Ratio and proportion calculator

The formula

$$a : b = c : d \quad\Longleftrightarrow\quad \frac{a}{b} = \frac{c}{d} \quad\Longrightarrow\quad a\,d = b\,c$$

Two ratios are in proportion when they describe the same relationship at different sizes. Knowing any three values gives the fourth.

Where it comes from

A ratio $a : b$ is just the fraction $a/b$. Saying two ratios are equal is saying two fractions are equal. Multiply both sides by $b$ and by $d$ to clear the fractions:

$$\frac{a}{b} = \frac{c}{d} \;\Rightarrow\; a\,d = b\,c$$

This is cross-multiplication. Then divide to isolate whichever value is missing. For example, $d = \dfrac{b\,c}{a}$.

Worked example

A paint color is mixed 3 parts blue to 4 parts yellow. You have 15 L of blue. How much yellow do you need?

$$3 : 4 = 15 : d \quad\Rightarrow\quad d = \frac{4 \times 15}{3} = 20\ \text{L}$$

Where proportions show up

• Maps and models. A 1:50,000 map means 2 cm is 100,000 cm, or 1 km.
• Mixing. 1:4 concentrate to water means 250 mL of concentrate for 1 L of water.
• Unit rates. If 6 bolts cost $1.80, then 20 bolts cost 1.80 \times 20/6 = \6.00$.

Watch out for

• Keep the order consistent. If the first ratio is blue:yellow, the second must also be blue:yellow.
• Part-to-part vs part-to-whole. A 1:4 mix has 5 parts in total, so the concentrate is 1/5 of it, not 1/4.

Last checked November 11, 2026