Rule of Three Calculator
Rule of Three Calculator
Find an unknown value when three values are known and the quantities are directly proportional. Enter matching units and make sure the first quantity is not zero.
Enter your values
Enter values and select Calculate.
How to Use the Rule of Three Calculator
Use this free Rule of Three Calculator to find a missing value when two quantities are directly proportional. If A units of one quantity correspond to B units of another, this calculator finds the value X that corresponds to C units. The calculation uses the direct rule of three, also called the unitary method or direct proportion method.
- Enter the first quantity (A) in the first field.
- Enter its corresponding quantity (B) in the second field.
- Enter the new quantity (C) in the third field.
- Select Calculate to find the corresponding unknown value (X).
- Select Clear to remove the entries and start a new calculation.
Use consistent units and confirm that the relationship is directly proportional. The first quantity (A) must not be zero.
What Is the Rule of Three?
The rule of three is a method for finding an unknown value from three known values in a proportion. In the direct rule of three, the two quantities increase or decrease together at a constant rate. For example, if the cost of a fixed item increases in proportion to the number of items purchased, a known price and quantity can be used to calculate the price for another quantity.
Direct Rule of Three Formula
A : B = C : X
X = (B × C) ÷ A
Multiply B by C, then divide the product by A. A must not be zero.
Worked Examples
Example 1: Calculate the cost of 5 items
If 2 items cost ₹40, what is the cost of 5 items?
A = 2, B = 40, C = 5.
X = (40 × 5) ÷ 2 = 100.
Result: 5 items cost ₹100.
Example 2: Calculate distance
If a vehicle travels 150 km in 3 hours at a constant speed, how far will it travel in 5 hours?
A = 3 hours, B = 150 km, C = 5 hours.
X = (150 × 5) ÷ 3 = 250.
Result: 250 km.
Example 3: Scale a recipe
If 4 servings require 300 grams of flour, how much flour is needed for 6 servings?
A = 4 servings, B = 300 grams, C = 6 servings.
X = (300 × 6) ÷ 4 = 450.
Result: 450 grams of flour.
Direct Proportion vs Inverse Proportion
Direct proportion means that when one quantity increases, the other increases in the same ratio; when one decreases, the other also decreases. Inverse proportion means that one quantity increases while the other decreases so that their product remains constant. This calculator applies the direct rule of three only. For an inverse relationship, rearrange the proportion using the appropriate inverse formula instead of using this result.
Common Uses of the Rule of Three
- Shopping: estimating the cost of a different number or quantity of items.
- Travel: estimating distance from time at a constant speed.
- Cooking: adjusting ingredient quantities for more or fewer servings.
- Work and production: estimating output when the rate remains constant.
- Education: solving arithmetic questions involving ratios and direct proportion.
Frequently Asked Questions
1. What is the rule of three?
The rule of three is a calculation method that uses three known values in a proportion to find a fourth, unknown value.
2. What formula does this calculator use?
For A : B = C : X, the direct rule of three formula is X = (B × C) ÷ A.
3. Is this a direct or inverse rule of three calculator?
This calculator uses direct proportion. Use it when both quantities change in the same direction at a constant rate.
4. Can I enter decimal values?
Yes. The input fields accept decimal values. Enter values with suitable precision and keep the units consistent.
5. Why can the first quantity not be zero?
The formula divides by A. Division by zero is undefined, so A must be a non-zero value.
6. Do the quantities need the same units?
The two corresponding quantities should use consistent units. A and C should describe the same type of quantity, while B and X should describe the other type.
7. What is a simple example of the rule of three?
If 2 items cost ₹40, then 5 items cost (40 × 5) ÷ 2 = ₹100, assuming the price per item stays constant.
8. Is the rule of three the same as cross multiplication?
They are closely related. Cross multiplication is an algebraic way to solve a proportion, and it produces the same formula for this direct relationship.
9. Can I use this calculator for speed and distance?
Yes, when speed is constant. For example, distance is directly proportional to travel time if the speed does not change.
10. Is this Rule of Three Calculator free?
Yes. You can use this calculator on SRIKAMI without a fee.
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