison a:b. Both A and B must be finite and strictly greater than zero.
Ratio C: The known first term c in the equivalent ratio c:x. C must also be strictly greater than zero.
Calculated X: The missing fourth term that preserves the proportion.

Formulas and variables

Solve the proportion

a/b = c/x ⇒ x = (b × c) / a

a > 0
b > 0
c > 0
a and b define the original ratio

Cross-multiplication gives ax = bc, then division by a isolates x.

Reduce a ratio

a:b = (a/g):(b/g), where g = gcd(|a|, |b|)

g = greatest common divisor after decimal inputs are converted to an integer scale

Reduction changes the scale, not the relationship between the two terms.

Assumptions and rounding

The compared quantities use the same or explicitly converted units.
A, B, and C must be finite and strictly positive; zero and negative entries are rejected.
Ratios with decimal terms are scaled to integers before greatest-common-divisor reduction, within the safe integer range.
The solved value keeps full precision and may be display-rounded to ten decimal places.

Worked examples

Scale 2:3 to start with 8

Solve 2:3 = 8:x.

Calculation

Write 2/3 = 8/x.
Cross-multiply: 2x = 3 × 8 = 24.
Divide by 2: x = 24 / 2 = 12.

Result: 2:3 = 8:12, so x = 12.

Reduce and scale 6:9

Reduce 6:9, then solve 6:9 = 10:x.

Calculation

gcd(6, 9) = 3, so 6:9 reduces to 2:3.
Use x = 9 × 10 / 6.
90 / 6 = 15; 10:15 also reduces to 2:3.

Result: The reduced ratio is 2:3 and x = 15.

Questions people ask

What is the difference between a ratio and a fraction?: Both express division, but a ratio compares quantities and may be written a:b, while a fraction is commonly treated as a number a/b. The same algebra can relate them.
Do the two quantities need the same units?: For a dimensionless ratio, yes. Convert units first—for example, compare 1 metre with 50 centimetres as 100 cm:50 cm = 2:1.
Why must A, B, and C all be positive?: This implementation models ratios of positive magnitudes. Rejecting zero and negative terms keeps reduction and proportional scaling within that stated domain.
Can a ratio contain decimals?: Yes. The reducer scales decimal terms to integers when safe, then divides by their greatest common divisor.

Boundaries and common mistakes

Do not compare values in different units without converting them first.
Keep the term order: 2:3 is not the same comparison as 3:2.
Cross-multiplication solves a proportion only when the corresponding terms are aligned correctly.

Sources and scope

OpenStax Prealgebra 2e — Solve Proportions and Their ApplicationsApplies to: Equivalent ratios, non-zero denominators, and the proportion relationships used here.

Variables, defaults, and limits

Ratio A: Ratio A is a number input. The displayed starter value is 2; it is an example, not a hidden assumption.; Default: 2; Accepted values: Minimum: 0.000000000001. Numeric entries must be finite and unambiguous.
Ratio B: Ratio B is a number input. The displayed starter value is 3; it is an example, not a hidden assumption.; Default: 3; Accepted values: Minimum: 0.000000000001. Numeric entries must be finite and unambiguous.
Ratio C: Ratio C is a number input. The displayed starter value is 8; it is an example, not a hidden assumption.; Default: 8; Accepted values: Minimum: 0.000000000001. Numeric entries must be finite and unambiguous.

Worked examples