Example 1
- 2 kg costs 5
- How much for 6 kg? → c = 6
x = 15
2 : 5 = 6 : 15 - price grows with mass.
Rule of three calculator
Type a known pair and a third number. If 2 matches 5, then 6 matches 15, because x = (5 × 6) ÷ 2. Three hours for 12 tasks give x = 20 at five hours at the same pace.
This calculator uses direct proportion: as one quantity grows, the other grows in the same fixed ratio. The first number in the pair cannot be zero.
Result
Fill in all three fields to find x.
How does it work?
In direct proportion two quantities grow together in a fixed ratio. If 2 matches 5, then 6 matches x. Write a : b = c : x, or a/b = c/x. Hence x = (b × c) ÷ a. 5 × 6 ÷ 2 = 15.
That is the classic rule of three from word problems: prices, pace, doses. 2 kg for 5, 6 kg for 15. 3 h → 12 tasks, 5 h → 20 tasks, because 12 × 5 ÷ 3 = 20. The first number in the pair cannot be zero.
Fields: First number in the proportion (a), Matches the first number (b), Second number, find its match (c). Type 2, 5, and 6, click Calculate. A comma and a period both parse. Keep units consistent in the problem: kilograms with kilograms, hours with hours.
The reduced ratio 12:8 → 3:2 lives on ratio of two numbers. Splitting 100 in 3:2 into 60 and 40 lives on divide in a ratio. Here three numbers build a fourth.
Without a, b, or c, nothing computes. a = 0 the calculator rejects. 2, 5, and 6 still give 15 no matter the header currency.
4 matches 10, 10 matches x = 25. 7 matches 21, 2 matches x = 6. Check 2, 5, and 6 first.
Formula
If a matches b, and c matches x, then:
x = (b × c) ÷ a (for a ≠ 0)
How to use
- Type the first number of the known pair (a), for example 2.
- Type the value that matches it (b), for example 5.
- Type the third number (c) whose match you want, for example 6.
- Click Calculate. 2 : 5 = 6 : 15. Three hours and 12 tasks with c = 5 give x = 20.
- Reducing 12:8 lives on ratio of two numbers. Splitting a whole in 3:2 lives on divide in a ratio.
x = 15 when 2 matches 5 and 6 looks for a pair
A known pair and a third number. If 2 matches 5, then 6 matches 15, because x = (5 × 6) ÷ 2. Three hours for 12 tasks give x = 20 at five hours.
- x
- The missing fourth number. (5 × 6) / 2 = 15. At 3 h → 12 tasks and 5 h you get x = 20. 4 km in 10 min and 8 km give x = 20 min.
- :
- Proportion writing 2 : 5 = 6 : 15. Finding a missing x, not splitting 100 in 3 : 2 into 60 and 40.
Examples
Example 2
- 3 h → 12 tasks
- 5 h → x tasks
x = 20
More time - more tasks at the same pace.
Example 3
- 4 km in 10 min
- 8 km in x min
x = 20
At constant speed, time grows with distance.
Example 4
- 1.5 matches 6
- 4.5 matches x
x = 18
Decimals work too - the ratio matters, not just whole numbers.
Related calculators
Frequently asked questions
What is x when 2 matches 5 and c = 6?
The unknown is 15. You multiply 5 by 6 and divide by 2, because the price scales with the mass.
How many tasks in 5 h if 3 h is 12?
You get 20. Same pace: 12 × 5 ÷ 3 = 20, five hours at twelve tasks per three hours.
What is the rule-of-three formula?
x = (b × c) ÷ a, from the proportion a/b = c/x. The first number a cannot be zero, because you divide by it.
How is this different from a 3:2 ratio?
A ratio shortens two numbers. Here you build a fourth from three. 12:8 → 3:2 lives on the ratio card, not here.
Does 4 : 10 = 10 : x give 25?
Yes. 10 × 10 ÷ 4 = 25, the same rule of three written with colons.
What if a = 0?
There is no result. Division by zero. The first number in the known pair must be nonzero.
What is x when 7 matches 21 and c = 2?
The unknown is 6. 21 × 2 ÷ 7 = 6, a pair three times smaller at the same ratio.
Do the units have to match?
In each pair, yes. Kilograms with kilograms, hours with hours. The page header does not convert 2 kg into pounds.
Where do I split 100 in the ratio 3:2?
On the ratio-split page. You get 60 and 40. Here there is no whole-amount field, only three numbers and a fourth unknown.
Is 15% of 200 the rule of three?
That is percent of a number, result 30, another calculator. The rule of three wants three known numbers and one unknown.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.