Free Regla de 3 Calculator
Use this calculator to solve the unknown value x in a proportion. It supports both direct proportion and inverse proportion.
What is the regla de 3?
The regla de 3 (rule of three) is a simple math method used to find an unknown value when you know three related values. It is one of the fastest tools for practical calculations in daily life, school, engineering, shopping, cooking, finance, and business planning.
In plain terms: if you know how two quantities relate, you can use that relationship to calculate a new equivalent value. This calculator automates that process so you avoid manual mistakes and get an answer instantly.
How this calculator works
1) Direct proportion
Use direct proportion when both values move in the same direction. If one increases, the other also increases. For direct rule of three:
- Relationship: a → b and c → x
- Formula: x = (b × c) ÷ a
Example: If 2 kg of apples cost $10, then 5 kg cost x = (10 × 5) ÷ 2 = 25. So, 5 kg cost $25.
2) Inverse proportion
Use inverse proportion when values move in opposite directions. If one increases, the other decreases. For inverse rule of three:
- Relationship: product stays constant
- Formula: x = (a × b) ÷ c
Example: If 4 workers finish a job in 6 days, then 8 workers would take x = (4 × 6) ÷ 8 = 3 days.
Step-by-step usage guide
- Select Direct proportion or Inverse proportion.
- Enter values for a, b, and c.
- Click Calculate x.
- Read the result and the formula breakdown displayed below the button.
Common real-world uses
Shopping and discounts
Compare prices by weight, volume, or quantity and estimate total cost quickly. This is very helpful when buying in bulk or comparing package sizes.
Cooking and recipes
Need to adjust ingredients from 4 servings to 10? A direct rule of three gives accurate scaling. This prevents over-salting, over-sweetening, or wasting ingredients.
Work planning and productivity
Inverse rule of three is useful for staffing and scheduling: more people can reduce completion time, or fewer resources can increase time.
Travel, speed, and distance
For many travel estimates, proportional reasoning helps determine fuel consumption, expected travel time, or distance under similar conditions.
Tips to avoid mistakes
- Double-check that you selected the correct proportion type (direct vs inverse).
- Keep units consistent (e.g., all in kg, all in hours, all in dollars).
- Do not divide by zero (this calculator warns you automatically).
- Round final results only at the end for better precision.
FAQ
Can I use decimal numbers?
Yes. The calculator accepts decimals with either a dot or a comma.
Is regla de 3 the same as solving proportions?
Yes. It is a practical shortcut for proportional equations.
When should I use inverse proportion?
Use inverse proportion when one quantity rises while the other falls, such as workers vs time, speed vs travel time (for fixed distance), or machines vs processing time.
Final thoughts
A good regla de 3 calculator saves time, improves accuracy, and helps you make faster decisions. Whether you are studying, budgeting, cooking, or managing projects, this method remains one of the most practical math tools you can use every day.