This ratio calculator finds missing values, reduces ratios to whole-number terms, and scales or compares the values you enter.
Solve, simplify or scale an entered ratio
Choose the task that matches the values you have. Find missing values uses two ratios with corresponding terms in the same order. Enter a question mark where a value is unknown. Simplify, Scale, Compare and Divide a total use their own relevant fields. Colons separate the terms; a slash belongs inside a simple fraction. This tool accepts mathematical values rather than deciding which mixture, share or recipe is appropriate.
The first term in one ratio matches the first in the other. Reversing only one pair changes the comparison.
Dividing the numerator term by the denominator term compares those two values. Parts of the combined total divides each nonnegative term by the sum.
Convert differing measurement units before comparing like quantities. A mass ratio is not automatically a volume ratio.
Missing value and decimal ratio examples
With First ratio 3:4 and Matching ratio 600:?, the common factor is 200. The completed equation is 3:4 = 600:800. Each term has been multiplied by that same factor.
For a decimal input of 0.75:1.25, Simplify returns 3:5. The exact fraction input 1/2:3/4:5/8 reduces to 4:6:5. Clearing denominators happens before the common-factor reduction.
Scaling 1:2.5:6.5 by 3 gives 3:15/2:39/2. The amounts change together; the proportions stay the same. This checks arithmetic, not cooking times or ingredient chemistry.
Pair comparisons and shares of a whole
A 1:3 pair does not give the first part that fraction of the whole. For a total of 24, Divide a total returns 6 and 18. The weights sum before the total is shared.
For 2:3:5 and a total of 120, the exact shares are 24, 36, 60. With equal weights and a total of 10, each share is 10/3. Rounded decimal shares may not sum exactly, so the fractional values remain authoritative. This mode does not allocate indivisible items or monetary pennies.
The pair percentage divides the numerator term by the denominator term. Each combined share has the sum of the nonnegative terms as its base. For other equations, use Percentage Calculator.
To convert a percentage to a ratio, use Simplify and enter its value, a colon and then 100. That compares the amount with its percentage base, rather than with the remainder.
Calculator Campus derives proportional sharing by taking each nonnegative weight as a fraction of the weight sum, then multiplying by the total. The cited fraction lesson supports those operations; it does not prescribe a fairness rule.
Exact fractions, signs and incomplete ratios
The calculator accepts 2 to 6 terms per ratio. It reduces finite decimals and simple integer fractions exactly; scientific notation is also accepted within the stated input limits. A negative input is allowed for algebraic ratios, and the first nonzero simplified term is made positive. Negative weights are rejected when dividing a nonnegative total.
A ratio containing only zeros has no useful nonzero scale and is rejected. The pair quotient is undefined when its denominator term is zero. Missing-value solving needs at least one matching known pair with a nonzero first value and a nonzero scale. Zero matched with a nonzero value, conflicting scale factors, or unknown values on both sides of the same position are rejected.
Exact fractions take precedence over decimals. An approximation marker means the displayed decimal has been rounded to 6 places. Input terms allow at most 64 characters, 12 decimal places and an exponent from -12 to 12; entered quantities and completed missing or scaled terms cannot exceed an absolute value of 1000000000000. Allocated shares follow the same cap. These are Calculator Campus limits, not mathematical limits. Derived scale factors, pair quotients, percentages and whole-number terms created to reduce a ratio can exceed that quantity cap.
A proportion here means equal ratios with one common scale. Inverse variation instead keeps a product constant and is outside this tool. Clinical dilution notation, resin formulations and mass-to-volume conversions need their own definitions or material data. Area Converter can convert compatible area measurements before a comparison.
Aspect Ratio Calculator uses compatible width and height measurements to preserve an image’s proportions and calculate fitted dimensions or centered crop.
Use the Percentage Point Calculator to subtract two percentage rates and label the signed point gap separately from relative change.
Use the Percent Error Calculator when one measurement is compared with a known, nonzero accepted reference. It separates absolute error from signed deviation.
For a load recorded with a completed repetition count, the One Rep Max Calculator applies sourced prediction equations and keeps their estimates separate from known-base arithmetic.
The Greatest Common Factor Calculator shows the integer divisor behind reduction, including a full Euclidean chain for a list.
To find a shared integer multiple or a common denominator, the Least Common Multiple Calculator folds the exact pair formula across the list.
The Prime Factorization Calculator decomposes one integer into prime powers and repeated factors; this differs from comparing a list.
A complete divisor list and product-checked factor pairs belong in the Factors Calculator, which also explains signed inputs.
When you need coefficients that reproduce the GCD, the Extended Euclidean Algorithm Calculator checks the original-input identity and its inverse residue.
The Standard Deviation Calculator measures spread around the mean, with sample and population conventions and explicit frequency-table input.
Use the Mean Median Mode Calculator to compare arithmetic center, ordered center, all tied repeated modes and range from the same observations or exact frequencies.
Use the Weighted Average Calculator to combine values with nonnegative relative weights and inspect their normalized contributions. It computes a generic mathematical average rather than a course-specific grading policy.