Quick Regla de Tres Calculator
Calculate the unknown value X from three known values using direct or inverse proportion.
What Is the Regla de Tres?
The regla de tres (rule of three) is one of the most practical math methods for daily life. It helps you find an unknown number when you already know three related values. If you have ever converted recipe portions, estimated travel costs, compared prices, or calculated time and productivity, you have used proportional reasoning.
This calculator makes that process immediate. Enter three numbers, choose whether the relationship is direct or inverse, and get the missing fourth value in seconds.
Direct vs. Inverse Proportion
Direct Proportion
In a direct proportion, both variables move in the same direction. If one goes up, the other also goes up. If one goes down, the other goes down.
- More items usually cost more money.
- More distance at constant speed usually takes more time.
- More workers (same productivity) can complete more output in the same period.
Formula: X = (B × C) ÷ A, based on A : B = C : X
Inverse Proportion
In an inverse proportion, variables move in opposite directions. If one goes up, the other goes down.
- More workers can reduce completion time for the same task.
- Higher speed can reduce travel time for the same distance.
Formula: X = (A × B) ÷ C, based on A × B = C × X
How to Use This Calculator
- Select Direct or Inverse.
- Enter Value A, Value B, and Value C.
- Click Calculate X.
- Review the result and the formula used.
Tip: Use the same units consistently. For example, do not mix kilometers with miles unless you convert first.
Real-World Examples
1) Shopping and Unit Price
If 3 kg of oranges cost $9, how much do 5 kg cost? This is direct proportion: A = 3, B = 9, C = 5. X = (9 × 5) ÷ 3 = 15. So, 5 kg cost $15.
2) Recipe Scaling
A recipe uses 2 cups of flour for 8 servings. How much flour for 12 servings? Direct proportion again: X = (2 × 12) ÷ 8 = 3 cups.
3) Work-Time Planning
If 4 workers finish a task in 9 days, how many days for 6 workers (same productivity)? This is inverse proportion: X = (4 × 9) ÷ 6 = 6 days.
Common Mistakes to Avoid
- Choosing the wrong proportion type: verify whether values move together (direct) or opposite (inverse).
- Mixing units: convert units before calculation (hours/minutes, kg/g, km/miles).
- Dividing by zero: direct proportion cannot have A = 0; inverse proportion cannot have C = 0.
- Input order confusion: keep each pair consistent so the relationship remains meaningful.
Why This Tool Is Useful
A reliable regla de tres calculator saves time and reduces mistakes in budgeting, education, engineering estimates, logistics, and personal decision-making. It is simple enough for students and practical enough for professionals.
Whether you call it a proportion calculator, rule of three calculator, or simple ratio solver, the core purpose is the same: quickly find an unknown value from a valid proportional relationship.
Final Thoughts
The regla de tres is a small math skill with a big impact. Use the calculator above whenever you need fast, accurate proportional calculations. For best results, always check context, units, and whether the relationship is direct or inverse.