How to use
- Solve a proportion: enter A, B and C in A : B = C : x to get x. Handy for scaling recipes, map distances or unit prices.
- Simplify a ratio: reduce A : B to its simplest whole-number form. Decimals like 1.5 : 2.25 work too.
- Split by ratio: enter a total and up to five parts. The table shows each share, rounded so that the shares add up to the total exactly.
How it works
| Calculation | Method | Example |
|---|---|---|
| Proportion | cross-multiply: A × x = B × C, so x = B × C ÷ A | 3 : 4 = 9 : x → x = 12 |
| Simplify | divide both numbers by their greatest common divisor | 1920 : 1080 → ÷ 120 → 16 : 9 |
| Simplify decimals | multiply by a power of 10 to clear decimals, then divide by the GCD | 1.5 : 2.25 → 150 : 225 → ÷ 75 → 2 : 3 |
| Split | share = total × part ÷ sum of parts | 900 split 1 : 2 : 3 → 150 / 300 / 450 |
Examples
- Scaling a recipe: a batter uses 250 g of flour to 150 ml of milk. For 400 g of flour, 250 : 150 = 400 : x gives 240 ml of milk.
- Aspect ratios: 1920 × 1080 is 16 : 9 and 2560 × 1080 is 64 : 27. Monitors at 2560 × 1080 are sold as “21 : 9”, which is a rounded label.
- Profit sharing: partners who invested in a 2 : 3 : 5 ratio split a profit of 50,000 as 10,000 / 15,000 / 25,000.
Why the shares always add up
Splitting 100 three ways gives 33.33… each. Rounding each share separately gives 33 + 33 + 33 = 99, and one unit goes missing.
This tool uses the largest remainder method. It rounds every share down, then hands out the leftover units (1, 0.1 or 0.01, depending on the rounding you pick) one at a time to the shares with the largest fractional parts. Ties go to the earlier part. So 100 becomes 34 / 33 / 33, which adds up to exactly 100 — useful for splitting a bill or allocating a budget to the cent.
FAQ
Can I use zero or negative numbers?
For a proportion, only A must be non-zero. Simplifying needs numbers greater than 0. When splitting, a part can be 0 (it gets nothing), but the parts must add up to more than 0.
How do I turn a ratio into percentages?
Divide each part by the sum of the parts and multiply by 100. For 16 : 9, that is 64% and 36%. The simplify mode shows these shares, and the percentage calculator handles other percent questions.