Solverly

Ratio & Proportion Solver

This tool keeps quantities in the right relationship—whether we’re matching a recipe to a new serving size, converting map scales, preserving an aspect ratio, mixing solutions, or comparing parts of a whole. It clarifies how two values change together so you can scale up or down without guesswork and ensure every proportion stays consistent.

The Ratio & Proportion Solver helps us find missing values, rebalance sets to a new total, and test “what-if” scenarios while keeping the same relative mix. The goal is reliable scaling and clean comparisons that reduce errors, save time, and make planning—across cooking, construction, design, science, and finance—straightforward.

Solve ratios and proportions with step-by-step cross-multiplication, scale to a target, or reduce ratios instantly.

Enter any three terms

Enter any three of a, b, c, d to solve the fourth.

Details

Final proportion
— : — = — : —
Show steps (cross-multiplication)
  1. Start with the proportion a/b = c/d.
  2. Cross-multiply to get ad = bc.
  3. Optionally, divide both parts of each ratio by their GCD to reduce.

Ratio & proportion results interpretation

  • Missing term shows the value that makes a:b = c:d true.
  • Reduced form expresses each ratio in least terms (e.g., 8:12 → 2:3).
  • Scale to total splits any total into parts that keep the same ratio (useful for budgets or mixing).
  • Inputs accept decimals. Watch for divide-by-zero when a side of a ratio is 0.

Examples

Example 1 — Find d
Given a:b = c:d with a=3, b=5, c=12, the missing d is (b×c)/a = (5×12)/3 = 20.
Example 2 — Reduce 18:24 = 27:36
Left GCD(18,24)=6 → 3:4; Right GCD(27,36)=9 → 3:4. Ratios match ⇒ proportion holds.
Example 3 — Scale 2:3 to a total of 250
Sum=5. Parts → 250×(2/5)=100 and 250×(3/5)=150.

FAQ

How do we know which term is missing?
Leave exactly one of a, b, c, d blank—our solver detects that position automatically.
Can ratios include decimals?
Yes. We scale decimals to integers internally so reduction works properly.
What if a or b is zero?
That creates divide-by-zero when solving certain positions. We guard and ask for adjustments.
What’s the fastest way to check a proportion?
Verify whether ad = bc. If true (within rounding), the proportion holds.
How does “scale to total” work?
We split the total by the ratio shares. For a:b and total T, parts are T×a/(a+b) and T×b/(a+b).
Can we scale c:d instead?
Yes—enter c and d as a new ratio, or swap roles to use the same method.

Ratio & Proportion: methods, shortcuts, and checks

Ratios compare parts; proportions state two ratios are equal. We rely on the identity ad = bc to solve unknown terms and to verify whether two ratios align within rounding.

Cross-multiplication

From a/b = c/d, multiply both sides by bd to get ad = bc. Solve any missing variable by dividing the product on one side by the known factor on the other.

Reduction and scaling

Reducing uses the greatest common divisor. Scaling keeps the same shape while changing magnitude—handy for budgets, recipes, or mixing solutions to a target total or percentage.

Rounding and tolerance

With decimals, rounding can introduce tiny differences. We recommend checking equality within a small tolerance when verifying proportions in measured data.