How the Ratio Calculator Works
A ratio compares two amounts, such as 4 to 3. Two ratios are in proportion when they are equal: 4 : 3 is the same as 8 : 6. The Ratio Calculator solves the missing number in a proportion. You enter A, B and C, and it finds D in A : B = C : D. It is useful for resizing a recipe, scaling a map or a picture, mixing paint, and converting prices.
What you enter
- A and B: the two numbers of the ratio you already know.
- C: the new amount that goes with A.
- D (the result): the amount that goes with B, worked out for you.
The formula
D = (B x C) / A
This is called cross multiplication: A x D = B x C, so D = B x C / A. A cannot be 0, because you cannot divide by zero. The answer is rounded to 6 decimal places.
A worked example
A screen has the ratio 4 : 3. If it is 1920 pixels wide, how tall is it?
| Step | Value |
|---|---|
| A : B | 4 : 3 |
| C | 1920 |
| D = 3 x 1920 / 4 | 1440 |
So 4 : 3 = 1920 : 1440. This is also the default example in the calculator.
More examples
| Situation | A : B = C : D | D |
|---|---|---|
| Recipe: 12 cookies need 2 cups of flour. How much for 30? | 12 : 2 = 30 : D | 5 cups |
| Speed: 3 hours cover 150 km. How far in 7 hours? | 3 : 150 = 7 : D | 350 km |
| Map 1 : 50,000. 3.5 cm on the map is how many cm? | 1 : 50000 = 3.5 : D | 175,000 cm (1.75 km) |
| Screen 16 : 9, width 1280 | 16 : 9 = 1280 : D | 720 |
- Situation: Recipe: 12 cookies need 2 cups of flour. How much for 30?
A : B = C : D: 12 : 2 = 30 : D
D: 5 cups - Situation: Speed: 3 hours cover 150 km. How far in 7 hours?
A : B = C : D: 3 : 150 = 7 : D
D: 350 km - Situation: Map 1 : 50,000. 3.5 cm on the map is how many cm?
A : B = C : D: 1 : 50000 = 3.5 : D
D: 175,000 cm (1.75 km) - Situation: Screen 16 : 9, width 1280
A : B = C : D: 16 : 9 = 1280 : D
D: 720
Chart: a 16 : 9 screen at three sizes
The blue bar is the width and the green bar is the height. The shape stays the same, because the ratio stays the same:
1280 wide ████████████████████ 720 high ███████████ 1920 wide ██████████████████████████████ 1080 high █████████████████ 2560 wide ████████████████████████████████████████ 1440 high ███████████████████████
Simplifying a ratio
To make a ratio simpler, divide both numbers by the same number. 20 : 30 becomes 2 : 3 when you divide by 10. 1920 : 1440 becomes 4 : 3 when you divide by 480.
Tips
- Keep the order. If A is the "small" amount of one kind, C must be an amount of the same kind. Mixing the order gives a wrong answer.
- Check the units. Both sides of a ratio must use the same units.
- Check that D makes sense. If C is bigger than A, then D must be bigger than B.
This tool gives an estimate for general information only. For medicine, building or other safety work, double-check the amounts.