CalculationTime

Ratio Calculator

Live math canvas

Your numbers, formula and explanation together

Ratio Calculator: 2:3. 12:18 totals 30. Shares 40% and 60%; scaled to 100: 40 and 60.

Formula applied

The exact method behind this answer

CalculationTime keeps the method visible so the number can be checked instead of blindly trusted.

Simplified ratio = first value ÷ common factor : second value ÷ common factor. Part share = part ÷ (first value + second value) × 100. Scaled part = target total × part share.
  1. Apply the formulaSimplified ratio = first value ÷ common factor : second value ÷ common factor. Part share = part ÷ (first value + second value) × 100. Scaled part = target total × part share.2:312:18 totals 30. Shares 40% and 60%; scaled to 100: 40 and 60.

Your live breakdown

Current inputs in the calculation

These values come from the controls above and update when the calculator changes.

First value
12
The first part of the ratio.
Second value
18
The second part of the ratio.
Scale to total
100 optional
Optional combined total for scaling the same ratio.

Resulting answer

2:3

12:18 totals 30. Shares 40% and 60%; scaled to 100: 40 and 60.

Answer
2:3
Live support
12:18 totals 30. Shares 40% and 60%; scaled to 100: 40 and 60.

Assumptions used

What this answer assumes

Use the simplified ratio for comparison and the scaled values for recipes, mixes, classroom worksheets or quote notes.

  • Both ratio parts are treated as non-negative quantities.
  • Whole-number values are simplified by their greatest common divisor; decimal values are reduced by decimal-place scaling before the same idea is applied.
  • If both parts are zero, the ratio is undefined because there is no total relationship to compare.
  • The optional target total scales the same relationship; it does not change the ratio itself.

Master’s Tip

How to use the result well

Master’s Tip: keep the original units beside the ratio. A 2:3 mix, classroom score split or map scale can share the same arithmetic while meaning very different things in practice.

Printable record

What belongs in the saved calculation

Save the inputs, result, formula, assumptions, page URL and date together so the calculation can be reviewed later.

First value
12
The first part of the ratio.
Second value
18
The second part of the ratio.
Scale to total
100 optional
Optional combined total for scaling the same ratio.

Embeddable calculator

Embed this calculator

Copy a clean iframe version with the required CalculationTime attribution link built in.

Formula

Simplified ratio = first value ÷ common factor : second value ÷ common factor. Part share = part ÷ (first value + second value) × 100. Scaled part = target total × part share.

Worked example

For 12 and 18, the greatest common divisor is 6. Divide both parts by 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3, so the simplified ratio is 2:3. The total parts are 5, so the first share is 40% and the second share is 60%. Scaled to 100, the parts are 40 and 60.

Professional note

Master’s Tip: keep the original units beside the ratio. A 2:3 mix, classroom score split or map scale can share the same arithmetic while meaning very different things in practice.

Regional and unit assumptions

Standard or basis: transparent proportional arithmetic. The page simplifies part-to-part ratios and shows part-to-whole percentages without claiming a trade, recipe, finance or statistical standard.

Ratio proof

Scale the same ratio

A simplified ratio preserves the relationship while scaled totals change the quantity. The page shows the original parts, simplified part-to-part ratio, part-to-whole percentages and the same relationship scaled to a target total.

Visible checks

What the page now proves

  • Simplified ratio
  • Part-to-whole percentages
  • Target-total scaling

Assumptions and limitations

Methodology & Accuracy

How this calculator is checked

CalculationTime pages are built around visible arithmetic: the formula, assumptions, worked example and practical limitations are shown so the result can be checked rather than simply trusted.

Formula used

Simplified ratio = first value ÷ common factor : second value ÷ common factor. Part share = part ÷ (first value + second value) × 100. Scaled part = target total × part share.

Standard or basis

Standard or basis: transparent proportional arithmetic. The page simplifies part-to-part ratios and shows part-to-whole percentages without claiming a trade, recipe, finance or statistical standard.

Where a calculator follows a named legal, trade or industry standard, that standard is cited visibly. Otherwise the page uses transparent general arithmetic and states its limits.

Master's Tip

Master’s Tip: keep the original units beside the ratio. A 2:3 mix, classroom score split or map scale can share the same arithmetic while meaning very different things in practice.

Related calculators

These cards are resolved from calculator data, category context and live-route status so the page links to useful next steps without hand-built link clutter.

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Questions

How do you simplify a ratio?

Find a common factor shared by both values, then divide both sides of the ratio by that factor.

What is the ratio 12 to 18 simplified?

The greatest common divisor of 12 and 18 is 6, so 12:18 simplifies to 2:3.

Is a ratio the same as a percentage?

No. A ratio compares quantities to each other. A percentage usually compares one quantity with the combined whole out of 100.

How do I scale a ratio to a total?

Add the ratio parts, divide each part by that total to get its share, then multiply each share by the target total.

Can a ratio include zero?

One side can be zero when the other side is positive, such as 0:5. A 0:0 ratio is undefined because there is no relationship to compare.

Calculation note

Ratios are a compact way to compare quantities. They are useful in recipes, maps, classrooms, mixtures, trade estimates and reports because the relationship can stay the same even when the total size changes.

Ratios preserve relationships

A ratio such as 2:3 says that for every two units of the first quantity there are three units of the second. Scaling to 20:30, 40:60 or 200:300 keeps the same relationship even though the total quantity changes.

Part-to-part and part-to-whole are different views

The ratio 2:3 compares the first part directly with the second part. The same relationship can also be expressed against the whole: the first part is 2 out of 5 total parts, or 40%, and the second part is 3 out of 5, or 60%.

Simplifying helps communication

Simplifying a ratio removes unnecessary scale from the comparison. A teacher, estimator or homeowner can understand 2:3 faster than 12:18, while still keeping the original numbers in the printable report for traceability.

Sources and further readingBritannica: Ratio