Proportion Calculator - Solve Ratios and Rule of Three

Q: What is a proportion calculator?

A proportion calculator solves equations such as a/b = c/d and finds the missing fourth value. It is commonly used for direct proportion, inverse proportion, and rule-of-three problems.

Q: What is the rule of three?

The rule of three is the standard method for solving a direct proportion when three values are known. If 5 kg costs $15, then 8 kg costs 15 x 8 / 5 = $24.

Q: What is the difference between direct and inverse proportion?

Direct proportion means both quantities move in the same direction. Inverse proportion means one increases while the other decreases, such as more workers needing fewer days.

Enter three known values to find the missing value in a proportion. Solve ratios, direct proportion, inverse proportion, and rule-of-three problems online.

Use this proportion calculator to find the missing value in a ratio or rule-of-three problem. Enter any three known numbers, choose direct or inverse proportion, and the calculator solves the fourth value.

Use direct proportion when both quantities increase or decrease together, such as price and quantity. Use inverse proportion when one quantity increases while the other decreases, such as workers and time.

Example: if 3 items cost $12, then 7 items cost $28. If 4 workers need 6 days, then 3 workers need 8 days.

Direct Proportion Formula

$$\frac {a}{b} = \frac {c}{d}\Rightarrow a=\frac {b \times c}{d}$$

$$\frac {a}{b} = \frac {c}{d}\Rightarrow b=\frac {a \times d}{c}$$

$$\frac {a}{b} = \frac {c}{d}\Rightarrow c=\frac {a \times d}{b}$$

$$\frac {a}{b} = \frac {c}{d}\Rightarrow d=\frac {b \times c}{a}$$

Input

Result

Fig. 1 Proportion graph

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Proportion Calculator FAQ

What is a proportion calculator?
A proportion calculator solves equations such as a/b = c/d and finds the missing fourth value. It is commonly used for direct proportion, inverse proportion, and rule-of-three problems.

How do I find the missing value in a proportion?
Enter the three known values and select the unknown value. For a direct proportion such as 3/4 = x/8, cross multiplication gives 3 x 8 = 4 x x, so x = 6.

What is the rule of three?
The rule of three is the standard method for solving a direct proportion when three values are known. If 5 kg costs $15, then 8 kg costs 15 x 8 / 5 = $24.

What is the difference between direct and inverse proportion?
Direct proportion means both quantities move in the same direction. Inverse proportion means one increases while the other decreases, such as more workers needing fewer days.

When is a proportion calculator useful?
It is useful for recipe scaling, currency conversion, unit conversion, map scale, speed and distance problems, pricing, and work-rate questions.

What mistakes should I avoid?
The main mistakes are mixing up direct and inverse proportion, placing values in the wrong order, and using inconsistent units on the two sides of the ratio.

Example

For a direct proportion, if 3 / 6 = x / 10, cross multiplication gives 3 x 10 = 6 x x, so x = 5.

For an inverse proportion, if 4 workers need 12 hours, then 8 workers need (4 x 12) / 8 = 6 hours.