Math

Ratio Calculator

What this does

Simplify any two-term ratio to lowest terms or solve the missing fourth term of a proportion a:b = c:d.

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Calculator inputs

Only used in solve mode: finds d such that a:b = c:d.

How to use it

Using the ratio calculator

  1. 01

    Choose simplify or solve

    Two-term cleanup, or completing the proportion a:b = c:d.

  2. 02

    Enter the terms

    Term c only participates in solve mode; the field marks that clearly.

  3. 03

    Use the result

    Simplified ratios for recipes and scales; solved terms for scaling quantities up or down.

Good to know

Ratios are multiplication in disguise

Saying 48:18 equals 8:3 claims both pairs express the same scaling factor of roughly 2.67-to-1. Simplifying exposes that factor, making it obvious whether two recipes, gear trains or budgets truly match proportionally.

Cross-multiplication, demystified

If a:b = c:d then a·d = b·c; the diagonals multiply equally. Isolating the unknown gives d = bc/a. This single identity powers unit conversions, map scales, screen aspect ratios and recipe resizing.

When proportions mislead

Proportions assume linearity. Doubling a cake recipe doubles flour, but doubling a city’s population does not double commute times. Check that the underlying relationship really scales before trusting the fourth term.

How it's calculated

The math behind this calculator

Simplify: divide both terms by GCD(a, b) Solve: d = (b × c) / a

Simplification divides both terms by their greatest common divisor; Euclid’s algorithm makes that instant even for large numbers. Solving cross-multiplies the proportion: multiplying b by c and dividing by a yields the fourth term that restores equality, with fractional answers kept to six decimals.

Assumptions & limitations

  • Ratio terms must be non-zero.
  • Proportions assume term order matters: a corresponds to c, b corresponds to d.
  • Fractional missing terms are shown rounded, not truncated.

Worked example

The ratio 48:18 simplifies to 8:3 once both terms divide by their GCD of 6.

FAQ

Frequently asked questions

Can ratios contain decimals?
Yes; simplification still applies after scaling; the GCD handles non-integers by working with their exact floating-point values.
What does solve mode actually find?
Given a, b and c it computes d so that a/b = c/d holds; the classic missing-term proportion problem.
Why reject zero terms?
A zero term destroys the proportion’s meaning: division by zero is undefined, so validation stops it early.

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