βοΈ Ratio Calculator
Simplify ratios, solve proportions, and scale ratios.
Simplified Ratio
How to Use This Calculator
Three tabs handle the three most common ratio tasks. "Simplify Ratio" reduces a ratio to its lowest terms. "Solve Proportion" finds a missing value in an a:b = c:? equation. "Scale Ratio" scales parts to a given total while keeping the proportion the same.
To simplify, enter A and B. The calculator divides both by their GCD and shows the simplified ratio plus each part as a percentage of the total.
To solve a proportion, enter three of the four values A, B, C, D and leave one blank. The calculator solves using cross-multiplication.
To scale, enter A:B and the desired total. The calculator multiplies each part by Total / (A + B) to find the scaled values.
Each tab shows both the formula and the numeric result so you can follow along with the working.
Ratio and Proportion Formulas
A ratio tells you how two quantities compare. 3:4 means for every 3 of the first there are 4 of the second. To simplify 12:18, divide both by GCD(12, 18) = 6 to get 2:3. To solve 3:4 = 9:?, cross-multiply to get ? = 4 Γ 9 / 3 = 12.
Worked Examples
Where This Comes Up in Real Life
Recipes use ratios. A shortcrust pastry uses a 2:1 flour-to-fat ratio by weight. To make enough for a 6-person pie needing 300 g of pastry total, scale 2:1 to a total of 300 g: flour = 200 g, fat = 100 g. If the recipe card says 2:1 for 4 people (total 200 g) and you want 6 servings, the proportion is 200 g for 4 people = ? g for 6 people, giving ? = 200 Γ 6 / 4 = 300 g.
Engineers use ratios for gear trains. A driving gear with 20 teeth meshing with a driven gear of 60 teeth gives a gear ratio of 20:60 = 1:3. For every revolution of the driving gear, the driven gear rotates 1/3 of a turn. If the engine spins at 3000 RPM, the output shaft turns at 1000 RPM. The torque is multiplied by the same factor in reverse: if input torque is 50 NΒ·m, output torque is 150 NΒ·m (ignoring friction). This is how transmissions trade speed for torque.
Frequently Asked Questions
How do I simplify a ratio?
Divide both values by their GCD. Example: 12:18 β GCD=6 β 2:3. A simplified ratio has no common factor other than 1.
How do I solve a proportion?
Cross-multiply: a/b = c/d β aΓd = bΓc. To find the missing value: if a:b = c:?, then ? = bΓc/a.
What is a ratio used for?
Ratios express relative quantities: map scales (1:50000), recipes (flour:water), aspect ratios (16:9), mixing solutions, gear ratios, and probability odds.
What is the difference between a ratio and a fraction?
A ratio compares two quantities (4:3 = 4 parts to 3 parts). A fraction represents a part of a whole (4/7 means 4 out of 7 total parts). The ratio 4:3 = fraction 4/7 for the first part.
How do I scale a ratio?
Multiply both parts by the same factor. 2:3 scaled to a total of 25 β factor = 25/5 = 5 β 10:15. Or scale to make one part a specific value.