Toolarithm

Math Calculator

Ratio Calculator

Simplify a two-part ratio, see each share of the total, and scale an equivalent ratio from a target first quantity. Use the formula section to follow the proportional math.

Live calculator

Ratio inputs

Simplified ratio

2:3

First share

40%

Second share

60%

Total parts

5

Equivalent ratio

Target first

30

Matching second

45

Scale factor

2.5

Output

Simplified Ratio

Scaling

Equivalent Quantity

Context

Shares of Total

No sign-upFormula shownPrint-friendly
What Can You Create?

Simplify and scale proportional relationships

Simplified ratio

Reduce two quantities to the smallest whole-number relationship.

Equivalent ratio

Scale the second quantity from a target first quantity while preserving the same relationship.

Share of total

See each ratio part as a percentage of the combined total.

Formula

Ratio formulas used on this page

Ratio work often starts by reducing two quantities, then scaling both parts by the same factor to keep the relationship unchanged.

Working formulas

Simplify

a:b = (a ÷ gcd(a,b)) : (b ÷ gcd(a,b))

Divide both quantities by their greatest common divisor.

Scale equivalent ratio

new second = target first x (b / a)

Use this when the first target quantity is known and the matching second quantity is needed.

Share of total

first share = a / (a + b)

Use this to connect a two-part ratio with percentage-of-total thinking.

Symbols

a - first quantity
The first part of the original ratio.
b - second quantity
The second part of the original ratio.
gcd - greatest common divisor
The largest whole number that divides both ratio quantities.
Read the Result

Interpret this calculation before using it

A ratio compares quantities in a stated order. Simplifying divides every term by a common factor without changing that comparison, while scaling multiplies every term by the same value. Ratios are not automatically fractions of a total: part-to-part and part-to-whole comparisons answer different questions even when they contain the same numbers.

Worked example

The ratio 24:36 has greatest common divisor 12, so it simplifies to 2:3. Multiplying both simplified terms by 5 gives the equivalent ratio 10:15. If 24 and 36 represent red and blue items, the part-to-whole fractions are 24/60 and 36/60, not 24/36 and 36/24.

Assumptions to keep

  • Terms are entered in the intended order and represent quantities that can be meaningfully compared.
  • Simplification uses a common factor; changing only one term creates a different ratio.
  • If units differ, convert them to a compatible basis before interpreting the ratio as dimensionless.

Limits of this result

A zero term can be displayed in some ratios but division-based forms may become undefined when the comparison denominator is zero. Negative ratios also need context because many physical part ratios are nonnegative. Preserve labels and units beside copied values so an equivalent number pair is not mistaken for the original quantities.

Useful next step: Fraction Calculator — Perform arithmetic on rational values when the task goes beyond simplifying or scaling a comparison.

Factual reference:OpenStax Prealgebra 2e
Why Users Love This Tool

Ratio results with proportional context

Clear simplification

  • The calculator reduces a two-part ratio using the greatest common divisor.
  • Equivalent ratio scaling uses the same factor for both quantities.
  • Share-of-total percentages connect ratios to percentage thinking.
  • Undefined scale cases are shown clearly when the first quantity is zero.

Practical interpretation

  • The formula section explains simplification, scale factors, and share calculations.
  • Related links connect ratios to fractions and percentages for broader number sense.
  • The tool supports recipe scaling, map examples, mixes, and classroom proportions.
  • Copy and print controls keep original quantities and equivalent results together.
Perfect For

Ratio support for proportions and scaling

Students

Practice simplifying ratios and building equivalent ratios with visible formulas.

Mixtures and recipes

Scale ingredient or mixture quantities while keeping the same relationship.

Maps and models

Use ratio thinking to compare scaled distances, drawings, or model dimensions.

How It Works

How it works in three quick steps.

1

Enter the two quantities

Add the first and second quantities that form the original ratio.

2

Review the simplified ratio

Use the simplified result and share percentages to understand the relationship.

3

Scale an equivalent ratio

Enter a target first quantity to calculate the matching second quantity with the same ratio.

Download & Print

Save or print a ratio comparison

Copy the ratio

Copy original quantities, simplified ratio, and equivalent scaled quantity.

Print the result

Print inputs, simplified ratio, share percentages, and formula notes.

Compare targets

Run multiple target first quantities to scale several equivalent ratios.

FAQ

Frequently Asked Questions

What does this ratio calculator do?
The ratio calculator simplifies a two-part ratio, shows each part as a share of the total, and scales an equivalent ratio from a target first quantity. It is useful for proportions, recipes, mixes, classroom comparisons, map scale examples, and any situation where two quantities need to keep the same relationship.
How do you simplify a ratio?
A ratio is simplified by dividing both quantities by their greatest common divisor. For example, 12:18 simplifies to 2:3 because both quantities can be divided by 6. The simplified ratio keeps the same relationship while using smaller numbers that are easier to compare, explain, or scale.
How do equivalent ratios work?
Equivalent ratios are created by multiplying or dividing both parts of a ratio by the same scale factor. If 2:3 is scaled by 5, it becomes 10:15. The quantities change, but the relationship stays the same. This calculator uses the entered target first quantity to find the matching second quantity for the same ratio.
Can a ratio include zero?
A ratio can include zero when one quantity is absent, such as 0:5. Some derived values then become undefined. For example, scaling from a first quantity of zero cannot produce a meaningful scale factor based on the first part. The calculator shows undefined in those cases instead of forcing a result.
What is the difference between a ratio and a fraction?
A fraction usually describes one number divided by another, while a ratio describes a relationship between quantities. They are closely related, and ratios can often be written as fractions, but the interpretation can differ. A ratio like 2:3 may describe two ingredients, two groups, or two map dimensions rather than a single part of a whole.
When should I use a ratio calculator instead of a percentage calculator?
Use a ratio calculator when the relationship between two quantities matters and you want to simplify or scale both parts together. Use a percentage calculator when you want one quantity as a share of a total or need percent change. The tools are related, so the ratio page also shows share-of-total percentages for context.
About This Tool

Why ratios are more than two numbers with a colon

A ratio describes how two quantities relate. The notation may be simple, but the interpretation can affect recipes, maps, classroom examples, business mixes, drawing scales, and proportional reasoning. Toolarithm's Ratio Calculator reduces two whole-number quantities into a simplified ratio, then shows share-of-total percentages and an equivalent ratio based on a target first quantity.

The calculator is designed to support both quick answers and learning. Simplification uses the greatest common divisor, equivalent ratios use a scale factor, and share-of-total values connect ratio work to percentages. Those views help users understand when a ratio is acting like a comparison, a fraction, or a proportional scaling rule. Related fraction and percentage tools are linked because the same relationship can often be rewritten in several ways. Keeping those links close helps students and everyday users move from one representation to another without losing the meaning of the original problem.

Editorial Transparency

Who maintains this page

Ownership and review

Written and maintained by the Toolarithm editorial team. No review date is shown without a maintained editorial record. No independent professional review is claimed.

Methodology

Equations are checked by substituting worked examples into the stated relationship and comparing the result with the interactive implementation.

Read the editorial methodology

Dates and sources

Review dates change only after a substantive method or content check.

Keep building

Explore more calculators

Calculators hub