∶ Ratio Calculator
Simplify ratios and scale proportionally. Runs privately in your browser.
What a ratio is actually telling you
A ratio expresses how two quantities relate: 4 parts cement to 1 part sand, a 16:9 screen, a 1:2 cordial mix. Simplification divides both numbers by their greatest common divisor, so 10:15 becomes 2:3. Scaling answers the practical follow-up: if the first quantity becomes N, what does the second become?
Ratios differ from fractions in what they emphasise: 1:2 as a ratio describes a relationship (one part to two parts), not the fraction 1/2 of a whole. Keeping that straight matters in mixing contexts, where 'half as much B as A' and 'half the total' are different instructions.
Simplification: divide both sides by GCD(a, b). Scaling: if a : b and a becomes N, then b becomes N × b ÷ a.
Mixing 1:4 cordial
A concentrate says mix 1:4 with water and you want 1 litre of drink: that's 5 parts total, so each part is 200 ml — 200 ml concentrate, 800 ml water. A photo is 4320 × 2880 pixels: GCD is 1440, so the ratio simplifies to 3:2. Scaling a 2:3 dough recipe from 300 g flour to 500 g flour requires 750 g water.
Ratio mistakes
- Adding across a ratio. Doubling '3:2' means 6:4, not 3+2 doubled = 5 doubled parts — the totals differ.
- Forgetting the total-parts step when converting a ratio to absolute quantities, as in the concentrate example.
- Simplifying ratio of different unit types (km to hours) where simplification is meaningless.
- Assuming ratios round-trip: 2:3 scaled by 1.5 gives 3:4.5, which then simplifies back to 2:3 — mid-scaling values can look like different ratios.
Ratio questions
How do I simplify a ratio with decimals?
Multiply both sides to clear decimals (2.5:5 → 5:10 → 1:2), or enter whole equivalents. The calculator's GCD approach assumes whole numbers.
What is 16:9 in simplest form?
Already simplest — GCD of 16 and 9 is 1. Enter 16 and 9 to confirm.
How do I scale a recipe from 4 to 6 servings?
Express the recipe as a ratio per serving, or scale the key ingredient: if 4 servings use 300 g flour, 6 servings need 450 g — enter 300 : X mode... practically, multiply every ingredient by 6/4 = 1.5.
Can I reverse a ratio?
Yes — if A:B is 4:1, then B:A is 1:4. Just swap the inputs.
Does it work for more than two numbers?
This version handles two-term ratios. Multi-term ratios (a:b:c) simplify by dividing by the GCD of all three — do that manually or in steps.
Related maths tools
Tip: double-check inputs before relying on results for important decisions.