Ratio Calculator
It reduces a ratio to its simplest form, converts it to percentages and a decimal, and scales it up or down to solve for a missing term.
16 : 24 simplified
2.00 : 3.00
Simplified
2.00:3.00
As a decimal
0.6667
Total parts
40.00
Share of a
40.00%
Share of b
60.00%
Solved x
15.0000
What it calculates
It reduces a ratio to its simplest form, converts it to percentages and a decimal, and scales it up or down to solve for a missing term.
Why it matters
Ratios drive recipes, mixing, model scales and aspect ratios. Scaling them by eye is where mistakes creep in.
Who it's for
Cooks scaling recipes, trades mixing materials, designers working to aspect ratios, and students on proportion problems.
Formula
- a : b
- The two terms of the ratio
- GCD
- Greatest common divisor used to simplify
- x
- The unknown term in a : b = c : x
Worked example
Simplify 16:24, then scale 2:3 up to 10
- 1GCD(16, 24) = 8
- 216:24 → 2:3
- 32:3 = 10:x, so x = 3 × 10 ÷ 2
16:24 simplifies to 2:3; scaling to 10 gives 10:15
How the ratio calculator works
Simplifying divides both terms by their greatest common divisor, which never changes the proportion. Solving a:b = c:x rearranges to x = b × c ÷ a — the cross-multiplication rule. Converting to percentages divides each term by the total of both, which is how you turn a mixing ratio into a share of the whole.
Simplifying divides both terms by their greatest common divisor, which never changes the proportion. Solving a:b = c:x rearranges to x = b × c ÷ a — the cross-multiplication rule you were taught at school.
Note that 1:3 means one part in four, not one third. Converting to percentages divides each term by the total of both, which is how a mixing ratio becomes a share of the whole.
Common mistakes
- Confusing a ratio with a fraction of the total: 1:3 means one part in four, not one third.
- Scaling only one term of the ratio.
- Mixing units, such as comparing grams to milliliters without converting.
Tips and best practice
- For a three-part ratio, scale all terms by the same multiplier rather than solving pairwise.
- Convert to percentages when you need shares of a total rather than parts of a mix.
Frequently asked questions
How do I simplify a ratio?
Divide both terms by their greatest common divisor. 16:24 both divide by 8, giving 2:3.
Is 1:3 the same as one third?
No. 1:3 means one part to three parts, so four parts in total — one quarter of the whole, not one third.
How do I solve a proportion?
Cross-multiply. For 2:3 = 10:x, multiply 3 by 10 and divide by 2 to get x = 15.
How do I scale a recipe?
Work out the multiplier from one known quantity, then apply the same multiplier to every ingredient.
Related calculators
Methodology & trust
- Formula source
- Standard proportion and GCD reduction.
- Last updated
- 2026-07-28
- Privacy
- Every calculation runs in your browser. No inputs are sent to a server or stored.
- Accessibility
- Keyboard navigable, labeled inputs and WCAG AA color contrast.