Rule of Three Calculator
Solve proportions with cross multiplication.
How to Use Rule of Three Calculator
- 1Enter the three known values (A, B, C)
- 2The calculator finds D = (B × C) / A
- 3Use this for unit conversions, recipe scaling, and proportional problems
About Rule of Three Calculator
The Rule of Three Calculator solves proportional reasoning problems instantly. If you know that A corresponds to B, and you want to know what C corresponds to, enter the three known values and the calculator finds the fourth using cross multiplication: D = (B x C) / A.
This technique is fundamental in everyday mathematics — scaling ingredients, converting units, estimating costs, and solving proportional problems in science and engineering. The calculator shows the formula used so you can understand and verify the result.
All calculations are performed locally in your browser with no server calls, giving you instant answers with complete privacy. Works on all devices including smartphones and tablets.
Key Features of Rule of Three Calculator
- Solve direct proportions: if A corresponds to B, find what C corresponds to
- Uses the formula D = (B x C) / A for cross multiplication
- Accepts integer and decimal values for all three inputs
- Instant result with clear formula display
- Works for any proportional scenario: cooking, conversions, scaling
- Shows the cross-multiplication step for educational clarity
- Copy result to clipboard easily
- Handles large and very small proportional values accurately
Examples
Recipe scaling
If 2 cups of flour makes 12 cookies, how much flour is needed for 30 cookies?
Input
A=2, B=12, C=30 (find D)
Output
D = 5 cups
Unit conversion via proportion
If 1 mile = 1.609 km, how many km is 5 miles?
Input
A=1, B=1.609, C=5 (find D)
Output
D = 8.045 km
Common Use Cases
- Scaling recipe ingredients for a different number of servings
- Converting between units when you know one conversion factor
- Estimating proportional costs based on a known price per unit
- Solving school math proportional reasoning problems
- Determining correct medicine dosages based on body weight
- Calculating projected revenue based on a known conversion rate
Troubleshooting
Entering zero as A (the first known value)
Solution
A cannot be zero because D = (B x C) / A would require division by zero. Enter a non-zero value for A.
Using inverse proportion when direct proportion is assumed
Solution
The Rule of Three assumes direct proportion (more of A means more of D). For inverse proportions (more of A means less of D), use the formula D = (A x B) / C instead.
Mixing up which values go in A, B, and C
Solution
The structure is: A is to B as C is to D. A and B are the known pair; C is the second known value; D is what you want to find.
Frequently Asked Questions
What is the rule of three?
The rule of three finds an unknown value when three values of a direct proportion are known. The formula is D = (B x C) / A, derived from the proportion A:B = C:D.
When should I use direct vs inverse proportion?
Use direct proportion when quantities increase or decrease together (more apples = more cost). Use inverse proportion when one quantity increases as the other decreases (more workers = fewer days to finish).
Can I use decimal values?
Yes. All three input fields accept decimal numbers. The result will also be a decimal if the calculation does not produce a whole number.
Is this the same as cross multiplication?
Yes. Cross multiplication and the rule of three are two names for the same process. Given A:B = C:D, you cross multiply to get A x D = B x C, then solve for D.
What is a practical example of using this tool?
If a car travels 120 km in 2 hours, how far does it go in 5 hours? Set A=2, B=120, C=5, and D = (120 x 5) / 2 = 300 km.
Can I solve for A, B, or C instead of D?
The tool solves for D (the fourth value). To find one of the other values, rearrange the known values so the unknown is always in the D position.
Is this tool the same as the ratio calculator?
They overlap but differ in focus. The ratio calculator simplifies a given ratio A:B. The rule of three calculator solves for a missing value in a four-part proportion.
Is my data private?
Yes. All calculations are performed locally in your browser. No data is transmitted or stored.