EVERYDAY MATH
Ratio calculator
Simplify a two- or three-part ratio, scale it, distinguish part-to-part percentages from part-to-whole shares, or solve one missing value in an equivalent proportion with shown work.
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No regional currency, unit or language profile is applied. This choice does not convert values or change formulas, results, routes or legal guidance.
Simplified ratio
2:3Equivalent ratio: 10:15- Original total
- 60
- Decimal multiplier
- 1
- Greatest common divisor
- 12
- Part-to-part: first ÷ second
- 0.666667
- First as % of second
- 66.67%
- Second as % of first
- 150%
- Part-to-whole shares
- 40% · 60%
Solved value
122 : 3 = 8 : 12- Shown work
- 3 × 8 ÷ 2 = 12
- Equality check
- Yes — both sides match
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Verification and calculation details
- Purpose
- Ratio calculator
- Variables and units
- Use the labelled fields and units shown in the calculator. Results use those units unless a conversion is stated.
- Formula and method
- The exact formula and worked example are shown below. Deterministic formula executed locally in the browser.
- Assumptions
- Only entered values and stated assumptions are included. Local fees, rules and professional requirements are excluded unless explicitly shown.
- Engine version
- 1.0.0
- Production verification baseline
- Release 63 · source
998803f - Verification run
release-v63-2026-09-20- Last verified
- — Automated release checks passing
Read the Calculation Standard · Report a calculation or source issue
How this calculator works
Normalize decimals to whole-number parts, then divide all parts by their greatest common divisor. Equivalent ratio = simplified ratio × scale factor. Part-to-part percentage = first ÷ second × 100. Part-to-whole share = part ÷ sum of all parts × 100. For a:b = c:d, solve the missing value by cross multiplication and division using the three known positive values.
Variables and inputs
- First value
- Required numeric input. finite numeric value; calculator-specific validation applies.
- Second value
- Optional numeric input. finite numeric value; calculator-specific validation applies.
- Third value
- Optional numeric input. finite numeric value; calculator-specific validation applies.
- Scale target or fourth proportion value
- Optional numeric input. finite numeric value; calculator-specific validation applies.
How to interpret the result
The calculator returns simplified two-part or three-part ratio, equivalent scaled ratio, first-to-second decimal and percentage comparisons, part-to-whole percentage share of each part, normalization factor, missing proportion value with completed equality and shown work. Read each output against the assumptions you entered, compare alternatives one variable at a time, and use the result as an estimate rather than a promise.
Common mistakes to avoid
- Mixing units or entering a rate as a decimal when the field requests a percentage.
- Rounding intermediate values instead of the final displayed result.
- Leaving out a cost, timing rule or local requirement listed in the assumptions below.
Practical uses
Use the ratio calculator to check a real scenario, compare a changed assumption and explain the arithmetic before relying on a quote, specification or decision.
Worked example
For 1.5:2.25:3, the calculator scales to 150:225:300, divides by 75 and returns 2:3:4. The corresponding shares are approximately 22.22%, 33.33% and 44.44%.
Assumptions and limitations
- ratio parts represent comparable quantities expressed in the same unit
- decimal parts are normalized before the greatest common divisor is applied
- results are estimates; confirm rates, prices, units and professional requirements that apply
Important notes
Results are estimates based on the values entered. Confirm rates, prices, units and professional requirements that apply in your location. Review the Answer Atlas Calculation Standard and corrections policy for formula, privacy and correction rules.
Frequently asked questions
Can I simplify decimal ratios?
Yes. The calculator safely normalizes decimal values to whole-number parts before reducing the ratio.
Can I compare three values?
Yes. Turn on the third part when you need a recipe, mix, scale or comparison ratio such as 2:3:4.
What is the difference between part-to-part and part-to-whole percentages?
For a ratio a:b, the part-to-part percentage is a ÷ b × 100. A part-to-whole share instead divides that part by a + b, or by the sum of every included part. The calculator reports both so they are not confused.
How do I solve a missing value in a proportion?
Choose the missing position and enter the other three positive values. The calculator uses cross multiplication, shows the completed proportion and verifies that both sides are equivalent.
Does Answer Atlas store my ratio values?
No. Ratio values are calculated in your browser and are not sent to our servers.